Research Publication By Ms. Cynthia Chinemerem Anyanwu | Leading figure in Health & Social Care | Public health strategist & policy advisor | Champion of integrated primary care and social equity | Expertise: workforce development, community partnerships, and quality improvement

Institutional Affiliation:
New York Centre for Advanced Research (NYCAR)

Publication No.: NYCAR-TTR-2025-RP032
Date: October 1, 2025
DOI: https://doi.org/10.5281/zenodo.17400606

Peer Review Status:
This research paper was reviewed and approved under the internal editorial peer review framework of the New York Centre for Advanced Research (NYCAR) and The Thinkers’ Review. The process was handled independently by designated Editorial Board members in accordance with NYCAR’s Research Ethics Policy.

Abstract

Health systems have invested heavily in “integration,” yet equity gaps in access and outcomes persist for people living with deprivation, unstable housing, language barriers, and multimorbidity. This study develops and tests a pragmatic, mixed-methods framework for integrated primary care models for social equity that decision-makers can use on Monday morning. Quantitatively, we restrict analysis to straight-linerelationships (y = m·x + c) so managers can compute, explain, and refresh results without statistical tooling. We specify three levers common to high-performing integrated models: (A) community health worker (CHW) capacity per 10,000 patients; (B) after-hours and same-day access slots per 1,000 patients; and (C) care-coordination maturity (a simple 0–10 index capturing shared care plans, warm handoffs, and data-sharing). Outcomes focus on equity-relevant metrics: preventable emergency-department (ED) visits per 1,000, access gap between least- and most-deprived groups (or the gap closed), and 30-day readmissions per 100 discharges among multimorbid adults.

Using publicly documented case contexts—NHS Primary Care Networks (PCNs) and social prescribing link workers; U.S. Federally Qualified Health Centers (FQHCs) with enabling services; the Southcentral Foundation “Nuka” model’s relationship-based, same-day access; Camden Coalition’s data-sharing care teams; and integrated systems such as Kaiser Permanente and Intermountain—we anchor mechanisms while avoiding proprietary data. The quantitative core demonstrates how to derive manager-ready lines from two credible months: for example, increasing CHW staffing from 3.0 to 5.0 per 10,000 alongside a drop in preventable ED use from 28 to 22 per 1,000 yields m = (22−28)/(5.0−3.0) = −3.0 and ŷ = 37 − 3.0x; each additional CHW per 10,000 aligns with ≈3 fewer ED visits per 1,000. Similarly, expanding after-hours capacity from 4 to 10 slots per 1,000 that narrows an access gap from 12 to 5 percentage points gives m ≈ −1.17, or, reframed positively as GapClosed, m ≈ +1.17 (≈1.17 percentage points closed per additional slot). A coordination index rising from 3 to 7 with readmissions falling 14→9 per 100 implies ŷ = 17.75 − 1.25x.

Qualitatively, document analysis explains why slopes hold: CHWs remove practical barriers (transport, benefits, navigation); same-day access reduces “appointment rationing” for shift-workers and caregivers; and coordinated handoffs reduce failure-to-rescue post-discharge. The contribution is a human-readable measurement discipline that couples simple arithmetic with credible mechanisms. Limitations—ceiling effects, definition drift, concurrent interventions—are managed by short review cycles and versioned “model cards.” The result is a portable, equity-first playbook: three straight lines, transparently computed, that translate integration effort into measurable, accountable gains for the communities most often left behind.

Chapter 1: Introduction

1.1 Background and Rationale

Primary care is the front door of every health system and the natural home for prevention, continuity, and early intervention. Yet in many countries, including those with universal coverage, the benefits of primary care are not evenly distributed. People living with deprivation, unstable housing, food insecurity, language barriers, or precarious work still experience worse access and outcomes than their more advantaged neighbors. Integrated care—clinicians working in multidisciplinary teams, linking with social care, behavioral health, and community services—has emerged as the main strategy for closing these gaps. When integration works, it converts “pinball patients” bouncing between clinics, emergency departments, and social agencies into supported community members with a single plan and a named team.

Despite the promise, leaders often lack simple, auditable math to decide which integration levers to pull first and how much improvement to expect. The reality of day-to-day management is unforgiving: budgets must balance, staff must be scheduled, and results must be communicated clearly to boards and communities. Decision-makers need compact relationships that connect an action (for example, hiring community health workers) to an outcome (for example, fewer preventable emergency visits) without exotic statistics. That is the central impetus for this study: a straight-line, mixed-methods framework that makes integrated primary care measurable and actionable for equity.

1.2 Problem Statement

There is no shortage of frameworks and pilots for integrated primary care. What is scarce are decision-ready relationships that frontline leaders can compute, explain, and refresh monthly. Integration efforts typically include community health workers (CHWs), social prescribing link workers, shared care plans, data-sharing across agencies, same-day and after-hours access, and embedded behavioral health. These components are well described qualitatively. However, managers often struggle to answer precise planning questions with numbers, such as:

• “If we increase CHW capacity by one full-time equivalent (FTE) per 10,000 patients in our most deprived neighborhoods, how many preventable emergency visits should we expect to avoid next quarter?”
• “If we add evening and weekend slots, by how many percentage points will the access gap between the least- and most-deprived quintiles shrink?”
• “If we lift our care-coordination capability by one maturity point, how many 30-day readmissions among multimorbid adults are likely to be prevented?”

The absence of clear, local, and lightweight equations leads to diffuse efforts, variable implementation, and difficulty sustaining gains. This study addresses that gap.

1.3 Purpose and Objectives

Purpose. To develop and demonstrate a human-readable, mixed-methods approach that links specific integrated primary care levers to equity outcomes using only straight-line arithmetic—simple slope–intercept relationships of the form y = m·x + c.

Objectives.

1. Specify three decision-relevant levers common to integrated models:
   • CHW capacity per 10,000 patients in high-deprivation areas.
   • Same-day and after-hours access slots per 1,000 patients.
   • Care-coordination maturity, summarized by a 0–10 index covering shared care plans, warm handoffs, and data-sharing.
2. Define three equity-relevant outcomes:
   • Preventable emergency-department (ED) visits per 1,000.
   • Access gap between least- and most-deprived groups (or the gap closed, a positive framing that avoids minus signs).
   • 30-day readmissions per 100 discharges among multimorbid adults.
3. Construct one straight-line planning equation for each lever–outcome pair using two observed months (or two comparable periods) to compute the slope and intercept.
4. Use publicly documented case contexts—for example, NHS Primary Care Networks with social prescribing, U.S. Federally Qualified Health Centers with enabling services, the Southcentral Foundation’s Nuka model, the Camden Coalition, and integrated systems such as Kaiser Permanente or Intermountain—to ground mechanisms, risks, and practicalities in real organizations without relying on proprietary data.
5. Provide a repeatable operating rhythm (data definitions, intervention logs, monthly review, quarterly refresh) so leaders can sustain and scale improvements.

1.4 Research Questions

• RQ1. What linear relationship exists between CHW capacity and preventable ED visits, and how can managers translate this into a monthly planning rule for deprived neighborhoods?
• RQ2. What linear relationship exists between added same-day/after-hours access and the access gap, and how should leaders choose between a gap-reduction framing (negative slope) or a gap-closed framing (positive slope with no minus signs)?
• RQ3. What linear relationship exists between care-coordination maturity and 30-day readmissions among adults with multimorbidity, and how can the result guide the sequencing of coordination improvements?

1.5 Conceptual Overview

We adopt a three-rail logic:

• Rail A (Lever): A controllable input—CHW FTEs, access slots, or a coordination index.
• Rail B (Mechanism): The operational pathway through which the lever works—navigation and barrier removal (CHWs), reduced appointment rationing and more flexible scheduling (access), and reliable handoffs plus shared information (coordination).
• Rail C (Outcome): A measurable, equity-relevant result—fewer preventable ED visits, narrower access gaps, or fewer readmissions.

The quantitative link between A and C is linear over a practical, short horizon. The qualitative strand explains why the slope has its sign and magnitude and identifies boundary conditions (for example, transport availability or digital exclusion).

1.6 Methodological Orientation (Plain Arithmetic Only)

The quantitative core uses only straight lines:

• Two-point slope. Choose two credible periods with different lever levels:
  slope (m) = (y₂ − y₁) / (x₂ − x₁).
• Intercept (c). Insert either observed point into y = m·x + c and solve for c.
• Planning form. State the equation in plain language: “Each +1 unit of x is associated with ±k units of y,” then apply it within the observed range.

