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 2 degree‐of‐freedom test has been developed, which is the sum of a 1 degree‐of‐freedom Pearson χ2‐test for the 2×2 table of group versus 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 degrees‐of‐freedom test to clustered data settings. We first propose the use of 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 Cox model with a non‐independence ‘working correlation’ between observations in a cluster. The methods proposed are applied to a General Social Survey study of days with mental health problems in a month, in which 52.3% of subjects report that they have no days with problems: a zero‐inflated outcome. A simulation study is used to compare our proposed test statistics with previously proposed zero‐inflated test statistics.