In oncology, the international WHO and RECIST criteria have allowed the standardization of tumor response evaluation in order to identify the time of disease progression. These semi-quantitative measurements are often used as endpoints in phase II and phase III trials to study the efficacy of new therapies. However, through categorization of the continuous tumor size, information can be lost and they can be challenged by recently developed methods of modeling biomarkers in a longitudinal way. Thus, it is of interest to compare the predictive ability of cancer progressions based on categorical criteria and quantitative measures of tumor size (left-censored due to detection limit problems) and/or appearance of new lesions on overall survival. We propose a joint model for a simultaneous analysis of three types of data: a longitudinal marker, recurrent events, and a terminal event. The model allows to determine in a randomized clinical trial on which particular component treatment acts mostly. A simulation study is performed and shows that the proposed trivariate model is appropriate for practical use. We propose statistical tools that evaluate predictive accuracy for joint models to compare our model to models based on categorical criteria and their components. We apply the model to a randomized phase III clinical trial of metastatic colorectal cancer, conducted by the Fédération Francophone de Cancérologie Digestive (FFCD 2000-05 trial), which assigned 410 patients to two therapeutic strategies with multiple successive chemotherapy regimens.
Multi-state models provide a relevant tool for studying the observations of a continuoustime process at arbitrary times. Markov models are often considered even if semi-Markov are better adapted in various situations. Such models are still not frequently applied mainly due to lack of available software. We have developed the R package SemiMarkov to fit homogeneous semi-Markov models to longitudinal data. The package performs maximum likelihood estimation in a parametric framework where the distributions of the sojourn times can be chosen between exponential, Weibull or exponentiated Weibull. The package computes and displays the hazard rates of sojourn times and the hazard rates of the semi-Markov process. The effects of covariates can be studied with a Cox proportional hazards model for the sojourn times distributions. The number of covariates and the distribution of sojourn times can be specified for each possible transition providing a great flexibility in a model's definition. This article presents parametric semi-Markov models and gives a detailed description of the package together with an application to asthma control.
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