Standard survival data measure the time span from some time origin until the occurrence of one type of event. If several types of events occur, a model describing progression to each of these competing risks is needed. Multi-state models generalize competing risks models by also describing transitions to intermediate events. Methods to analyze such models have been developed over the last two decades. Fortunately, most of the analyzes can be performed within the standard statistical packages, but may require some extra effort with respect to data preparation and programming. This tutorial aims to review statistical methods for the analysis of competing risks and multi-state models. Although some conceptual issues are covered, the emphasis is on practical issues like data preparation, estimation of the effect of covariates, and estimation of cumulative incidence functions and state and transition probabilities. Examples of analysis with standard software are shown.

Purpose Outcome of childhood acute lymphoblastic leukemia (ALL) improved greatly by intensifying chemotherapy for all patients. Minimal residual disease (MRD) levels during the first months predict outcome and may select patients for therapy reduction or intensification. Methods Patients 1 to 18 years old with ALL were stratified on the basis of MRD levels after the first and second course of chemotherapy. Thereafter, therapy was substantially reduced in patients with undetectable MRD (standard risk) and intensified in patients with intermediate (medium risk) and high (high risk) levels of MRD. Seven hundred seventy-eight consecutive patients were enrolled. The method of analysis was intention-to-treat. Outcome was compared with historical controls. Results In MRD-based standard-risk patients, the 5-year event-free survival (EFS) rate was 93% (SE 2%), the 5-year survival rate was 99% (SE 1%), and the 5-year cumulative incidence of relapse rate was 6% (SE 2%). The safety upper limit of number of observation years was reached and therapy reduction was declared safe. MRD-based medium-risk patients had a significantly higher 5-year EFS rate (88%, SE 2%) with therapy intensification (including 30 weeks of asparaginase exposure and dexamethasone/vincristine pulses) compared with historical controls (76%, SE 6%). Intensive chemotherapy and stem cell transplantation in MRD-based high-risk patients resulted in a significantly better 5-year EFS rate (78%, SE 8% v 16%, SE 8% in controls). Overall outcome improved significantly (5-year EFS rate 87%, 5-year survival rate 92%, and 5-year cumulative incidence of relapse rate 8%) compared with preceding Dutch Childhood Oncology Group protocols. Conclusion Chemotherapy was substantially reduced safely in one-quarter of children with ALL who were selected on the basis of undetectable MRD levels, without jeopardizing the survival rate. Outcomes of patients with intermediate and high levels of MRD improved with therapy intensification.

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Multi-state models are a very useful tool to answer a wide range of questions in survival analysis that cannot, or only in a more complicated way, be answered by classical models. They are suitable for both biomedical and other applications in which time-toevent variables are analyzed. However, they are still not frequently applied. So far, an important reason for this has been the lack of available software. To overcome this problem, we have developed the mstate package in R for the analysis of multi-state models. The package covers all steps of the analysis of multi-state models, from model building and data preparation to estimation and graphical representation of the results. It can be applied to non-and semi-parametric (Cox) models. The package is also suitable for competing risks models, as they are a special category of multi-state models. This article offers guidelines for the actual use of the software by means of an elaborate multi-state analysis of data describing post-transplant events of patients with blood cancer. The data have been provided by the EBMT (the European Group for Blood and Marrow Transplantation). Special attention will be paid to the modeling of different covariate effects (the same for all transitions or transition-specific) and different baseline hazard assumptions (different for all transitions or equal for some).