Using recurrent time-to-event models with multinomial outcomes to generate toxicity profiles

Most clinical studies, which investigate the impact of therapy simultaneously, record the frequency of adverse events in order to monitor safety of the intervention. Study reports typically summarise adverse event data by tabulating the frequencies of the worst grade experienced but provide no details of the temporal profiles of specific types of adverse events. Such 'toxicity profiles' are potentially important tools in disease management and in the assessment of newer therapies including targeted treatments and immunotherapy where different types of toxicity may be more common at various times during long-term drug exposure. Toxicity profiles of commonly experienced adverse events occurring due to exposure to long-term treatment could assist in evaluating the costs of the health care benefits of therapy. We show how to generate toxicity profiles using an adaptation of the ordinal time-to-event model comprising of a two-step process, involving estimation of the multinomial response probabilities using multinomial logistic regression and combining these with recurrent time to event hazard estimates to produce cumulative event probabilities for each of the multinomial adverse event response categories. Such a model permits the simultaneous assessment of the risk of events over time and provides cumulative risk probabilities for each type of adverse event response. The method can be applied more generally by using different models to estimate outcome/response probabilities. The method is illustrated by developing toxicity profiles for three distinct types of adverse events associated with two treatment regimens for patients with advanced breast cancer.