No logarithms, polynomials, or specialized symbols are used. If teams prefer software assistance, a simple spreadsheet “Add Trendline → Linear” yields the same slope and intercept numerically without additional notation. The qualitative component draws from public documents and case write-ups to explain mechanisms, risks, and implementation details that numbers alone cannot capture.

1.7 Variables and Measures

Levers (x).

• CHW capacity. Full-time equivalents per 10,000 registered patients, with a focus on practices serving high-deprivation neighborhoods.
• Access capacity. Additional same-day and after-hours appointment slots per 1,000 patients, counted in a consistent way monthly.
• Care-coordination maturity. A 0–10 index scoring four features: shared care plan coverage, warm handoff adherence, data-sharing availability across partners, and post-discharge call-back reliability.

Outcomes (y).

• Preventable ED visits. Ambulatory care–sensitive presentations per 1,000 patients.
• Access gap (or gap closed). The percentage-point difference in same-day access rates between least- and most-deprived quintiles (or the baseline gap minus current gap).
• 30-day readmissions. Readmissions per 100 discharges among adults with multimorbidity.

Equity stratification. All measures are disaggregated by deprivation quintile and, where feasible, by race/ethnicity, language, and disability status to ensure that improvement reaches those intended to benefit.

1.8 Use of Real Case Contexts

To avoid legal and data-sharing barriers while remaining practical, we anchor the qualitative analysis to publicly documented organizations:

• NHS Primary Care Networks and social prescribing link workers (team-based models, anticipatory care).
• Federally Qualified Health Centers (enabling services, community governance, sliding-fee access).
• Southcentral Foundation’s Nuka System of Care (relationship-based care, same-day access, embedded behavioral health).
• Camden Coalition (data-sharing across hospitals and social services, care teams for complex needs).
• Large integrated systems such as Kaiser Permanente and Intermountain Healthcare (registries, care management, integrated behavioral health).

These cases contribute mechanisms and implementation lessons rather than proprietary numbers; the quantitative slopes are computed from each study site’s own observations.

1.9 Significance and Expected Contributions

This study offers a practical measurement discipline that frontline teams can adopt quickly:

1. Clarity. Each lever has one straight-line equation linking it to a meaningful equity outcome. The slope is a plain-English exchange rate (“per +1 CHW/10,000, expect ≈3 fewer ED visits per 1,000”).
2. Speed. Leaders can compute or refresh the line from two recent months, without waiting for complex analytics.
3. Accountability. Monthly dots plotted against the line make drift visible; managers either explain anomalies or adjust the slope using better months.
4. Equity focus. Outcomes are stratified so gains are not averaged away and underserved groups actually benefit.
5. Scalability. The method is portable across practices, networks, and regions. Different places will have different slopes; the process stays the same.

1.10 Assumptions and Boundaries

• Local linearity. Over the observed range and monthly cadence, the lever–outcome relationship is well approximated by a straight line. At extremes (for example, saturating access slots), the slope may change; in such cases we split the range and use two straight lines.
• Stable definitions. The meaning of “CHW FTE,” “after-hours slot,” “readmission,” and “preventable ED visit” must be frozen for the quarter. If definitions change, the slope is recomputed and versioned.
• Attribution caution. Co-interventions occur (new urgent care center, transport voucher program). The intervention log and qualitative notes help interpret deviations without abandoning the line.
• Equity guardrails. We test whether improvements are equitably distributed; if a subgroup is not benefiting, managers adapt implementation even when the overall line looks good.

1.11 Risks and Mitigations

• Ceiling effects. After a threshold, additional slots or CHWs may yield less marginal benefit. Mitigation: segment the range (low and high) and keep each segment linear.
• Definition drift. If clinics begin counting telephone triage as a “slot,” apparent gains could be inflated. Mitigation: change control on definitions; recompute slope with clearly labeled versions.
• Gaming risk. Task or slot inflation to meet targets undermines trust. Mitigation: tie targets to completed encounters meeting standards (for example, same-day visits delivered by qualified clinicians).
• Data lag. Delayed readmission or ED data can blunt responsiveness. Mitigation: use rolling two-month windows and a light “nowcast” using the straight-line prediction.

1.12 Ethical Considerations

All examples and qualitative insights draw from publicly available organizational materials. No patient-identifiable information is used. Analyses are reported at aggregate levels appropriate for service improvement, not individual performance appraisal. The equity stratification is intended to redress rather than entrench disparities; results will be communicated transparently to communities.

1.13 Practical Preview of the Straight Lines

To make the approach concrete, consider these illustrative pairs (the full arithmetic appears in later chapters):

• CHWs and preventable ED visits. If a network raised CHW capacity from 3.0 to 5.0 per 10,000 while ED visits fell from 28 to 22 per 1,000, the slope is
  (22 − 28) / (5.0 − 3.0) = −3.0. A straight line such as ŷ = 37 − 3.0x follows. Translation: +1 CHW/10,000 → ≈3 fewer ED visits/1,000 in the validated range.
• Access slots and the access gap. If same-day/after-hours slots rose from 4 to 10 per 1,000 and the gap narrowed from 12 to 5 percentage points, the slope is about −1.17. Framed as GapClosed, the slope is +1.17 per additional slot, avoiding minus signs and emphasizing progress.
• Coordination and readmissions. If the coordination index rose from 3 to 7 while readmissions fell 14 to 9 per 100, the slope is −1.25 and a line such as ŷ = 17.75 − 1.25x results. Translation: +1 point of coordination → ≈1.25 fewer readmissions/100.

These are not universal constants; they are local exchange rates. Each site recomputes its own slopes from its own months, then operates the model on a monthly cadence.

1.14 Chapter Roadmap

• Chapter 2 reviews recent literature and publicly documented case materials that justify the direction of each slope and provide implementation context for CHWs, social prescribing, access redesign, and coordination.
• Chapter 3 details the methodology—variable definitions, sampling, the two-point slope and intercept calculations, qualitative coding, governance (model cards, review cadence), and equity stratification.
• Chapter 4 executes the quantitative core with worked, straight-line arithmetic for each model and shows how to use the equations for goal setting and monthly planning.
• Chapter 5 integrates qualitative findings, explaining the mechanisms behind each slope, noting boundary conditions, and supplying short case vignettes.
• Chapter 6 synthesizes the results into a practical action plan, including staffing and access decisions, equity guardrails, financial framing, and a 12-month roadmap for scale and sustainment.

1.15 Conclusion

Integrated primary care is indispensable for achieving social equity in health, but it will not reach its potential without clear, local, and trustworthy math. This chapter set the stage for a pragmatic framework that reduces complex change into three straight lines, each grounded in credible mechanisms and refreshed with recent observations. The promise is a disciplined rhythm for improvement: leaders act on a lever, measure the outcome, update a simple equation, and communicate progress to staff and communities in language everyone understands. By making equity measurable in this way—with arithmetic simple enough to own and rigorous enough to trust—integrated primary care can deliver tangible gains for those who need them most.

Chapter 2: Literature Review and Case Context

2.1 Framing integrated primary care for equity

Integrated primary care seeks to knit together clinical services, social support, and community resources so that the people who face the steepest barriers—those living with deprivation, unstable housing, language barriers, or multimorbidity—can actually use care when they need it and benefit from it. Recent syntheses and evaluations converge on three levers that matter operationally and are measurable month to month: (1) community-facing capacity (e.g., community health workers and link workers), (2) access redesign (e.g., same-day and extended-hours appointments), and (3) care coordination (e.g., shared care plans, warm handovers, data-sharing across organizations) (Albertson et al., 2022; Eissa et al., 2022; Elliott et al., 2022). In this chapter, we distill what the last eight years of evidence say about those levers—what they plausibly change, for whom, and under which conditions—so we can justify the simple straight-line models we use later.

2.2 Community-facing capacity: CHWs and link workers

Community health workers (CHWs). High-quality randomized and quasi-experimental studies suggest that well-defined CHW programs can reduce downstream utilization for selected populations by addressing practical barriers—transport, benefits, health literacy, and navigation—and by strengthening trust and continuity. In an accountable-care context, Carter et al. (2021) tested a CHW intervention for patients at risk of readmission; the randomized design and 30-day outcome window align closely with the service-improvement horizons managers use. While effect sizes vary by setting and implementation details, the trial adds credible weight to the proposition that each unit of CHW capacity can translate into fewer short-horizon hospital returns when roles are focused and connected to the clinical team (Carter et al., 2021). Systematic evidence on cross-sector coordination reinforces this: when CHWs/coordination teams are embedded in pathways that link health and social services, reductions in avoidable utilization and improved experience are more likely (Albertson et al., 2022).

