Article
Comparing Treatments in the Presence of Crossing Survival Curves: An Application to Bone Marrow Transplantation
Division of Biostatistics, Medical College of Wisconsin, 8701 Watertown Plank Road, Milwaukee, Wisconsin 53226, USA.
Biometrics (Impact Factor: 1.57). 02/2008; 64(3):73340. DOI: 10.1111/j.15410420.2007.00975.x Source: PubMed
ABSTRACT
In some clinical studies comparing treatments in terms of their survival curves, researchers may anticipate that the survival curves will cross at some point, leading to interest in a longterm survival comparison. However, simple comparison of the survival curves at a fixed point may be inefficient, and use of a weighted logrank test may be overly sensitive to early differences in survival. We formulate the problem as one of testing for differences in survival curves after a prespecified time point, and propose a variety of techniques for testing this hypothesis. We study these methods using simulation and illustrate them on a study comparing survival for autologous and allogeneic bone marrow transplants.
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 "The stratified version of these tests, which should account for matching, is inefficient when the number of strata increases and the stratum size is small [1]. Furthermore, these methods are less sensitive when proportional hazard is not satisfied and this might often be the case, especially in the clinical setting that motivated this paper, i.e. the comparison of bone marrow transplantation and chemotherapy in the treatment of leukemia [2,3]. "
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ABSTRACT: Background: In the absence of randomization, the comparison of an experimental treatment with respect to the standard may be done based on a matched design. When there is a limited set of cases receiving the experimental treatment, matching of a proper set of controls in a non fixed proportion is convenient. Methods: In order to deal with the highly stratified survival data generated by multiple matching, we extend the multivariate permutation testing approach, since standard nonparametric methods for the comparison of survival curves cannot be applied in this setting. Results: We demonstrate the validity of the proposed method with simulations, and we illustrate its application to data from an observational study for the comparison of bone marrow transplantation and chemotherapy in the treatment of paediatric leukaemia. Conclusions: The use of the multivariate permutation testing approach is recommended in the highly stratified context of survival matched data, especially when the proportional hazards assumption does not hold. 
 "We are particularly interested in using these techniques in pseudoobservation regression problems. The pseudoobservation approach has been suggested as a method for direct censored data regression modeling for the survival function (Logan et al., 2008), the cumulative incidence function (Klein and Andersen, 2005), for the mean survival time Andersen et al. (2004), for multistate probabilities (Andersen et al., 2003) and for mean quality of life (Andrei and Murray, 2007). In this approach pseudoobservations are formed as the difference between the full sample and leave one out estimator based on an approximately unbiased estimator of the parameter of interest. "
Article: Cutpoint selection for discretizing a continuous covariate for generalized estimating equations
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ABSTRACT: We consider the problem of dichotomizing a continuous covariate when performing a regression analysis based on a generalized estimation approach. The problem involves estimation of the cutpoint for the covariate and testing the hypothesis that the binary covariate constructed from the continuous covariate has a significant impact on the outcome. Due to the multiple testing used to find the optimal cutpoint, we need to make an adjustment to the usual significance test to preserve the typeI error rates. We illustrate the techniques on one data set of patients given unrelated hematopoietic stem cell transplantation. Here the question is whether the CD34 cell dose given to patient affects the outcome of the transplant and what is the smallest cell dose which is needed for good outcomes. 
 "Klein et al. [18], investigated the performance of naive test (difference between the two survival curves). Logan et al. [19] focused on crossing survival curves (that contradict the PH assumptions). A number of methods for comparing two survival curves after a prespecified time point. "