The New England Journal of Statistics in Data Science

Disease registries often involve cohorts of patients seen repeatedly at tertiary care centers with biospecimens collected at periodic clinic visits. With such registries it is possible to study the association between time-dependent biomarkers and a failure time of interest through Cox regression. However it can be prohibitively expensive or labor-intensive to assay all biospecimens for all members of the registry and in practice it is common to select a single biosample to assay for each individual. We derive the asymptotic bias of estimators obtained from the Cox model based on common strategies. We investigate the nature of this bias from a joint multistate model for the marker and failure processes. Alternative selection methods are then developed for consistent and efficient sub-sampling under budgetary constraints. The asymptotic relative efficiency of regression coefficients obtained from the Fisher information is then explored and an optimal design is identified within a class of designs. The proposed selection method is illustrated in a registry of patients with psoriatic arthritis where we investigate the association between a time-dependent biomarker (ESR_CRP) and the risk of developing arthritis mutilans.