The choice of time scales in survival analysis has implications: calendar time versus patients' time-to-event

In the EvaCoM project, a retrospective cohort study of Germany-wide health insurance data of 29607 geriatric patients with fractures, the use of different time scales led to contradicting estimates in the Cox proportional hazards model. Here, the impact of quality audit, resulting in certification, of healthcare providers was of interest, with possible time scales being calendar time in which the audit acts or a patient's time-to-event. For the analysis the patients were divided into groups depending on whether the certification occurred before or after the patient's hospitalization, which adds a temporal component to the intervention (treatment in a certified hospital or not). A Cox model in calendar time found a harmful association of the audit with mortality (hazard ratio (HR) 1.13; 95% CI [1.04-1.23]), but in "time since hospital admission" no significant association was found (HR 1.04 [0.99-1.10]).

To investigate these contradictions, the hazards in "time since hospital admission" are parametrically approximated with piecewise linear functions and transformed to calendar time by deriving patient-specific hazards based on their hospital admission date. A Poisson regression with both time scales simultaneously is used to investigate the contradictory results further. Matching is used to analyse the association in calendar time without using an additional time scale.

The analysis of the approximated and transformed hazards leads to the conclusion that using calendar time causes a structural bias, because, in calendar time, patients of the pre-certification group enter the study earlier than those in the post-certification group. In combination with time-dependent and decreasing hazards, this leads to an artificial increase of the hazard ratio. A Poisson regression using both time scales (HR 1.00 [0.92-1.08]) and a Cox regression on matched data (HR 0.99 [0.90-1.09]) confirmed this result, finding no significant association between audits and mortality.

In EvaCoM, the estimation of significant association in calendar time is a consequence of a structural bias caused by patients being shifted in calendar time and not a true harmful effect. The choice of time scale may severely impact the results. We present methods to disentangle the effects of different time scales.