Adjusted Score Tests of Homogeneity for Poisson Processes

Abstract

Tests of homogeneity are being increasingly used for the analysis of event time data, but relatively little attention has been paid to their distributional properties in settings with small to moderate sample sizes. Here we consider tests of homogeneity for recurrent event data in which the null model is a Poisson process and the alternative is a mixed Poisson process. We examine score and adjusted score statistics in the context of parametric and semiparametric regression models, where the adjustments correct for the bias induced by substituting the maximum likelihood estimates of the parameters into the test statistic. We report the results of simulation studies suggesting that the adjusted score statistics are superior in terms of size and power. We also find that the adjusted score test in the semiparametric regression model does not perform particularly well in small samples, but the adjusted score test based on a piecewise exponential model has satisfactory performance. The latter thus provides an attractive alternative in terms of robustness and frequency properties, and we recommend using this test statistic for datasets of small to moderate size. We illustrate and contrast the methods by application to a clinical trial.