A temporal correlation function for the association between patient-reported outcome and clinical endpoints

For clinical trials with multiple endpoints, the primary interest is usually to evaluate the relationship of these endpoints and treatment interventions. Studying the correlation of two clinical trial endpoints can also be of interests. For example, the association between patient-reported outcome and clinically assessed endpoint could answer important research questions and also generate interesting hypothesis for future research. However, it is not straightforward to quantify such association. In this article, we proposed a multiple event approach to profile such association with a temporal correlation function, visualized by a correlation function plot over time with a confidence band. We developed this approach by extending the existing methodology in recurrent event literature. This approach was shown to be generally unbiased and could be a useful tool for data visualization and inference. We demonstrated the use of this method with data from a real clinical trial. Although this approach was developed to evaluate the association between patient-reported outcome and adverse events, it can also be used to evaluate the association of any two endpoints that can be translated to time-to-event endpoints.