Fractional polynomial adjustment for time-varying covariates in a self-controlled case series analysis

The self-controlled case series method is a statistical approach to investigating associations between acute outcomes and transient exposures. The method uses cases only and compares time at risk after the transient exposure with time at risk outside the exposure period within an individual, using conditional Poisson regression. The risk of outcome and exposure often varies over time, for example, with age, and it is important to allow for such time dependence within the analysis. The standard approach for modelling time-varying covariates is to split observation periods into blocks according to categories of the covariate and then to model the relationship using indicators for each category. However, this can be inefficient and can lead to problems with collinearity if the exposure occurs at approximately the same time in all individuals. As an alternative, we propose using fractional polynomials to model the relationship between the time-varying covariate and incidence of the outcome. We present the results from an analysis exploring the association between rotavirus vaccination and intussusception risk as well as a simulation study. We conclude that fractional polynomials provide a useful approach to adjusting for time-varying covariates but that it is important to explore the sensitivity of the results to the number of categories and the method of adjustment.