Discrete proportional hazards models for mismeasured outcomes

Outcome mismeasurement can lead to biased estimation in several contexts. Magder and Hughes (1997, American Journal of Epidemiology 146, 195-203) showed that failure to adjust for imperfect outcome measures in logistic regression analysis can conservatively bias estimation of covariate effects, even when the mismeasurement rate is the same across levels of the covariate. Other authors have addressed the need to account for mismeasurement in survival analysis in selected cases (Snapinn, 1998, Biometrics 54, 209-218; Gelfand and Wang, 2000, Statistics in Medicine 19, 1865-1879; Balasubramanian and Lagakos, 2001, Biometrics 57, 1048-1058, 2003, Biometrika 90, 171-182). We provide a general, more widely applicable, adjusted proportional hazards (APH) method for estimation of cumulative survival and hazard ratios in discrete time when the outcome is measured with error. We show that mismeasured failure status in a standard proportional hazards (PH) model can conservatively bias estimation of hazard ratios and that inference, in most practical situations, is more severely affected by poor specificity than by poor sensitivity. However, in simulations over a wide range of conditions, the APH method with correctly specified mismeasurement rates performs very well.