Regression Discontinuity Design: A Practical Guide for Clinical Researchers

Regression Discontinuity Design (RDD) is the closest thing observational research has to a randomized experiment — and it's hiding in every threshold-based clinical decision you've ever made. Age cutoffs for screening, lab values triggering treatment, BMI thresholds for surgery eligibility — anywhere a number crosses a line and something changes, RDD can extract causal evidence.

What Is Regression Discontinuity Design?

RDD exploits the fact that units (patients, hospitals, regions) just above and just below a threshold are nearly identical — except that one group gets treated and the other doesn't. The treatment effect is estimated from the jump in the outcome at the cutoff.

The logic is simple: if a patient with a hemoglobin A1c of 6.49% is essentially the same as a patient at 6.51%, but one gets diagnosed with diabetes and the other doesn't, any difference in downstream outcomes near that cutoff is causal.

Sharp vs. Fuzzy RDD

Sharp RDD

Treatment assignment is deterministic at the cutoff. Everyone above gets treated; everyone below doesn't. No exceptions.

• Medicare eligibility at age 65 (everyone qualifies at the birthday)
• Scholarship awards based on a test score cutoff
• Hospital performance penalties based on readmission rate thresholds

Fuzzy RDD

The cutoff increases the probability of treatment but doesn't guarantee it. Some people above the cutoff don't get treated; some below do. Think of it as an instrumental variable where the instrument is "being above the cutoff."

• Clinical guidelines recommending statins above a cholesterol threshold (doctors don't always follow)
• Recommended screening ages (some patients get screened early, some late)
• BMI thresholds for bariatric surgery (not every eligible patient opts in)

When to Use It

RDD requires three conditions:

1. A continuous running variable — age, test score, lab value, admission date, distance. It must be measured before treatment and not manipulable by the individual.
2. A known cutoff — a clear threshold where treatment probability changes. The cutoff must be exogenous (not determined by the outcome).
3. Sufficient density near the cutoff — you need enough observations on both sides. If observations are sparse near the threshold, your estimates will be noisy.

The Critical Assumption: No Manipulation

The validity of RDD depends on one thing: units cannot precisely manipulate their running variable to land on their preferred side of the cutoff. If patients can game their lab values, if hospitals can tweak their reported metrics, if students can choose their test date strategically — your design is compromised.

"Precise manipulation" is the problem. Imprecise influence is fine. A student can study harder (imprecise — they don't control their exact score), but a hospital that rounds down readmission rates to avoid a penalty (precise) violates the assumption.

Bandwidth Selection: The Make-or-Break Choice

RDD estimates are local — they use data near the cutoff. The bandwidth determines how "near" is near. This is the single most consequential methodological choice in any RDD analysis.

The Bias-Variance Tradeoff

• Too narrow: Low bias (you're comparing truly similar units) but high variance (few observations → wide confidence intervals)
• Too wide: Low variance (lots of data) but high bias (units far from the cutoff aren't comparable)

Data-Driven Bandwidth Selection

Don't pick bandwidth by eye. Use formal methods:

• Imbens-Kalyanaraman (IK) optimal bandwidth — minimizes mean squared error
• Calonico, Cattaneo & Titiunik (CCT) robust bandwidth — accounts for bias in the bandwidth selection itself. This is the current standard.
• Cross-validation — less common but useful for irregular data

Estimation: Local Polynomial Regression

The standard approach fits separate polynomial regressions on each side of the cutoff within the bandwidth. The treatment effect is the gap between the two fitted lines at the cutoff.

Polynomial Order

• Linear (order 1): Default and recommended. Simple, stable, interpretable.
• Quadratic (order 2): Can capture curvature but is more sensitive to outliers. Use only with a wider bandwidth.
• Higher orders (3+): Almost never justified. They create wild extrapolation near the boundary.

Kernel Weighting

Observations closer to the cutoff get more weight. Common kernels:

• Triangular: Default. Zero weight at the bandwidth edge. Best for point estimation at the cutoff.
• Uniform: Equal weight to all observations in the bandwidth. Simpler but slightly less efficient.
• Epanechnikov: Middle ground. Results usually similar to triangular.

