## Modelling Cumulative Effects of Time-varying Exposures/Risk Factors in Cohort Studies

Time-varying covariates are increasingly used in survival analyses of cohort studies to model the effects of prognostic factors and treatments whose values change during the follow-up. An accurate evaluation of time-varying covariate/exposure effects on survival requires defining an etiologically appropriate â€˜exposure metricâ€™. This is complicated by the fact that potentially relevant information about the impact of a given time-varying prognostic factor on the current hazard is represented by the *vector* of its past values, rather than by a single value. Indeed, most time-varying factors or exposures are likely to have *cumulative effects* on the hazard. Modelling cumulative effects poses two important methodological challenges. Firstly, the impact of past exposure values on the current hazard likely depends on the time elapsed since those values were measured. Secondly, the form of the dose-response relationship between the prognostic factor and hazard is also typically unknown. We have developed a flexible method for estimating a weight function assigning weights to past values of the time-varying exposure or prognostic factor, within the Cox proportional hazards regression analyses of (prospective or retrospective) cohort studies. Recently, we have extended this weighted cumulative exposure (WCE) model to allow for simultaneous flexible, spline-based estimation of the weight function and possibly non-linear dose response curve, representing the effect of a continuous time-varying exposure or prognostic factor on the logarithm of the hazard. We will present some pharmaco-epidemiologic applications of the WCE model to investigate the adverse effects of selected medications. The new non-linear extension of the WCE model will then be applied to re-assess the effects of repeated measures of blood pressure on cardiovascular (CVD) mortality and morbidity, in a large, long-term CVD cohort study.

This is joint work with Marie-Pierre Sylvestre, PhD, Adjunct Professor, Research Centre of the University of Montreal Hospital Centre, Montreal.

#### Prof. Michal Abrahamowicz

**Michal Abrahamowicz** is a James McGill Professor of Biostatistics at the Department of Epidemiology, Biostatistics and Occupational Health of McGill University. He obtained his PhD in Statistics& Econometrics from Krakow, Poland. His research involves both development of new, flexible statistical methods for survival analyses and collaborative research on applications of these methods in health research. He is the Principal Investigator on 2 major grants from the Canadian Institutes for Health Research (CIHR) that focus on the development, validation and applications of new statistical methods for pharmaco-epidemiology.

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Abrahamowicz_seminar_MelbourneWCEFeb2013.pdf | 1.26 MB |