The analysis of complex patterns of longitudinal binary response: an example of transient dysphagia following...

In many clinical trials, treatment is given in phases and the prevalence of symptoms is recorded longitudinally. As a result, complex non-linear response patterns may be observed as the prevalence of symptoms changes as a consequence of treatment. In such cases, although profiles of the marginal response over time give an informative description of the data, they do not allow a formal treatment comparison or adjustment for covariates of interest. Here we analyse previously reported data on transient dysphagia in patients with non-small-cell lung cancer treated with radiotherapy. We use a generalized estimating equation approach for repeated measurement binary response to give robust standard errors taking account of the dependence of observations taken on the same subject, alongside a natural cubic spline to represent the complex shape of the marginal response. This provides a reasonable model for the marginal response and allows unbiased estimation of an apparent treatment difference. The effect of different choices for the working correlation matrix is discussed, as is the modelling of treatment group differences that vary over time. We conclude that these models provide a powerful tool for the analysis of such data that can now be applied using generally accessible software.