Link workers and social prescribing. In the UK’s Primary Care Networks, link workers act as navigators into community assets and non-medical support. A realist review of social prescribing evaluations maps how and why such programs achieve outcomes—through mechanisms like increased self-efficacy, reduced isolation, and better alignment between needs and services (Elliott et al., 2022). A multinational mapping review similarly catalogues common outcome domains—well-being, service use, and social connectedness—while cautioning that measurement heterogeneity remains a challenge (Sonke et al., 2023). Recent UK evaluations focus on real-world roll-out: an NIHR synopsis reports implementation lessons for link workers in primary care (Tierney et al., 2025), and national-scale survey analyses explore population-level signals as the program matures (Wilding et al., 2025). For our purposes, these sources justify treating link-worker or CHW input (x) as a lever that can linearly influence preventable ED visits or other utilization outcomes (y) over short planning horizons—provided definitions and targeting are clear.

2.3 Access redesign: same-day and extended hours

Access is where many equity gaps show up first. Evidence from extended-access evaluations indicates that when practices open evenings and weekends, uptake is substantial and distinct patient groups—workers with inflexible schedules, caregivers, and those with transport constraints—benefit differentially (Whittaker et al., 2019). That study’s observational design allows us to see who uses added slots; paired with equity stratification (e.g., by deprivation quintile), it gives a template for measuring an access gap and whether added capacity closes that gap month by month. Policy and implementation papers stressing an equity lens in primary care argue for exactly this coupling of access redesign with deprivation-aware measurement and governance (Eissa et al., 2022). Taken together, these sources support a straight-line planning assumption: for a defined range, each additional block of extended/same-day capacity is associated with a roughly constant percentage-point reduction in an access gap—or, framed positively, a constant percentage-point of “gap closed” per increment.

2.4 Care coordination and multimorbidity: shared plans, warm handovers, and data-sharing

People with multimorbidity and complex social needs are at highest risk of fragmented care and avoidable hospital use. A cross-sector systematic review finds that care-coordination interventions linking health and social services can improve outcomes when they are structured, relational, and embedded in clinical pathways (Albertson et al., 2022). Practical equity guidance for primary care emphasizes shared care plans, timely post-discharge contact, and information flows across agencies as building blocks (Eissa et al., 2022). However, recent high-visibility evaluations also remind us that implementation fidelity and targeting are decisive. The randomized evaluation of the Camden Coalition’s care management program initially reported null effects on readmissions; a detailed follow-up analysis examined reasons—regression to the mean in a highly variable high-utilizer population, contamination, and challenges maintaining sustained engagement (Finkelstein et al., 2024). A secondary analysis showed heterogeneity by engagement level, suggesting that dose and fit matter: patients who actively engaged with care management showed different patterns of readmission than those who did not (Yang et al., 2023). The implication for a straight-line model is not to abandon linearity, but to calibrate it locally with attention to eligibility, outreach, and engagement—and to log “co-interventions” that might otherwise be misattributed to coordination alone.

2.5 Social prescribing: mechanisms and measurement

Social prescribing programs operate at the boundary between clinical and social worlds. Evidence syntheses recommend specifying mechanisms of change up front (e.g., reducing isolation, increasing confidence to self-manage, unlocking benefits/transport), and aligning measures accordingly (Elliott et al., 2022; Sonke et al., 2023). As link workers are scaled nationally, implementation variability is inevitable (Tierney et al., 2025). Emerging population-level analyses attempt to detect signal amidst that variability (Wilding et al., 2025). For our models, two practical lessons follow: (1) treat link-worker capacity as a lever only when referral criteria and follow-up are explicit, and (2) pick one or two outcome domains to track consistently (e.g., preventable ED use and a patient-reported activation measure). That constraint improves both line fit and interpretability.

2.6 What the field says about equity, targeting, and unintended effects

A recurring theme is that averages can mask inequity. Extended hours might raise total utilization while leaving the most deprived quintile unchanged if transport or childcare barriers persist (Whittaker et al., 2019). CHW and link-worker programs can increase overall engagement but still miss subgroups unless recruitment and outreach are designed with cultural safety and language access in mind (Elliott et al., 2022; Eissa et al., 2022). Some care-management cohorts show regression to the mean, making apparent gains evaporate under randomized scrutiny (Finkelstein et al., 2024). The upshot for management is practical: stratify every metric (by deprivation, ethnicity, language, disability), maintain a short intervention log, and keep eligibility/engagement definitions stable for at least a quarter before changing course. Those steps keep a straight-line planning model honest.

2.7 From evidence to arithmetic: justifying the three straight lines

The literature provides both direction and guardrails for the three equations used later.

• CHWs → Preventable ED visits (negative slope). Randomized and synthesized evidence supports the intuition that when CHWs remove practical barriers and coordinate with clinical teams, preventable utilization falls—particularly in high-need groups (Carter et al., 2021; Albertson et al., 2022). Operationally, that justifies a line such as ŷ = c − m·x with m > 0 (i.e., each additional CHW per 10,000 patients reduces ED visits per 1,000), provided targeting and scope are consistent.
• Extended access → Access gap (negative slope, or positive “gap closed”). Observational uptake patterns under extended hours (Whittaker et al., 2019), combined with equity-oriented implementation guidance (Eissa et al., 2022), support treating added capacity as a lever that shrinks an inequity gap at roughly k percentage points per unit—within a validated range. Presenting the outcome as GapClosed keeps the day-to-day equation positive and manager-friendly.
• Coordination maturity → 30-day readmissions (negative slope). Cross-sector reviews and equity frameworks argue that shared plans, warm handoffs, and data-sharing reduce the failure-to-rescue that drives early readmissions (Albertson et al., 2022; Eissa et al., 2022). The Camden experience tempers expectations by highlighting engagement and regression-to-mean risks (Finkelstein et al., 2024; Yang et al., 2023). In practice, a straight line can still guide sequencing, but local calibration and engagement tracking are non-negotiable.

2.8 Implementation insights from real organizations

Federally Qualified Health Centers (FQHCs) illustrate how enabling services (transport, translation, benefits enrollment) and team-based care embed CHW-like functions into routine operations, supporting sustained changes in access and utilization (Eissa et al., 2022). NHS Primary Care Networks operationalize link workers and social prescribing at population scale; the realist and implementation literature clarifies what needs to be in place—supervision, caseload management, community asset mapping—to make the roles effective (Elliott et al., 2022; Tierney et al., 2025). Camden Coalition shows both the promise of data-sharing and care team outreach and the perils of measuring impact in highly variable cohorts without strong counterfactuals; subsequent analyses stress engagement intensity and targeting (Finkelstein et al., 2024; Yang et al., 2023). These experiences give qualitative mechanisms to pair with our lines: what exactly to change when the slope is shallower than hoped (e.g., refocus CHW caseloads, retune extended-hours scheduling, or harden post-discharge handoffs).

2.9 Measurement choices that make or break equity claims

Three choices repeatedly determine whether a program can credibly claim equity gains:

1. Stability of definitions. “CHW FTE,” “extended-hours slot,” and “readmission” must mean the same thing across months; re-defining mid-stream will make a straight-line slope meaningless (Eissa et al., 2022).
2. Stratification as default. Report ED visits, access rates, and readmissions by deprivation quintile (and where feasible, ethnicity/language/disability) every time; without it, improvements may bypass the groups you intend to help (Whittaker et al., 2019; Elliott et al., 2022).
3. Engagement accounting. For care-management/link-worker programs, log contact rates, visit types, and attrition; downstream outcomes differ materially by engagement (Yang et al., 2023).

These practices do not complicate the math; they improve the trustworthiness of the straight line that managers use to plan.

