Using fractional polynomials to model the effect of cumulative duration of exposure on outcomes: applications to cohort and nested case-control designs

PURPOSE Determining the nature of the relationship between cumulative duration of exposure to an agent and the hazard of an adverse outcome is an important issue in environmental and occupational epidemiology, public health and clinical medicine. The Cox proportional hazards regression model can incorporate time-dependent covariates. An important class of continuous time-dependent covariates is that denoting cumulative duration of exposure. METHODS We used fractional polynomial methods to describe the association between cumulative duration of exposure and adverse outcomes. We applied these methods in a cohort study to examine the relationship between cumulative duration of use of the antiarrhythmic drug amiodarone and the risk of thyroid dysfunction. We also used these methods with a conditional logistic regression model in a nested case-control study to examine the relationship between cumulative duration of use of bisphosphonate medication and the risk of atypical femur fracture. RESULTS Using a cohort design and a Cox proportional hazards model, we found a non-linear relationship between cumulative duration of use of the antiarrhythmic drug amiodarone and the risk of thyroid dysfunction. The risk initially increased rapidly with increasing cumulative use. However, as cumulative duration of use increased, the rate of increase in risk attenuated and eventually levelled off. Using a nested case-control design and a conditional logistic regression model, we found evidence of a linear relationship between duration of use of bisphosphonate medication and risk of atypical femur fractures. CONCLUSIONS Fractional polynomials allow one to model the relationship between cumulative duration of medication use and adverse outcomes.