Unmasking the Trend Sought by Jonckheere‐Type Tests for Right‐Censored Data

Medical and epidemiological studies often involve groups of subjects associated with increasing levels of exposure to a risk factor. Survival of the groups is expected to follow the same order as the level of exposure. Formal tests for this trend fall into the regression framework if one knows what function of exposure to use as a covariate. When unknown, a linear function of exposure level is often used. Jonckheere‐type tests for trend have generated continued interest largely because they do not require specification of a covariate. This paper shows that the Jonckheere‐type test statistics are special cases of a generalized linear rank statistic with time‐dependent covariates which unfortunately depend on the initial group sizes and censoring distributions. Using asymptotic relative efficiency calculations, the Jonckheere tests are compared to standard linear rank tests based on a linear covariate over a spectrum of shapes for the true trend.