Performance of quantile regression methods with discrete outcomes: A simulation study with applications to environmental epidemiology.

BACKGROUND

Quantile regression helps identify how associations vary across the outcome variable's distribution. Using simulations and data from the Maternal-Infant Research on Environmental Chemicals study, we showed that frequentist quantile regression can produce implausible results where the point estimates are integers or rational numbers and the outcome variable is discrete, which is common in health research. Applying "dithering" (also known as jittering) or using Bayesian quantile regression can prevent such implausible results, but the optimal strategy is unclear.

METHODS

We conducted simulations with discrete outcomes to compare the bias and variability of point estimates of undithered frequentist, dithered frequentist, and Bayesian quantile regression. We also compared the coverage and interval-width variance of these methods' confidence or credible intervals.

RESULTS

The dithered frequentist method generated point estimates that were less variable than the undithered frequentist method. The Bayesian method had the least variable point estimates, but when the sample size was low (n = 100), it exhibited bias when modeling a binary or discrete covariate. The dithered frequentist method with xy-bootstrapped confidence intervals had nominal coverage and produced intervals with relatively consistent widths. The Bayesian method with adjusted intervals also had nominal coverage, but more variable interval widths. The Bayesian method with unadjusted intervals had poor coverage.

CONCLUSION

In our simulations with discrete outcomes, dithered frequentist quantile regression (particularly with xy-bootstrapped confidence intervals) had the best overall performance. The Bayesian method with adjusted intervals is an acceptable strategy, although it was biased under certain scenarios and generated credible intervals with more variable widths.