Abstract
Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.
Highlights
Zero-inflated distributions—a mixture of a point distribution and some other non-zero distribution (s)—are common in biomedical studies
In addition to excess zeros, analysis is made more difficult by the distribution of the non-zero data, which is most likely asymmetric or multimodal
The ideal statistical test for comparing zero-inflated distributions would simultaneously test for equality of both 1) the proportion of zero values and 2) the non-zero distribution, and do so with little to no assumptions regarding the data
Summary
Zero-inflated distributions—a mixture of a point distribution and some other non-zero distribution (s)—are common in biomedical studies. The ideal statistical test for comparing zero-inflated distributions would simultaneously test for equality of both 1) the proportion of zero values and 2) the non-zero distribution, and do so with little to no assumptions regarding the data. Lachenbruch [6] [7] proposed two-part models to test for equality of distributions with respect to probabilities of zeros and location parameters in continuous distributions for the non-zero data. Because excess zeros are typical of count data, several tests for zero-inflated Poisson distributions have been developed using likelihood ratio methods [8] [9] and exact tests [10], but these assume the data follow a Poisson distribution, a tenet that may be problematic.
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