Common Failure Modes

1. Running Variable Manipulation

The #1 threat to RDD validity. Always test for it. In clinical settings, look for:

• Providers rounding lab values (HbA1c of exactly 6.5% suspiciously common?)
• Patients timing procedures to meet age cutoffs
• Hospitals adjusting reported metrics near penalty thresholds

Fix: Run the McCrary density test. Plot the histogram of the running variable. If bunching is evident, RDD may not be valid for your setting.

2. Discontinuities in Covariates

If other characteristics jump at the cutoff, the treatment isn't the only thing changing. Check that baseline covariates are smooth through the cutoff.

Fix: Run balance tests — estimate the "effect" of the cutoff on pre-treatment covariates. They should show no discontinuity. Plot them.

3. Bandwidth Sensitivity

If your result only appears at one specific bandwidth and disappears at others, it's probably noise, not signal.

Fix: Report results at half, main, and double bandwidths. Plot the effect as a continuous function of bandwidth choice.

4. Too Few Observations Near the Cutoff

RDD is inherently a local estimator. If your sample is small or the running variable is discrete (e.g., age in years rather than days), you may not have enough observations for meaningful inference.

Fix: Report effective sample sizes within the bandwidth. For discrete running variables, consider the Kolesár & Rothe (2018) honest confidence intervals.

5. Extrapolation Beyond the Cutoff

RDD identifies the effect at the cutoff only. It does not tell you what happens far from the cutoff. A drug that works at the threshold dose tells you nothing about double the dose.

This is a feature, not a bug. Be honest about external validity — RDD trades generalizability for internal validity.

Clinical Applications

RDD is everywhere in clinical research — most researchers just don't recognize it. Here are some prominent examples:

Modern Extensions

Geographic RDD

When treatment assignment is determined by location (e.g., different health policies on either side of a state border), geographic RDD compares outcomes for people living just on either side of the boundary. Requires careful handling of distance as the running variable.

Regression Kink Design (RKD)

Instead of a jump in treatment at the cutoff, RKD exploits a change in slope. Example: a tax benefit that increases at a different rate above an income threshold. The treatment intensity changes, not treatment itself.

Multi-Cutoff RDD

When the same policy has multiple thresholds (e.g., different insurance subsidy levels at different income brackets), you can combine estimates across cutoffs for a more comprehensive picture. See Cattaneo et al. (2016) for pooling strategies.

RDD with Covariates

Including covariates in RDD is not required for identification (the design handles confounding), but it can improve precision. Use them for efficiency, not for bias correction. If your result changes meaningfully after adding covariates, question the design, not the covariates.

Software

Reporting Checklist

RDD vs. Other Methods

Key References

• Thistlethwaite, D.L. & Campbell, D.T. (1960). Regression-discontinuity analysis: An alternative to the ex post facto experiment. Journal of Educational Psychology. — The original RDD paper.
• Imbens, G.W. & Lemieux, T. (2008). Regression discontinuity designs: A guide to practice. Journal of Econometrics. — The definitive practical guide.
• Lee, D.S. & Lemieux, T. (2010). Regression Discontinuity Designs in Economics. Journal of Economic Literature. — Comprehensive review.
• Cattaneo, M.D., Idrobo, N. & Titiunik, R. (2020). A Practical Introduction to Regression Discontinuity Designs. Cambridge Elements. — Modern textbook treatment.
• Calonico, S., Cattaneo, M.D. & Titiunik, R. (2014). Robust nonparametric confidence intervals for regression-discontinuity designs. Econometrica. — The CCT bandwidth and inference method.
• McCrary, J. (2008). Manipulation of the running variable in the regression discontinuity design. Journal of Econometrics. — The original density test.
• Gelman, A. & Imbens, G. (2019). Why high-order polynomials should not be used in regression discontinuity designs. Journal of Business & Economic Statistics. — The "don't use cubics" paper.
• Card, D., Dobkin, C. & Maestas, N. (2008). The impact of nearly universal insurance coverage on health care utilization. American Economic Review. — Classic clinical RDD.