Does Faster Follow-Up Actually Prevent Readmissions — Or Just Look Like It Does?

Background and the Confounding Problem

The CMS Hospital Readmissions Reduction Program penalizes hospitals with excess 30-day readmissions across six conditions — AMI, heart failure, pneumonia, COPD, CABG, and hip/knee arthroplasty — by reducing all Medicare inpatient payments, not just readmission-related claims, by up to 3%. At Riverside Regional, an estimated 73.5% of FY2023 discharges carried an HRRP-penalized primary diagnosis, and readmission rates for heart failure (18.0%) and COPD (16.2%) sit close to the penalty threshold. The system's 7-day follow-up rate of 78.4% also falls below the NCQA HEDIS benchmark of 85%, with substantial variation by payer and neighborhood.

The assignment's core challenge is this: a raw comparison of readmission rates between patients who did and didn't receive follow-up would be biased, because the two groups differ systematically on more than just follow-up. Patients who miss follow-up are disproportionately Medicaid or uninsured (29.1% and 32.5% miss rates vs. 18.2% for Medicare), live in higher-vulnerability neighborhoods (26.5% miss rate in the highest SVI quartile vs. 17.2% in the lowest), and are more likely to be rural. Every one of these characteristics also independently predicts readmission. A naïve comparison conflates the effect of follow-up with the effect of structural disadvantage — producing an upwardly biased estimate of how protective follow-up actually is.

Three estimators, in order of rigor

• Naïve logistic regression — follow-up as the sole predictor. Establishes the biased baseline.
• Multivariable logistic regression (no weights) — follow-up plus all measured confounders in the outcome model, correcting for observed confounding through covariate adjustment alone.
• IPW doubly-robust estimation — a propensity model for follow-up receipt generates stabilized inverse probability weights, which are then applied to a weighted outcome regression that also includes the full confounder set. The doubly-robust property means the estimate stays consistent if either the propensity or the outcome model is correctly specified. The canonical estimate uses Stata's teffects ipwra, which integrates both steps with correct standard-error propagation.

All models use heteroskedasticity-robust standard errors. The estimand throughout is the Average Treatment Effect: the expected change in 30-day readmission probability if the entire population received follow-up versus if none did.

Sample Characteristics

All variables were complete with no random missingness; the structural missingness in same-diagnosis readmission (observed only among the 368 readmitted patients) is by design.

p-values from two-sample t-tests for continuous variables. SVI = Social Vulnerability Index.

Propensity Score Model and Diagnostics

The propensity model regressed 7-day follow-up receipt on all measured covariates: age, sex, race/ethnicity, payer, primary diagnosis, Elixhauser comorbidity score, length of stay, discharge disposition, hospital unit, rural ZIP flag, and SVI quartile (log pseudolikelihood = −1,255.08; Wald χ²(29) = 95.31, p < 0.001; pseudo-R² = 0.038). Predicted propensity scores ranged from 0.44 to 0.94 (mean 0.784, SD 0.083) — matching the observed follow-up rate.

Only two covariates were significant predictors of follow-up receipt: payer status and SVI quartile. Medicaid (β = −0.565, p < 0.001) and Self-Pay/Uninsured patients (β = −0.768, p < 0.001) had significantly lower odds of follow-up relative to Commercial, and each SVI quartile increase reduced the log-odds of follow-up by 0.202 (p < 0.001). Age was also significant (β = −0.015/year, p < 0.001). Diagnosis, race/ethnicity, discharge disposition, and hospital unit were not — follow-up access in this system runs on insurance coverage and neighborhood disadvantage, not clinical need.

Positivity

Every patient must have a non-zero probability of both receiving and missing follow-up given their covariates. The payer × SVI cross-tabulation confirmed this: all 16 cells showed follow-up rates strictly between 0.596 and 0.863, with no structural zeros or ones — weighting was valid across the full sample.

SMD = (mean treated − mean untreated) / pooled SD; conventional adequate-balance threshold is |SMD| < 0.10. SVI quartile — the largest pre-weighting imbalance at −0.230 — falls to −0.002 after stabilized IPW, confirming the propensity model removed confounding from social vulnerability.

Primary Results

The progression from naïve to adjusted estimates below traces the direction and size of the confounding bias the assignment asks a student to characterize.

OR = odds ratio; AME = average marginal effect in percentage points; DR-ATE = doubly-robust average treatment effect. teffects IPWRA uses a linear-probability outcome model and is the preferred canonical estimate; the IPW doubly-robust logit row uses a logistic outcome model with stabilized pweights.

The near-convergence of the regression-only (−6.7 pp) and IPW-weighted logit (−6.5 pp) estimates is reassuring — both approaches are capturing the same confounding structure. The canonical teffects IPWRA estimate of −7.2 pp is the primary result for reporting, since it correctly propagates estimation uncertainty from both the propensity and outcome models through one integrated procedure.

