STATISTICAL INFERENCE IN QUANTILE REGRESSION FOR ZERO-INFLATED OUTCOMES

Abstract

An extension of quantile regression is proposed to model zero-inflated outcomes, which have become increasingly common in biomedical studies. The method is flexible enough to depict complex and nonlinear associations between the covariates and the quantiles of the outcome. We establish the theoretical properties of the estimated quantiles, and develop inference tools to assess the quantile effects. Extensive simulation studies indicate that the novel method generally outperforms existing zero-inflated approaches and the direct quantile regression in terms of the estimation and inference of the heterogeneous effect of the covariates. The approach is applied to data from the Northern Manhattan Study to identify risk factors for carotid atherosclerosis, measured by the ultrasound carotid plaque burden.

Keywords: Constrained post-estimation smoothing; Nonnormal asymptotic distribution; Quantile regression; Zero-inflated outcomes.

Figure 1:

Plots of carotid plaque data. (a) Frequency histograms of plaque area (plaqarea, left) and echodensity (plaqden, right) in carotid plaque data. (b) Empirical quantiles of plaque echodensity (plaqden) against systolic bloodpressure. The relationship is nonlinear because the proportion of zeros changes with systolic blood pressure.

Figure 2:

Piecewise estimator of the conditional quantile function Q_Y (τ|x).

Figure 3:

Estimated AQEs of selected covariates by the proposed method (without smoothing) on all quantiles of echodensity, which are presented as the differences between the dashed and solid lines. Significant AQEs are highlighted by the shaded area.