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

Stuart R. Lipsitz, Garrett M. Fitzmaurice, Debajyoti Sinha, Alexander P. Cole, Christian P. Meyer and Quoc‐Dien Trinh

Journal of the Royal Statistical Society Series C, 2020, vol. 69, issue 2, 393-411

Abstract: 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.

Date: 2020
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https://doi.org/10.1111/rssc.12396

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