A new two-part test based on density ratio model for zero-inflated continuous distributions

Abstract

In this paper, we consider testing the hypothesis concerning the means of two independent semicontinuous distributions whose observations are zero-inflated, characterized by a sizable number of zeros and positive observations from a continuous distribution. The continuous parts of the two semicontinuous distributions are assumed to follow a density ratio model. A new two-part test is developed for this kind of data. The proposed test takes the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution. The test is proved to follow a χ2 distribution with two degrees of freedom. Simulation studies show that the proposed test controls the type I error rates at the desired level, and is competitive to, and most of the time more powerful than two popular tests. A real data example from a dietary intervention study is used to illustrate the usefulness of the proposed test.