Outcome-Driven Regression: Choosing the Right Model Based on Y in Clinical Research

Why start with Y?

Because the distribution and scale of the outcome (not the exposure) dictate:

1. The likelihood function behind the model.

2. Which effect measure is naturally produced (mean diff, OR, RR, HR, IRR …).

3. The mathematical assumptions we must check to keep inference valid.

Below is a tiered roadmap, moving from the simplest outcomes to the most complex, with compact Stata code, interpretation cues, and the key diagnostic you should run every single time.

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1. Continuous Outcomes  (e.g., blood pressure, length‑of‑stay)

Model	Default effect	Core Stata syntax
Gaussian (linear) regression	β = mean difference	regress Y X1 X2
Robust / Huber‑White covariance	Same β, wider CI	regress Y X1 X2, vce(robust)
Linear mixed‑effects (cluster / repeated)	subject‑specific β	`mixed Y X1 X2

Assumptions & Checks

1. Linearity – scatter + lowess or twoway (scatter Y X1) (lfit Y X1).

2. Homoskedasticity – rvfplot, look for “megaphone”.

3. Normal residuals – qnorm r, name(res) after predict r, resid.

4. Independence – if violated, use cluster() SEs, GEE, or mixed.

Interpretation nugget lincom _b[X1]*10  immediately gives the change in Y per 10‑unit  increase in X1 – far more clinically intuitive than the raw coefficient.

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2. Binary Outcomes  (e.g., stroke yes/no)

Model (choose by estimand)	Effect	Stata
Logistic regression	Odds Ratio (OR)	logistic Y i.exposure controls
Modified Poisson (log‑binomial via Poisson+robust)	Risk Ratio (RR)	glm Y i.exposure, fam(poisson) link(log) vce(robust) eform
Linear probability model	Risk Difference (RD)	glm Y i.exposure, fam(bin) link(id) vce(robust)

Assumptions

• Correct link (logit/log).

• No complete separation – watch for “note: outcome = exposure predicts success perfectly”; if seen, use firthlogit.

• Independence; if matched, switch to clogit.

• Rare outcome? OR ≈ RR. If common (>10 %), prefer RR/RD models.

Post‑estimation essentials

estat gof, group(10)     // Hosmer‑Lemeshow calibration
lroc                    // Discrimination (AUC)

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3. Count Outcomes  (Events without person‑time)

Model	Effect	When to choose
Poisson	Incidence Rate Ratio (IRR)	Variance ≈ mean
Negative Binomial	IRR	Over‑dispersion (α > 0)

poisson events i.treatment, irr
estat gof           // if Pearson χ² / df >> 1 → over‑dispersed
nbreg events i.treatment, irr

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4. Rates  (Events per person‑time)

Just add the exposure (offset) term:

gen log_pt = ln(pyrs)
poisson events i.treatment, offset(log_pt) irr vce(robust)

Key assumption – correct person‑time; mismeasured denominators will bias the IRR, whatever model you run.

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5. Time‑to‑Event Outcomes

Model	Effect	Checks
Cox proportional hazards	Hazard Ratio (HR)	PH assumption (estat phtest, stphplot)
Flexible parametric (stpm2)	Time‑varying HR, RMST	Use when PH fails
Fine & Gray competing‑risk	Sub‑distribution HR	For competing events

Bare‑bones Cox workflow

stset time, fail(death==1)
stcox i.exposure confounders, vce(robust)
estat phtest
stphplot, by(exposure)

If PH is violated for exposure:

stpm2 i.exposure, df(4) scale(hazard) tvc(exposure) dftvc(2)

Plot adjusted survival: stcurve, survival at1(exposure=0) at2(exposure=1)

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6. Ordered Categorical Outcomes  (e.g., mild / mod / severe)

Model	Assumption	Test
Ordinal (ologit)	Proportional odds (PO)	oparallel
Generalised ordered (gologit2)	—	Works when PO fails

ologit stage i.exposure otherVars, or
oparallel

Fail → ssc install gologit2 →

gologit2 stage i.exposure, autofit or

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7. Unordered Categorical Outcomes  (>2 classes, no natural order)

mlogit outcome i.exposure covs, baseoutcome(0) rrr

Interpret each R as the risk relative to the base category.

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8. Repeated Measures / Clusters

Population‑averaged (GEE)

xtgee Y i.exposure time, i(id) corr(exchangeable) ///
      family(gaussian) link(identity) vce(robust)

Subject‑specific (Mixed)

mixed Y i.exposure##c.time || id: time, cov(un)

Choose GEE when you care about the average treatment effect; mixed when you need individual trajectories.

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9. Putting It All Together – Decision Flow

1. Identify Y (scale, distribution, censoring, clustering).

2. Pick the default model from the table above.

3. Run diagnostics listed for that model.

4. If an assumption breaks, upgrade (robust SE, NB, stpm2, gologit2, mixed).

5. Report effect + 95 % CI + assumption checks so readers trust your estimates.

Copy‑and‑Save “Assumption Check‑Block” Template

/* 1. Fit chosen model */
<model command here>

/* 2. Linearity & LOESS */
twoway (scatter Y X1) (lowess Y X1)

/* 3. Influential points */
predict cooksd, cooksd
graph box cooksd

/* 4. Residual diagnostics */
predict resid, residuals
hist resid, normal
rvfplot

/* 5. Robustness */
<same model>, vce(robust)

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Final Take‑aways

• Outcome first, always – let Y tell you the family/link.

• Think of assumptions as contracts; violate them and the effect you quote can’t be trusted.

• When in doubt, add a robust option or move to a semiparametric / non‑parametric alternative.

• Document every decision (model choice, diagnostics, fixes) – it’s the best prophylaxis against reviewer infection.

Happy modelling — and may your residuals forever be well‑behaved!