Using Cox regression to develop linear rank tests with zero-inflated clustered data.

Zero-inflated data arise in many fields of study. When comparing zero-inflated data between two groups with independent subjects, a two degree-of-freedom test has been developed, which is the sum of a 1 degree-of-freedom Pearson chi-square test for the 2×2 table of group vs dichotomized outcome (0,> 0) and a 1 degree-of-freedom Wilcoxon rank-sum test for the values of the outcome > 0. Here, we extend this 2 degree-of-freedom test to clustered data settings. We first propose using an estimating equations score statistic from a time-varying weighted Cox regression model under naive independence, with a robust sandwich variance estimator to account for clustering. Since our proposed test statistics can be put in the framework of a Cox model, to gain efficiency over naive independence, we apply a generalized estimating equations (GEE) Cox model with a non-independence 'working correlation' between observations in a cluster. The proposed methods are applied to a General Social Survey study of days with mental health problems in a month, in which 52.3% of subjects report they have no days with problems, a zero-inflated outcome. A simulation study is used to compare our proposed test statistics to previously proposed zero-inflated test statistics.