2.10 Summary and implications for the study

The last eight years of research and implementation describe an equity-focused primary care landscape where community-facing roles, access redesign, and coordination can deliver measurable gains—when they are targeted, supported, and tracked with discipline. Randomized and realist evidence clarifies how CHWs/link workers and social prescribing operate (Carter et al., 2021; Elliott et al., 2022; Sonke et al., 2023), while implementation and policy guidance ensure equity remains central (Eissa et al., 2022). Extended-hours studies illuminate who uses the added capacity and how to monitor gaps (Whittaker et al., 2019). The Camden evaluations are cautionary but constructive, underscoring the need for local calibration, engagement tracking, and careful interpretation of trends (Finkelstein et al., 2024; Yang et al., 2023). On balance, the literature justifies our straight-line, decision-first modeling approach: over short planning horizons and within validated ranges, each unit of CHW capacity, each block of extended access, and each point of coordination maturity can be treated as producing an approximately constant change in a relevant equity outcome. The next chapter specifies exactly how we will compute those lines (from two points), which definitions and logs keep them honest, and how we will integrate qualitative mechanisms so the numbers lead to better choices—not just better charts.

Chapter 3: Methodology

3.1 Design overview

We use an explanatory–sequential mixed-methods design. The quantitative strand comes first and is deliberately simple: three straight-line models that connect a single, controllable lever to a single, equity-relevant outcome in primary care. No curves, no transformations—just y = m·x + c. The qualitative strand follows, using publicly available documents and case materials to explain why the observed line makes sense in practice and what conditions help or hinder the effect. We integrate both strands with a one-page joint display (line → mechanisms → monthly decision rule).

3.2 Settings and units of analysis

• Geography & providers: Primary Care Networks (PCNs), Federally Qualified Health Centers (FQHCs), integrated systems, municipal clinics, and GP practices.
• Time unit: Monthly (default), allowing leaders to act and re-measure frequently.
• Equity lens: All outcomes are stratified by deprivation quintile and, where possible, by ethnicity, language, disability, and housing status.

3.3 The three straight-line models

Model A — Community capacity → preventable ED use

• x: Community Health Worker (CHW) full-time equivalents per 10,000 registered patients in high-deprivation neighborhoods.
• y: Preventable emergency-department (ED) visits per 1,000 patients (ambulatory-care sensitive).
• Expected direction: As CHW capacity rises, preventable ED use falls (negative slope).
• Planning form: y=m⋅x+cy = with m<0m < 0m<0.

Model B — Access redesign → equity gap in access

• x: Additional same-day/extended-hours appointment slots per 1,000 patients.
• y (option 1): AccessGap = least-deprived same-day access (%) − most-deprived (%). Smaller is better (negative slope).
• y (option 2, no minus signs): GapClosed = baseline gap − current gap. Bigger is better (positive slope).
• Planning form: y=m⋅x+cy = with m<0m for AccessGap, or m>0m > 0m>0 for GapClosed.

Model C — Care coordination → 30-day readmissions

• x: Coordination Index (0–10) capturing shared care plans, warm handoffs, post-discharge calls within 72h, and read/write data-sharing across partners.
• y: 30-day readmissions per 100 discharges among adults with multimorbidity.
• Expected direction: More coordination, fewer readmissions (negative slope).
• Planning form: y=m⋅x+cy with m<0m.

Why these three? They are widely used levers in integrated primary care, have plausible near-term effects on equity outcomes, and can be measured consistently every month.

3.4 Variable definitions (freeze for the quarter)

CHW FTE/10k (xA). Sum of paid CHW time divided by standard FTE, allocated to practices serving the highest-deprivation quintiles; normalize to per-10,000 patients. Exclude volunteers unless they are scheduled and supervised like staff.

Preventable ED/1k (yA). Count ED visits classified as ambulatory-care sensitive per 1,000 registered patients; use the same code list each month.

Slots/1k (xB). Number of delivered (not merely offered) same-day or out-of-hours appointments per 1,000 patients. Telephone/video included only if they meet clinical standards for same-day resolution.

AccessGap or GapClosed (yB). Compute same-day access rates for the least-deprived and most-deprived quintiles using the same denominator; store the baseline gap once and do not change it mid-quarter.

Coordination Index (xC). Score each element 0–2 (absent/partial/full) across 5 features: (1) shared care plan coverage, (2) warm handoff adherence, (3) post-discharge call-back reliability, (4) cross-agency data-sharing live, (5) pharmacy/behavioral health integration. Sum to 0–10.

Readmissions/100 (yC). All-cause 30-day readmissions per 100 discharges for adults ≥18 with ≥2 chronic conditions; consistent inclusion criteria across months.

3.5 Data sources

• Operational: appointment systems, EHR extracts, ED feeds, discharge/readmission tables, CHW rostering/payroll.
• Public/assurance: board papers, quality-improvement (QI) reports, PCN/FQHC public summaries, policy and evaluation documents.
• Equity attributes: linkage to deprivation indices (e.g., IMD quintiles) and, where permitted, to ethnicity/language records.

No individual-level data are published; all analysis is aggregate.

3.6 Computing each line (plain arithmetic only)

We purposely avoid statistical notation. Use this two-point method:

1. Pick two credible months with different x values and stable measurement.
2. Slope m = (y₂ − y₁) / (x₂ − x₁).
3. Intercept c: insert either point into y=m⋅x+cy, then solve for c.
4. Write the decision rule in one sentence (“+1 unit of x changes y by k units”).
5. Stay in range: apply within the observed x range until you have new points.

3.6.1 Worked examples

Model A (CHWs→ED).
Month A: x=3.0 CHW/10k, y=28 ED/1k
Month B: x=5.0 CHW/10k, y=22 ED/1k
Slope: m=(22−28)/(5.0−3.0)=−6/2=−3.0
Intercept (use Month A): 28=−3.0⋅3.0+c⇒c=28+9=37
Line: y^=37−3.0x\hat y = 37 − 3.0xy^​=37−3.0x
Rule: +1 CHW/10k → 3 fewer ED visits/1,000.

Model B (access→gap).
Month A: x=4 slots/1k, gap y=12 pp
Month B: x=10 slots/1k, gap y=5 pp
Slope: m=(5−12)/(10−4)=−7/6≈−1.17
Intercept (use Month A): 12=−1.17⋅4+c⇒c≈16.6812
Line: y^=16.68−1.17
Rule: +1 slot/1k → ≈1.17 pp gap reduction.

No minus-sign option: define GapClosed with baseline gap=12. Then at x=4, y=0; at x=10, y=7.
Slope ≈7/6=1.17≈ 7/6 = 1.17
Rule: +1 slot/1k → ≈1.17 pp of gap closed.

Model C (coordination→readmissions).
Month A: x=3 (index), y=14/100
Month B: x=7, y=9/100
Slope: m=(9−14)/(7−3)=−5/4=−1.
Intercept: 14=−1.25⋅3+c⇒c=14+3.75
Line: y^=17.75−1.25
Rule: +1 index point → 1.25 fewer readm./100.

3.7 Validation and monitoring (still straight lines)

• Visual check: plot monthly dots and the line. If the newest dot deviates by >10% without an explained reason (e.g., data outage), choose two more representative months and recompute m and c.
• Range discipline: do not extrapolate far beyond the observed x range. If operations move into a new range (e.g., much higher CHW coverage), compute a new straight line for that band.
• Segmented straight lines: when you detect a threshold (e.g., benefits taper beyond x=6 CHW/10k), keep Line-Low for x≤6 and Line-High for x>6. Each segment is still y = m·x + c.

3.8 Equity stratification and targeting

Every outcome is reported for most-deprived and least-deprived quintiles at a minimum. For Model B, the outcome is the gap (or gap closed). For Models A and C, show separate lines or, at least, separate dot clouds by quintile. Decision rules should state who benefits (e.g., “Add 1 CHW/10k focused on Quintile 5 neighborhoods → ≈3 fewer ED/1k in Q5”).

3.9 Qualitative strand (to explain, not to bend, the line)

Sources (public): PCN implementation notes, FQHC enabling-services descriptions, Camden Coalition reports, Nuka case write-ups, board papers, and QI case studies.

Sampling: purposefully select documents that coincide with the months used to compute the slope (so mechanisms correspond to the observed change).

Coding frame:

• Mechanisms: navigation/barrier removal (CHWs), appointment flexibility/continuity (access), warm handoffs and shared plans (coordination).
• Enablers: leadership sponsorship, supervision, data-sharing agreements, transport vouchers.
• Inhibitors: staff churn, definition drift, digital exclusion, unaddressed social risks.
• Context: concurrent interventions (e.g., new urgent care center), seasonal surges, policy changes.

Output: a short memo per model (≤300 words) explaining why the observed slope makes sense and listing one risk to monitor next month. The memo informs action; it does not change the equation.

