Survival analysis: time-dependent effects and time-varying risk factors

Abstract

In traditional Kaplan-Meier or Cox regression analysis, usually a risk factor measured at baseline is related to mortality thereafter. During follow-up, however, things may change: either the effect of a fixed baseline risk factor may vary over time, resulting in a weakening or strengthening of associations over time, or the risk factor itself may vary over time. In this paper, short-term versus long-term effects (so-called time-dependent effects) of a fixed baseline risk factor are addressed. An example is presented showing that underweight is a strong risk factor for mortality in dialysis patients, especially in the short run. In contrast, overweight is a risk factor for mortality, which is stronger in the long run than in the short run. In addition, the analysis of how time-varying risk factors (so-called time-dependent risk factors) are related to mortality is demonstrated by paying attention to the pitfall of adjusting for sequelae. The proper analysis of effects over time should be driven by a clear research question. Both kinds of research questions, that is those of time-dependent effects as well those of time-dependent risk factors, can be analyzed with time-dependent Cox regression analysis. It will be shown that using time-dependent risk factors usually implies focusing on short-term effects only.