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Conditioning Regimens

Comparison of 100-day mortality rates associated with i.v. busulfan and cyclophosphamide vs other preparative regimens in allogeneic bone marrow transplantation for chronic myelogenous leukemia: Bayesian sensitivity analyses of confounded treatment and center effects

Bone Marrow Transplantation volume 33, pages 1191–1199 (2004)Cite this article

Summary:

We evaluated the 100-day mortality rates associated with busulfan-based myeloablative conditioning regimens based on data from 1812 chronic myelogenous leukemia patients who underwent allogeneic blood or marrow transplantation (allotx). In all, 47 patients received intravenous (i.v.) busulfan and cyclophosphamide (i.v.BuCy2) with allotx at MD Anderson Cancer Center (MDACC) during 1995–1999. The remaining 1765 patients, whose data were supplied by the International Bone Marrow Transplant Registry (IBMTR), received alternative preparative regimens, primarily Cy-total body irradiation (∼45%) or oral BuCy (∼35%) during 1997–1998. As patients were not randomized between conditioning regimens, the i.v.BuCy2-versus-alternative treatment effect is confounded with a possible center effect due to nontreatment differences associated with factors differing between MDACC and the IBMTR centers. Additional complications are that the i.v.BuCy2-MDACC patients all survived 100 days, and three prognostic subgroups were included. Bayesian sensitivity analyses were performed to assess treatment effect on the probability of 100-day mortality, over a range of possible MDACC-versus-IBMTR center effects. For these patients, the posterior probability that i.v.BuCy2 was superior to alternative conditioning regimens ranges from 0.54 to 0.99, depending on prognosis and the magnitude of the assumed center effect.

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Acknowledgements

The i.v.BuCy2 studies at the MDACC were sponsored by Grants FD-R-001650-02 from the Food and Drug Administration and by CA49639 and CA16672-27 from the National Cancer Institute. Peter Thall's research was partially supported by NIH Grant R01 CA 83932. We thank two referees for their thoughtful and constructive comments on an earlier version of the manuscript.

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Authors and Affiliations

  1. Department of Biostatistics, University of Texas, M.D. Anderson Cancer Center, Houston, TX, USA

    P F Thall

  2. Department of Blood and Marrow Transplantation, University of Texas, MD Anderson Cancer Center, Houston, TX, USA

    R E Champlin & B S Andersson

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  1. P F Thall
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  3. B S Andersson
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Corresponding author

Correspondence to P F Thall.

Appendix

Appendix

The Bayesian paradigm for statistical analysis is concerned with two objects, the model parameters, which we denote by θ and the observed data. Parameters may be such factors as probabilities, median survival times, or the effects of treatments or patient characteristics on a given outcome. Thus, while parameters are not observed, they characterize important aspects of the observed phenomenon. In the Bayesian framework, parameters are considered random quantities to reflect the fact that one has uncertainty about them. Consequently, a key component of the Bayesian model is a prior probability distribution on θ. The likelihood of observing the data for a given parameter θ also is a probability distribution. Bayes’ Theorem formally combines one's prior with the likelihood to obtain the posterior, f(θ|data), which characterizes one's uncertainty about θ, and hence about the phenomenon, after observing the data. Thus, f(θ|data) is the basis for inference and decision-making in Bayesian analysis.

The methodology used here relies on two closely related probability distributions, the binomial and the beta. Consider the general setting where one observes the number of times, X, that a particular event occurs out of N independent trials, and the probability of the event in each trial is π. Then X follows a binomial probability distribution characterized by N and the parameter π and X has mean Nπ and variance Nπ(1−π). In most settings N is known, since it is simply the number of trials, but π is generally unknown. The most commonly used prior for π in such settings is the beta distribution. If π follows a beta distribution with parameters a and b, denoted π∼beta[a,b], then π has mean μ=a/(a+b) and variance μ(1−μ)/(a+b+1). The sum n=a+b may be interpreted as the prior sample size, so that larger n corresponds to more prior information. An equivalent, often useful way to express the beta[a,b] distribution is in terms of its mean and effective sample size, μ and n, so that π∼beta[μn, (1−μ)n]. Let Y=N−X denote the number of times that the event does not occur in the N trials. Once X and N have been observed, the posterior distribution of π is also beta, but with updated parameters a+X and b+Y, denoted π|X, N∼beta[a+X, b+Y]. The posterior mean of π|X,N is (a+X)/(n+N) and the posterior variance is (a+X)(b+Y)/{(n+N)2(n+N+1)}. The posterior mean (a+X)/(n+N) may be considered a Bayesian estimator of π, and it may be contrasted with the usual, non-Bayesian empirical mean, X/N. Some simple algebra shows that the posterior mean equals the weighted average μ{n/(n+N)}+(X/N)/{N/(n+N)} of the prior mean, μ=a/(a+b), and the empirical mean, X/N, and that the weights are proportional to the prior and actual sample sizes, n and N.

In comparing two binomial samples with probabilities π1 and π2 following beta distributions, we computed posterior probabilities of the form Pr(π2>π1|Data) using the following Splus program.

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Thall, P., Champlin, R. & Andersson, B. Comparison of 100-day mortality rates associated with i.v. busulfan and cyclophosphamide vs other preparative regimens in allogeneic bone marrow transplantation for chronic myelogenous leukemia: Bayesian sensitivity analyses of confounded treatment and center effects. Bone Marrow Transplant 33, 1191–1199 (2004). https://doi.org/10.1038/sj.bmt.1704461

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