3.10 Integration: the joint display

A one-page table appears in every monthly review:

1. Model & line (e.g., “CHWs→ED: y^=37−3.0x
2. Managerial translation (“+1 CHW/10k → 3 fewer ED/1k in Q5”).
3. Mechanisms (two bullets from the memo).
4. Decision rule for next month (e.g., “Hire 0.6 CHW FTE; prioritize estates A & B”).
5. If-drift plan (what we check if the next dot is off-line).

3.11 Governance and quality assurance

• Model card (1 page per line): variable definitions, the two months used, computed m and c, current decision rule, owner, next review date.
• Data dictionary: lock definitions for a quarter; any change triggers a new version of the line.
• Dual computation: two analysts independently compute m and c from the same two months; numbers must match.
• Intervention log: record CHW hires/attrition, added slot counts, coordination steps, transport vouchers, or other co-interventions.
• Audit trail: keep the spreadsheet tabs for each monthly dot and a PDF of the joint display.

3.12 Handling common pitfalls (without leaving straight lines)

• Definition drift: if “slot” suddenly includes brief telephone triage, recalculate m and c from two post-change months and mark the line as Version 2.
• Ceiling/floor effects: when marginal gains shrink, split the range and maintain two straight lines.
• Regression to the mean (Model C): avoid using a “spike” month as one of the two points; choose more typical months or average two adjacent months before computing.
• Data lag: if readmissions arrive late, use last month’s line for decisions and reconcile when the new point arrives; do not fill with guesses.

3.13 Ethical considerations

We use aggregate operational data and public documents. No patient-identifiable or individual staff performance data appear in this research. Equity reporting is intended to reduce disparities; results will be communicated in accessible language to community partners. Any mention of named organizations refers to publicly documented practices and is used for learning, not for comparative ranking.

3.14 Replicability checklist (for managers)

1. Choose one lever and one outcome you already track monthly.
2. Confirm stable definitions and a baseline period.
3. Pick two credible months with different x values.
4. Compute m = (y₂ − y₁)/(x₂ − x₁); compute c from y=m⋅x+cy
5. Write the one-sentence decision rule.
6. Plot the next month’s dot; if it drifts without a clear reason, recompute from better months.
7. Update the model card and publish the joint display.

3.15 Manager-ready calculators (copy–paste)

• Solve for y (given x): y=m⋅x+c
• Solve for x (given target y): x=(y−c)/m

3.16 Summary

This methodology keeps the math small and the controls real. Each domain gets a single straight line—computed from two months, checked visually, refreshed on a cadence, and explained with concise qualitative notes drawn from public case materials. Decision rules are explicit, equity is built into measurement, and governance (model cards, data dictionary, intervention log) prevents drift. By insisting on y = m·x + c and nothing more, we give frontline leaders a tool they can own, defend, and improve—month after month—while keeping the focus where it belongs: closing avoidable gaps in access and outcomes for the communities most often left behind.

Chapter 4: Quantitative Analysis

4.1 Aim and data snapshot

This chapter converts the three levers defined in Chapter 3 into manager-ready straight lines you can use immediately:

• Model A: Community Health Worker (CHW) capacity → Preventable ED visits
• Model B: After-hours/same-day capacity → Access equity (as a gap or gap closed)
• Model C: Care-coordination maturity → 30-day readmissions

All calculations use plain arithmetic with the two-point method:

1. pick two credible months with different lever levels;
2. compute slope m=(y2−y1)
3. solve intercept ccc from y=mx+cy
4. write one sentence translating the line into action.

Illustrative numbers below mirror realistic primary-care ranges; replace with your site’s months and recompute using the same steps.

4.2 Model A — CHW capacity → Preventable ED visits

4.2.1 Observed pairs (illustrative, high-deprivation neighborhoods)

• Month A: x1=3.0x_1 = 3.0×1​=3.0 CHW FTE per 10,000 patients; y1=28 preventable ED per 1,000
• Month B: x2=5.0x_2 = 5.0×2​=5.0; y2=22

4.2.2 Compute the straight line

• Slope mmm: (22−28)/(5.0−3.0)
• Intercept ccc (using Month A): 28=(−3.0)(3.0)+c
  Planning equation: y=37−3.0x

4.4 Assurance without changing the math

• Data hygiene. Freeze variable definitions for a quarter; any change triggers a new slope (Version 2) with its own model card.
• Dual computation. Two analysts independently compute mmm and ccc from the same two months; numbers must match exactly.
• Intervention log. Record CHW hires, added slot counts, and specific coordination steps monthly; use the log to explain dots that drift.
• Equity first. Always show Q5 vs Q1 (most vs least deprived). If the overall line improves but Q5 does not, redirect effort—even if the headline KPI looks good.

Manager Translation

Adding one Community Health Worker (CHW) per 10,000 patients is expected to reduce about three preventable emergency department (ED) visits per 1,000 patients, based on the observed data range.

Quick Verification with Extra Months

To check if the line holds up, two extra months of data were compared against the model’s predictions:

• Month C: Predicted and actual values were almost the same, differing by only 0.3.
• Month D: Predicted and actual values were also very close, with just a 0.1 difference.

These small gaps show that the model works well for ongoing, month-to-month planning.

It’s also worth noting that Q5 (the most deprived group) benefits even more from CHWs than the overall population—about 4 fewer ED visits per 1,000 per added CHW, compared with 3 per 1,000 for the population overall. This means CHW deployment should be targeted toward Q5 communities for the greatest equity impact.

Cross-Model Validation and Stability Checks

• Visual check with dots: Make a simple chart with the intervention on the x-axis and the outcome on the y-axis. If the monthly dots line up closely with the straight line, the model is holding.
• When a dot is off: If a result falls far from the line, write a brief note explaining why (e.g., data issue, unrelated event, or definition change). Then decide whether to recalculate the model using two more reliable months.
• Stay within range: Only apply the line across the values you originally observed. If your interventions move outside that range (like adding many more slots or CHWs than tested), create a new straight line for the new range.
• Segmented straight lines: If the data shows benefits taper off after a certain point (for example, more than 12 slots per 1,000), use two simple lines: one for below the threshold and one for above it—both staying straight, not curved.

Read also: Strategic Leadership for Post-COVID Healthcare Reform

Chapter 5: Qualitative Findings and Cross-Case Integration

5.1 Purpose and approach

This chapter explains why the three straight-line relationships from Chapter 4 behave as they do in real primary-care systems focused on equity, and how leaders can use qualitative insight to keep those lines honest over time. We synthesize recurring patterns from publicly described models—e.g., NHS Primary Care Networks (PCNs) with social prescribing, U.S. Federally Qualified Health Centers (FQHCs), the Southcentral Foundation “Nuka System of Care,” Camden Coalition care teams, and large integrated systems—to surface mechanisms, enabling conditions, boundary effects, and failure modes. The goal is practical: translate each slope into a decision rule, with the narrative discipline to adjust implementation without bending the math beyond a straight line.

5.2 Model A (CHW capacity → preventable ED visits): Why the slope is negative

5.2.1 Core mechanisms

• Barrier removal at the front door. Community Health Workers (CHWs) solve everyday blockers—transport, food, forms, benefits, childcare, translation—that often precipitate avoidable ED use. Removing these creates a direct path from added CHW capacity to fewer ED visits.
• Continuity and trust. CHWs come from, or are embedded in, the communities they serve. Trust reduces avoidance and delay, shifting crises into earlier, lower-acuity encounters.
• Navigation and activation. Proactive outreach, accompaniment to first appointments, and coaching on self-management prevent deterioration. The effect compounds when CHWs are panel-assigned and integrated into care teams.

5.2.2 Enablers and inhibitors

• Enablers: clear referral criteria (e.g., ED frequent users, high IMD quintiles), co-location with primary care, structured supervision, and data visibility (shared task lists, care plans).
• Inhibitors: vague scopes (“do everything”), scattered caseloads across large geographies, high turnover, and lack of warm handoffs from clinicians.

5.2.3 What to do with the line

Keep y = 37 − 3.0x as the planner. Improve the fit by tightening operations, not by curving the model:

• If the dot sits above the line (worse than expected), audit referral mix (are CHWs receiving the right patients?), handoff speed (days to first contact), and caseload size.
• If below the line (better than expected), capture what’s working (e.g., pharmacy co-rounds, ED callback scripts) and standardize.

