Journal of Data Science

Abstract: In many clinical trials, information is collected on both the frequency of event occurrence and the severity of each event. For example, in evaluating a new anti-epileptic medication both the total number of seizures a patient has during the study period as well as the severity (e.g., mild, severe) of each seizure could be measured. In order to arrive at a full picture of drug or treatment performance, one needs to jointly model the number of events and their correlated ordinal severity measures. A separate analysis is not recommended as it is inefficient and can lead to what we define as “zero length bias” in estimates of treatment effect on severity. This paper proposes a general, likelihood based, marginal regression model for jointly modeling the number of events and their correlated ordinal severity measures. We describe parameter estimation issues and derive the Fisher information matrix for the joint model in order to obtain the asymptotic covariance matrix of the parameter estimates. A limited simulation study is conducted to examine the asymptotic properties of the maximum likelihood estimators. Using this joint model, we propose tests that incorporate information from both the number of events and their correlated ordinal severity measures. The methodology is illustrated with two examples from clinical trials: the first concerning a new drug treatment for epilepsy; the second evaluating the effect of a cholesterol lowering medication on coronary artery disease.