Correcting the Results of the Wrong Model: Treatment Effects under Early Detection of Cancer

Early detection of cancer leads to variability of the point of diagnosis advanced by the amount of the so-called lead time, a random variable. Estimated treatment effects by the proportional hazards (PH) model may be biased if this variability is ignored. We study how true and PH-estimated treatment effects differ in screened vs. unscreened populations and offer an approximate correction for the reported PH-based estimate that does not require raw data, targeting a meta-analysis-type application. We rely on a joint cancer incidence and survival model of prostate cancer to furnish key information for the correction. The procedure is applied to a series of prostate cancer data analyses using the PH models reported in the literature. Simulations are used for assessing the quality of the method and sensitivity analyses.