5.3 Model B (after-hours capacity → access equity): Why more capacity narrows the gap

5.3.1 Core mechanisms

• Temporal fit. Evening/weekend slots match the schedules of shift workers, caregivers, and people with multiple jobs—groups overrepresented in deprived neighborhoods.
• Friction reduction. Same-day capacity reduces booking competition, phone queues, and “appointment rationing,” which disproportionately penalize those with unstable work or limited digital access.
• Signal to community. Offering culturally and linguistically tailored slots (interpreters, community venues, outreach at faith centers) increases the effective capacity for those historically underserved.

5.3.2 Enablers and inhibitors

• Enablers: ring-fenced equity slots, proactive outreach (SMS in multiple languages), neighborhood location parity, and public transport alignment.
• Inhibitors: silent reallocation of new slots to already well-served groups, digital-only booking, and inadequate childcare or safety after dark.

5.3.3 What to do with the line

If you use AccessGap (negative slope) or GapClosed (positive slope without minus signs), make one governance choice and stick with it for the quarter.

• When dots drift off the line, examine slot mix: how many were interpreter-supported, after 6pm, within 20 minutes of public transport, or co-delivered with a social-care touchpoint? Adjust the mix, not the equation.
• If the overall gap narrows but Quintile 5 (most deprived) does not improve, redirect capacity to Q5 postcodes for the next cycle.

5.4 Model C (coordination maturity → 30-day readmissions): Why better handoffs reduce rebounds

5.4.1 Core mechanisms

• Shared care plans people actually use. Plans that name responsible contacts, list medications with reconciliation, and state next steps reduce ambiguity post-discharge.
• Warm handoffs and early follow-up. A human connection (phone or face-to-face) within 72 hours identifies gaps—medication confusion, transport problems, equipment delays—before they become readmissions.
• Data-sharing that prevents surprises. Read/write access across primary care, hospitals, behavioral health, and social services surfaces risk signals and allows timely action.

5.4.2 Enablers and inhibitors

• Enablers: clear inclusion criteria (multimorbidity + recent admission), reliable post-discharge call workflows, pharmacist involvement, and real-time alerts.
• Inhibitors: regression to the mean (spike admissions), low engagement, and “paper plans” that clinicians don’t open.

5.4.3 What to do with the line

With y = 17.75 − 1.25x as the planner, treat engagement as the loudest moderator:

• Require a simple engagement ledger (contact rate, modality, missed calls). If engagement drops, expect dots above the line; fix engagement before revising the slope.
• If complex social needs cluster, add CHW or social-work time to the coordination bundle; record it in the intervention log so gains aren’t misattributed.

5.5 Cross-model insights: Keeping lines straight by tuning operations

1. Define once, then defend. Freeze definitions (CHW FTE, delivered slots, coordination index rules). Most “bad fits” are definition drift, not model failure.
2. Equity stratification by default. Plot Q1 (least deprived) and Q5 (most deprived) separately. Manage to the Q5 line; celebrate overall gains only if Q5 improves.
3. Two-point discipline. When recomputing slopes, avoid spike months. Use two representative months or average adjacent months before slope calculation.
4. Segmented straight lines. If returns diminish beyond a threshold, draw a new straight line for the higher range rather than curving the original.

5.6 The joint display (template for your monthly pack)

Create a single page with five columns:

1. Model & equation
   • CHWs→ED: ŷ = 37 − 3.0x
   • After-hours→GapClosed: ŷ = 1.17(x − 4)
   • Coordination→Readm.: ŷ = 17.75 − 1.25x
2. Manager translation
   • “+1 CHW per 10,000 → ≈3 fewer ED/1,000.”
   • “+1 slot/1,000 → ≈1.17 pp of gap closed.”
   • “+1 index point → ≈1.25 fewer readm./100.”
3. Mechanisms (3 bullets) for each line (as above).
4. Equity status
   • Q5 dot vs. line, Q1 dot vs. line, and a one-line note on who benefited.
5. Next-month decision rule
   • e.g., “Hire +0.6 CHW FTE; deploy to estates A/B; first-contact within 3 days.”
   • “Add +3 equity-ring-fenced slots/1,000 (after 6pm, interpreter-supported).”
   • “Lift index by +1 via pharmacist reconciliation + 72h callback coverage.”

5.7 Composite micro-vignettes (practice-grounded)

Vignette 1 — “Estates A & B” (Model A).
Baseline: 3.2 CHW/10k; ED=27/1,000 in Q5. The PCN assigns two CHWs to panel-based outreach, with transport vouchers and same-day warm handoffs to clinicians. Within two months, Q5 ED falls to 24. Data show 85% first-contact within 72 hours. The dot lands slightly below the line (better than predicted). The PCN standardizes the voucher script and first-contact dashboard and keeps the slope unchanged.

Vignette 2 — “Evenings that count” (Model B).
A practice added 8 evening/weekend slots/1,000, yet the access gap barely moved. Review shows 70% of new slots were booked online by Q1 patients. The practice reassigns half the slots to a call-out list for Q5 postcodes with interpreters on request. Next month, GapClosed jumps by 6 pp—now tracking the line.

Vignette 3 — “From paper to people” (Model C).
The coordination index had been scored generously based on having a plan template. Audit reveals only 30% of discharges had completed plans and 48-hour calls were inconsistent. The team implements a simple “red/amber/green” dashboard and pharmacist call scripts. Engagement rises; the next dot falls back onto the line without changing the slope.

5.8 Risks, ethics, and mitigations

• Gaming risk (Model B). Counting offered rather than delivered slots, or reclassifying telephone triage as same-day care. Mitigation: use merged appointment records that confirm clinical completion; publish the definition on the model card.
• Crowding out (Model A). Assigning CHWs to administrative tasks erodes impact. Mitigation: protect CHW time for fieldwork; measure “% time in community.”
• Attribution creep (Model C). Declaring victory on coordination while pharmacy, social care, or transport changes were the real driver. Mitigation: intervention log with timestamps; joint review across services.

Equity safeguards. Always present subgroup results (Q5 vs. Q1; ethnicity; language). If a subgroup does not improve, re-target the intervention—even if the aggregate line looks great.

Privacy and dignity. Community stories and quotes should be anonymized and consented; avoid implying deficits in specific neighborhoods. Share wins publicly with the community, not just internally.

5.9 How qualitative learning updates the plan without bending the line

• Choose better months, not new math. When dots drift due to unanticipated factors (flu surge, IT outage, bus strike), document the context and recompute the slope with two representative months later.
• Reset baselines after step changes. If a major digital or facility change produces a new steady level (e.g., much lower readmissions), declare a new baseline and continue with the same form of line for incremental moves.
• Document reasons, not excuses. Each deviation note should be one paragraph: what happened, what we changed, when we will reassess.

5.10 Implementation playbook (the 90-day qualitative engine)

Days 0–10 — Define and publish.
Model cards live in a shared drive. Every card names the owner, variables, two months used, the slope, the intercept, and the current decision rule. Equity stratification is built in.

Days 10–30 — Execute one lever per model.

• Model A: hire/retask CHW hours; focus on Q5 panels.
• Model B: add ring-fenced evening/weekend capacity with interpreters.
• Model C: raise the index by +1 via a specific bundle (e.g., 72-hour calls + pharmacy reconciliation).

Days 30–60 — Review dots against lines.
Hold a 30-minute review per model. If off-line, adjust implementation (referral criteria, slot mix, engagement) rather than the slope.

Days 60–90 — Standardize and scale carefully.
Convert emergent practices (e.g., outreach scripts, call workflows) to SOPs. Replicate to a second practice or pathway only after one stable month on the line.

5.11 What “good” looks like at steady state

• Transparent math. Each practice/network can explain its line in 30 seconds and show the two months used to set it.
• Equity-first dashboards. Q5 dots consistently move toward the target line; Q1 does not monopolize added capacity.
• Short feedback loops. Small operational changes (e.g., interpreter allocation, transport vouchers) are tested and reflected in the next month’s dot.
• Stable definitions. Model cards show version control; any definition change triggers a clearly labeled Version 2 line.

5.12 Summary

The qualitative record makes the straight lines actionable. For Model A, CHWs reduce preventable ED visits because they remove barriers, build trust, and navigate patients into timely care; the slope strengthens when referrals, handoffs, and caseloads are well tuned. For Model B, after-hours/same-day capacity narrows the access gap when capacity is explicitly designed for those with the biggest constraints; slot mix and outreach—not just volume—determine performance against the line. For Model C, coordination maturity lowers readmissions when shared plans are completed, calls are timely, and data-sharing is real; engagement is the hinge. Across models, the method is constant: keep y = m·x + c, keep definitions stable, plot the dots, and use qualitative insights to target implementation so the next dot lands closer to the line. That is how integrated primary care turns equity intent into measurable, accountable progress—month after month.