Full covariate results

Reference categories: Payer = Commercial; Race/Ethnicity = Asian; Primary Diagnosis = AMI; Discharge Disposition = AMA/Other; Hospital Unit = Cardiology. Robust standard errors throughout. Model fit: Wald χ²(30) = 111.82 (p < 0.001); pseudo-R² = 0.054.

Effect Modification by Payer and Social Vulnerability

Stratified IPW-weighted models test whether the follow-up effect differs by subgroup — the question that actually determines where to target intervention resources.

4 observations excluded from the Self-Pay/Uninsured subgroup due to perfect prediction in one race/ethnicity cell. All subgroup models include age, sex, race/ethnicity, primary diagnosis, Elixhauser score, length of stay, discharge disposition, hospital unit, and rural ZIP flag, with stabilized IPW weights applied.

Sensitivity Analysis: Robustness to Unmeasured Confounding

Because this is an observational study, unmeasured confounders — health literacy, informal caregiver support, housing stability, food security, transportation access — cannot be fully captured. The E-value framework (VanderWeele & Ding, 2017) quantifies the minimum association an unmeasured confounder would need with both follow-up receipt and readmission to fully explain away the estimated effect.

Even Medicaid status — the strongest measured confounder in the outcome model, at OR = 2.03 — falls below the E-value threshold of 2.61. Unmeasured confounding of this magnitude can't be ruled out entirely, but the rich covariate set (diagnosis, comorbidity, length of stay, SVI, rural residence, payer, discharge disposition) substantially limits the plausible unmeasured-confounding space. The finding is considered robust under realistic assumptions.

Discussion

The doubly-robust IPW analysis estimates that 7-day post-discharge follow-up reduces 30-day readmission probability by 6.5 to 7.2 percentage points, depending on estimator. This is clinically meaningful, statistically robust, and survives correction for the substantial confounding by payer and social vulnerability that inflates the naïve comparison. It's consistent with the broader literature — systematic reviews of post-discharge follow-up interventions report reductions of 4–8 percentage points — and the E-value analysis suggests the result is unlikely to be fully explained by unmeasured confounding.

The adjustment narrows the effect but doesn't erase it. Follow-up isn't the whole story of why patients get readmitted, but it's a real, addressable piece of the risk — one the system currently delivers unevenly across payer groups and social-vulnerability strata.

Payer and social risk as independent drivers

The two most striking findings aren't about follow-up at all: Medicaid patients carry twice the readmission odds of commercially insured patients after full adjustment including follow-up receipt, and rural patients carry 74% higher odds independent of both follow-up and payer. Neither can be fixed by a scheduling intervention. They reflect the downstream consequences of medication access barriers, food and housing insecurity, and limited rural primary-care capacity. A strategy that focuses on follow-up rates alone will plateau; it needs to be paired with social-needs screening, medication assistance, community health worker navigation, and post-acute care partnerships.

Implications for intervention strategy

The priority segment — Medicaid patients with heart failure or COPD in SVI Q3–Q4 ZIP codes — represents 7.8% of discharges (n = 195) but carries a 21.5% readmission rate and a 33.8% follow-up miss rate. Closing half the follow-up gap in this segment alone, at the adjusted 6.5-point effect size, would prevent an estimated 6–8 readmissions annually, with cost avoidance of roughly $72,000–$96,000 at an average readmission cost of $12,000.

Limitations

• Unmeasured confounding — health literacy, informal caregiver support, housing stability, food security, and transportation access aren't captured; SVI and the rural flag are ZIP-level proxies only.
• Follow-up ascertainment — the 7-day indicator reflects documented outpatient and telehealth visits; informal contacts (e.g., phone triage) of equivalent clinical value may be undercounted.
• Cross-sectional observation — each patient appears once, at their index discharge, limiting analysis of high-utilizer trajectories.
• Subgroup power — the Self-Pay/Uninsured subgroup (n = 160) is underpowered for the fully-adjusted model; its point estimate should be read cautiously.
• Simulated data — generated for instructional purposes using published parameter values from the readmissions literature. Findings should not be cited as evidence from real patient data without independent replication.

Conclusion

Three independent estimation strategies converge in the same direction with overlapping confidence intervals: 7-day post-discharge follow-up reduces 30-day readmission probability by roughly 6.5–7.2 percentage points, after correcting for confounding by payer status and neighborhood social vulnerability. The naïve estimate overstated this benefit by about 2.7 points, and an E-value of 2.61 indicates the finding is robust to plausible unmeasured confounding.

The analysis surfaces a clear hierarchy of readmission risk drivers — payer status, rural residence, comorbidity burden, and social vulnerability — of which follow-up addresses only one strand. The highest-value intervention target is Medicaid patients with HRRP-penalized diagnoses in high-vulnerability ZIP codes: a structured care-navigation program for this segment, paired with social-needs screening and medication access support more broadly, is the most cost-effective path to reducing readmissions, improving HRRP performance, and advancing equity at Riverside Regional.

The greatest benefit shows up exactly where it's hardest to deliver. That inverse relationship between intervention difficulty and intervention payoff is the whole argument for targeted outreach.