Mitigating bias from intermittent measurement of time-dependent covariates in failure time analysis

Cox regression models are routinely fitted to examine the association between time-dependent markers and a failure time when analyzing data from clinical registries. Typically, the marker values are measured periodically at clinic visits with the recorded value carried forward until the next assessment. We examine the asymptotic behavior of estimators from Cox regression models under this observation and data handling scheme when the true relationship is based on a Cox model using the current value of the marker. Specifically, we explore the impact of the marker process dynamics, the clinic visit intensity, and the marginal failure rate on the limiting value of the estimator of the marker effect from the Cox model. We also illustrate how a joint multistate model that accommodates intermittent observation of the time-varying marker can be formulated. Simulation studies demonstrate that the finite sample performance of the naive estimator aligns with the asymptotic results and shows good performance of the estimators from the joint model. We apply both methods to data from a study of bone markers and their effect on the development of skeletal complications in metastatic cancer.