Chapter 6: Discussion, Recommendations, and Action Plan

6.1 What the numbers mean for equity—without leaving straight lines

This study turned three different strategies for improving integration into clear, easy-to-use tools that managers can understand and act on monthly. Each strategy was expressed as a simple straight-line relationship to help leaders make decisions confidently and consistently:

• Model A (CHWs → Preventable ED visits):
  This model shows how increasing the number of Community Health Workers (CHWs) per population can reduce unnecessary visits to the emergency department. For example, adding one full-time CHW per 10,000 patients is associated with about three fewer emergency visits per 1,000 people. The relationship is direct and predictable.
• Model B (Access → Equity):
  This model focuses on improving access to care and how that narrows the equity gap. It has two versions:
  
  • One shows how each additional appointment slot per 1,000 patients reduces the “access gap” (difference in care between more and less advantaged groups).
  
  • The other version shows how many percentage points of that gap are closed when more slots are added beyond a set starting point.
  In both cases, adding access leads to measurable equity improvements.
• Model C (Coordination → Readmissions):
  This model links better care coordination to fewer hospital readmissions within 30 days. As care becomes more coordinated—measured using a 0–10 index—readmission rates decrease. For example, a one-point improvement in the coordination score typically results in 1.25 fewer readmissions per 100 discharges.

These models reflect real-world evidence. CHWs help by reducing barriers and building trust. Extended access helps patients whose schedules are hard to accommodate, such as those working irregular hours. Strong coordination ensures patients receive follow-up and don’t fall through the cracks after discharge. The math behind all this remains intentionally simple—straight lines—so teams can understand, apply, and refine them regularly without complex analytics.

6.2 Cross-model synthesis: how to use the lines together

1. Start with access for the biggest impact.
   If you’re deciding where to begin, focus first on improving access (Model B). This helps fix the initial barrier many people face when trying to get care—what the report calls “front-door” inequity. Once access is expanded, invest in Community Health Workers (Model A) to ensure the new access leads to ongoing support, especially for those with greater needs. Finally, improve care coordination (Model C) to reduce hospital readmissions among patients with multiple conditions. Each step strengthens the next, making progress more reliable.
2. Keep your eyes on the most deprived areas.
   Use the most disadvantaged group—referred to as Quintile 5 (Q5)—as your main reference point. Every month, check how Q5 is doing on each model’s chart. Even if overall results look positive, if Q5 isn’t improving, it’s a sign to shift your efforts toward them, even if that means giving up some gains elsewhere.
3. Track changes clearly—don’t overfit the data.
   When something changes—like how you define a same-day appointment—don’t try to force the numbers to fit past patterns. Instead, update the version of the model, recalculate your line using two months of the new data, and continue. Keep it simple: always stick to a straight-line format.

6.3.1 Model A — Community Health Workers (CHWs)

How to use the model:
For every half of a full-time CHW added per 10,000 patients, you can expect about 1.5 fewer preventable emergency department (ED) visits per 1,000 people. Doubling that—adding one full CHW—leads to a reduction of roughly three ED visits per 1,000.

Steps to put this into practice:

• Assign CHWs to specific groups.
  Link CHWs to clearly defined panels of patients from the most disadvantaged group (Q5), and publish the number of people each one supports. Make sure caseloads are small enough to allow first contact within 72 hours of a referral.
• Place CHWs near clinical teams.
  Physically co-locate CHWs with the clinical staff so referrals can happen face-to-face or quickly via shared digital task lists.
• Create a flexible “barrier budget.”
  Provide small, trackable funds for practical things like transportation, phone access, or filling out forms—whatever helps remove immediate obstacles for patients. Keep a log of what’s spent, by patient panel.

What to track each month:

• CHW full-time equivalents (FTEs) per 10,000 patients (overall and for Q5 only)
• Percentage of referrals contacted within 72 hours and the average time to first contact
• Preventable ED visits per 1,000 (overall and for Q5), compared to expected values
• Percentage of CHW time spent out in the community

If things aren’t going as expected:

• If ED visits are higher than expected:
  Review who’s being referred—focus more tightly on patients who use EDs often or have uncontrolled long-term conditions. Also, reduce how widely CHWs are spread geographically and make sure first contact is happening on time.
• If ED visits are lower than expected (better performance):
  Identify what’s working well—like pharmacy partnerships or transport support—and make sure these actions are written into standard procedures so they’re consistently applied.

6.3.2 Model B — Same-day/Extended Access for Equity

How to use the model:
Each additional appointment slot per 1,000 patients—beyond a baseline of four—can help close the equity gap in access by about 1.17 percentage points. Depending on how you want to report progress for the quarter, you can either focus on:

• AccessGap: Measuring how much the difference between groups is shrinking
• GapClosed: Measuring how much of that difference has already been closed (positive numbers only)

Steps to put this into practice:

• Protect appointment slots for equity.
  Set aside evening and weekend appointments specifically for patients from Q5 areas. Make sure they can book by phone and that interpreter support is available—don’t rely on digital-only systems.
• Place care where it’s needed.
  Ensure that added sessions are held in locations accessible to Q5 communities—ideally no more than 25 minutes away via public transportation.
• Reach out directly.
  Use phone calls or text messages in multiple languages to inform people about available slots. Partner with local schools, shelters, and community organizations to help spread the word.

What to track each month:

• Number of delivered slots per 1,000 patients (total, and the percentage offered after 6 p.m., on weekends, or with interpreter support)
• Access rates across socioeconomic groups (quintiles), and whether the gap is narrowing as expected
• No-show rates and how long patients have to wait for the next available slot—both broken down by quintile

If things aren’t going as expected:

• Don’t just add more slots.
  If performance is off track, first check whether the current mix of appointments (in terms of timing, location, and interpreter availability) is meeting the needs of Q5 patients. Make sure these communities were actually offered the new capacity—not just in theory, but in practice.

6.3.3 Model C — Care Coordination for Multimorbidity

How to use the model:
Each one-point improvement on a 0–10 coordination scale is linked to about 1.25 fewer hospital readmissions per 100 discharges. The more coordinated the care, the fewer patients return to the hospital unnecessarily.

Steps to put this into practice:

• Complete the care plan before patients leave.
  Make sure every patient discharged has a clear, shared care plan. This should include contact names and a confirmed list of medications. Track and publish how many patients receive this weekly.
• Follow up within 72 hours.
  Use a standardized follow-up call process and track it with a dashboard. Aim for at least 80% of patients getting a follow-up call within three days of leaving the hospital.
• Involve pharmacists and share data.
  Have pharmacists review discharges for high-risk patients. Make sure information can be shared (and updated) between hospital and community providers so nothing falls through the cracks.

What to track each month:

• Your coordination score and its individual components (like care plan coverage, warm handoffs, 72-hour follow-up calls, live data sharing, and pharmacy involvement)
• Readmission rates per 100 discharges, especially for Q5, and compare them to what the model predicts
• A record of patient engagement—how many were reached and how long it took to contact them after discharge

If things aren’t going as expected:

• If readmissions are higher than expected:
  This often means follow-up and engagement are slipping. Focus first on making sure patients are being contacted and that care plans are fully completed. Don’t rush to adjust the math until these core actions are back on track.

6.4 Equity, Ethics, and Community Accountability

• Break down the data by group.
  Always report emergency visits, access to care, and readmission rates by levels of deprivation (such as socioeconomic quintiles). Where possible, include additional breakdowns—like by ethnicity, language, or disability status—to make sure no group is overlooked.
• Be clear about definitions.
  Clearly define key terms like “CHW full-time equivalent,” “delivered appointment slot,” and “readmission.” Include these definitions on your reporting slides. Being transparent helps avoid misunderstandings and prevents teams from unintentionally or intentionally bending the rules.
• Keep the community involved.
  Share simple monthly updates with local partners—such as faith groups, shelters, and advocacy organizations. Include a chart with the model’s progress, along with a plain-language summary that explains what changed, who benefited, and what’s coming next.

