A rank test for bivariate time-to-event outcomes when one event is a surrogate.

In many clinical settings, improving patient survival is of interest but a practical surrogate, such as time to disease progression, is instead used as a clinical trial's primary endpoint. A time-to-first endpoint (e.g., death or disease progression) is commonly analyzed but may not be adequate to summarize patient outcomes if a subsequent event contains important additional information. We consider a surrogate outcome very generally as one correlated with the true endpoint of interest. Settings of interest include those where the surrogate indicates a beneficial outcome so that the usual time-to-first endpoint of death or surrogate event is nonsensical. We present a new two-sample test for bivariate, interval-censored time-to-event data, where one endpoint is a surrogate for the second, less frequently observed endpoint of true interest. This test examines whether patient groups have equal clinical severity. If the true endpoint rarely occurs, the proposed test acts like a weighted logrank test on the surrogate; if it occurs for most individuals, then our test acts like a weighted logrank test on the true endpoint. If the surrogate is a useful statistical surrogate, our test can have better power than tests based on the surrogate that naively handles the true endpoint. In settings where the surrogate is not valid (treatment affects the surrogate but not the true endpoint), our test incorporates the information regarding the lack of treatment effect from the observed true endpoints and hence is expected to have a dampened treatment effect compared with tests based on the surrogate alone. Published 2016. This article is a U.S. Government work and is in the public domain in the USA. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.