| Summary: | In the context of oncological drug trials, the semi-parametric Cox proportional hazards model is traditionally used to establish treatment efficacy based on patient response to treatment. However, the analysis is limited to answering questions about treatment efficacy only, since the focus is usually on a single event of interest (such as significant tumour shrinkage).
It would instead be in the interest of patients to address whether a clinically effective drug is potentially beneficial, in terms of whether it can treat cancer while being relatively tolerable compared to alternative treatments. To address this, we propose modelling the entire patient history using a semi-Markov multi-state model so that we can simultaneously consider all possible events that can be experienced by patients. Furthermore, if one defines all possible events to be detrimental to the patient, we can quantify differences in patient benefit by considering each of the active and control treatment arms and the time patients spend in one or more states.
We propose two general statistical procedures to compare patients in each treatment arm. The first procedure is based on differences in expected sojourn time in subsets of states of interest, while the second procedure is based on differences in the survival function of the holding time in specific states. In each case, the test statistic is a function of the maximum likelihood estimates of model parameters. The delta method is used for statistical inference. Properties of the proposed statistical procedures are assessed by means of a simulation study, including analyses of power and effects of model misspecification. The main result is that each test is able to detect significant patient benefit relatively easily, with limiting factors being sample size and high rates of right-censoring.
Finally, a real dataset is analysed and our method is compared to each of the Cox proportional hazards model and the Fine-Gray proportional hazards model. The main conclusion is that our method is more flexible and insightful when considering patient benefit.
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