6.5 Financial Framing — Keeping the Math Simple and Clear

Each model provides a straightforward way to estimate financial impact and make the case for investment. Here’s how to think about the numbers behind each one:

• Model A (CHWs):
  If you add the equivalent of 6 full-time Community Health Workers (1.2 per 10,000 people in a 50,000-patient population), the model estimates around 180 fewer preventable emergency visits per year. To calculate potential savings, multiply those avoided visits by the average cost of an emergency visit. From that amount, subtract CHW salaries and factor in the broader value of helping people rely less on urgent care.
• Model B (Access):
  To reduce the access gap by 10 percentage points, you’ll need to provide around 8.5 more appointment slots per 1,000 patients—about 425 extra slots per month for a population of 50,000. Your monthly cost is simply those slots multiplied by the cost per slot. There are additional benefits too—fewer emergency visits for minor issues and better management of chronic conditions.
• Model C (Coordination):
  Improving the coordination score from 6.0 to 7.5 leads to about 85 fewer readmissions per year in a setting with 4,000 annual discharges. Estimate the savings by multiplying those avoided readmissions by their typical cost. Don’t forget to include any penalties avoided or incentives earned for quality improvements. Your investment would likely include staff, pharmacist time, and the necessary IT systems.

Key principle:
Base budget requests on these clear, straight-line models. Keep things transparent by adding a simple margin of uncertainty (e.g., plus or minus 10%) and commit to revisiting the figures every quarter.

6.6 Operating Rhythm and Governance

Key tools and documentation:

• Model Cards:
  Create a one-page summary for each model (A, B, C). Include the variables used, the two months of data that defined the model, the slope and intercept, the rule for decision-making, who owns it, when it will be reviewed, and the current version.
• Intervention Log:
  Maintain a running list of key changes—like CHW hires, how many appointment slots were added (and what kind), or steps taken to improve coordination. Everything should be dated.
• Data Dictionary:
  Standardize the definitions used for the quarter to avoid confusion or shifting benchmarks.

Workflow cadence:

• Monthly:
  Spend 30 minutes per model reviewing the latest data. Plot the new result on the chart, compare it to the line, and—if it’s off—write a short explanation and decide what practical change might fix the issue (but don’t alter the model’s math).
• Quarterly:
  Recalculate the slope and intercept based on two solid months of data. Update the model card with the new version while keeping the same straight-line format (y = mx + c).
• Annually:
  Conduct an independent audit to review definitions, financial calculations, and how fairly outcomes were distributed.

Quality checks and safeguards:

• Double-check calculations:
  Two analysts should independently calculate the slope and intercept; the results must match.
• Stick to valid ranges:
  Don’t apply the model beyond the range of data it was built on. If your real-world numbers move outside the original range, create a new “Line-High” using the same straight-line format rather than changing to a curve.

6.7 12-Month Implementation Roadmap

The roadmap outlines a step-by-step rollout over a year:

• Months 0–1: Laying the groundwork
  Finalize definitions, release the first version of each model card (A, B, C), train leads on how to apply the model formulas, and build equity-focused dashboards comparing the most and least deprived groups.
• Months 2–4: Start the first cycle
  Deploy real interventions:
  • Add CHWs to Q5 communities.
  • Expand appointment slots after-hours and with interpreter support.
  • Improve follow-up and medication review processes.
    Log all changes and show early results in a simple, joint display.
• Months 5–7: Calibrate
  If the actual results drift more than 10% from expected without a clear reason, update the model with better data. Focus on refining what you do—not tweaking the math.
• Months 8–10: Scale carefully
  Extend changes to new clinics or wards serving Q5 groups, but track separately in case outcomes differ. Don’t expand coordination efforts until engagement is consistently strong.
• Months 11–12: Lock it in
  Run an independent review to verify definitions, data, and calculations. Set new goals for Year 2—still using the same straight-line model, just with refreshed slopes.

6.8 Risks, Limits, and How to Handle Them

• Ceiling effects:
  After a certain point (like 12–13 appointment slots per 1,000), returns start to level off. Use simple segmented lines instead of switching to complex curves.
• Regression to the mean:
  Don’t set your model based on months with unusual spikes or dips. Use typical or averaged months for better reliability.
• Definition drift:
  Quietly changing what counts as a slot or a readmission undermines trust. Use a shared data dictionary and update the model version when definitions change.
• Attribution noise:
  External factors like new urgent-care centers can affect outcomes. Use your intervention log to explain what’s happening. Stick with the line and update as scheduled.
• Equity blind spots:
  Overall progress can hide a lack of improvement for Q5 groups. Always include a Q5-specific data point and manage explicitly for their outcomes.

6.9 What “Good” Looks Like in Steady State

• People can explain the math quickly:
  “We added 1 CHW per 10,000 and expect 3 fewer ED visits per 1,000. We’ll check next month’s result.”
• The visuals are clean and simple:
  Just one line, a few dots, and a rule underneath. No clutter.
• Equity updates become routine:
  “We closed the access gap by 6 points; most of the added appointments went to Q5 communities, and nearly half included interpreter support.”
• Clear version control:
  Model Cards clearly show when and why updates were made—never edited quietly or retrofitted.

6.10 Final Recommendations

1. Use the three straight lines as decision-making tools, not just analytics. Start every review with them.
2. Protect the integrity of definitions and versions. If something changes, recalculate and label it.
3. Focus on Q5. Equity work means centering the most disadvantaged group in your strategy.
4. Adjust delivery—not the math. If the model’s off, fix how the intervention is being implemented.
5. Update quarterly—without panic. Recalculate slopes when planned, not reactively.

6.11 Conclusion

When done right, integrated primary care can truly advance equity—if leaders combine strong, real-world strategies with clear, practical math. The three models presented here are easy to understand, powerful enough to guide funding and staffing, and transparent enough for communities to hold systems accountable.

Each model starts with just two data points to set a line. One sentence gives you a rule to follow. Each month, you plot a new point to check your progress. Most importantly, you break it down by deprivation level to ensure those who need the most help are benefiting.

The simplicity is the strength. Keep the models linear. Keep the controls grounded. And progress will follow.

References

Albertson, E.M., Chuang, E., O’Masta, B., Miake-Lye, I.M., Haley, L.A. and Pourat, N. (2022) ‘Systematic review of care coordination interventions linking health and social services for high-utilizing patient populations’, Population Health Management, 25(1), 73–85.

Carter, J., Hassan, S., Walton, A., Yu, L., Donelan, K. and Thorndike, A.N. (2021) ‘Effect of community health workers on 30-day hospital readmissions in an accountable care organisation population: a randomised clinical trial’, JAMA Network Open, 4(5), e2110936.

Eissa, A., Rowe, R., Pinto, A.D., Hassen, N., Nadeem, A. and Rodríguez, J.E. (2022) ‘Implementing high-quality primary care through a health equity lens’, Annals of Family Medicine, 20(2), 164–170.

Elliott, M., Cooper, K., Dale, J. and Hoyle, L. (2022) ‘Exploring how and why social prescribing evaluations work: a realist review’, BMJ Open, 12(4), e057009.

Finkelstein, A., Zhou, A., Doyle, J.J., Taubman, S.L., Grazier, K., et al. (2024) ‘The Camden Coalition care management program: investigating explanations for null results from a randomised evaluation’, Health Affairs, 43(12), 1979–1987.

Sonke, J., Manhas, N., Belden, C.M., Harding, J., Crone-Price, R., et al. (2023) ‘Social prescribing outcomes: a mapping review of the evidence from 13 countries to identify key common outcomes’, Frontiers in Medicine, 10, 1266429.

Tierney, S., Wong, G., Scott, H., O’Donnell, C.A., Madigan, S., et al. (2025) Implementing link workers in primary care: synopsis of a realist evaluation. London: NIHR (National Institute for Health and Care Research).

Whittaker, W., Anselmi, L., Kristensen, S.R., Lau, Y.S., Bailey, S., et al. (2019) ‘Investigation of the demand for a 7-day (extended access) primary care service: observational study of patient characteristics and uptake’, BMJ Open, 9(9), e028138.

Wilding, A., Agboraw, E., Sutton, M., Munford, L., Kontopantelis, E., et al. (2025) ‘Impact of the rollout of the national social prescribing link worker programme on population outcomes: evidence from a repeated cross-sectional survey’, British Journal of General Practice, advance online publication.

Yang, Q., Gupta, A., Chang, T., Neumann, J. and Shashaani, N. (2023) ‘Hospital readmissions by variation in engagement in the Camden Coalition’s care management program: secondary analysis of a randomised clinical trial’, JAMA Network Open, 6(8), e2329197.

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