Establishing a Predictive Survival Model for Patients with Leukemia Adjusting for the Random Effect of Pre Leukemia

Myelodysplastic syndrome (MDS), sometimes referred to as pre-leukemia or smoldering leukemia, is a group of diseases usually characterized by failure of the bone marrow to produce enough normal blood cells. In about one-third of patients, the disease transforms into acute leukemia. In high-risk MDS, the bone marrow contains too many immature blood cells known as blasts. Patients with high-risk MDS survive for an average of six to 12 months. We have taken data from a large clinical trial and re-examined it considering the pre-leukemia as a random event in a Weibull distribution model. We have taken the intercept, stress effect and shape parameter of the distribution to be random effects as well with realistic prior distributions based on previous shapes of the survival experience of subjects with this disease. We demonstrate how the model performs under relevant clinical conditions. The conditions are all tested using a Bayesian statistical approach allowing for the robust testing of the model parameters under various stress conditions which we introduce into the model. The convergence of the parameters to stable values are seen in trace plots which follow the convergence patterns This allows for precise estimation for determining clinical conditions under which the survival pattern will change. We give a numerical example of our results. The major platform for the theoretical development follows the Bayesian methodology and the multiple parameter Weibull model with random effects having carefully chosen hyper parameters. Wew have done the basic infrastructure for the analysis using the commercially available WinBugs software employing the Markov Chain Monte Carlo (MCMC) methodology. The BUGS language allows a concise expression of the model to denote stochastic (probabilistic) relationships and to denote deterministic(logical) relationships. The stochastic parameters , however specified, may be given proper but minimally informative prior distributions, while the logical expression for the variance in the model allows the standard deviation (of the random effects distribution) to be estimated. Fixed effect model approaches are also handled rather well with the software. As seen in the WinBugs manual by Spiegelhalter et. al (2003) also at www.mrc.bsu.cam.ac.uk/bugs/winbugs/ manual14.pdf, the WinBUGS software uses compound documents, which comprise various different types of information (formatted text, tables, formulae, plots, graphs, etc.) displayed in a single window and stored in a single file for application to the problem at hand. This manual describes the WinBugs software an interactive Windows version of the BUGS program for Bayesian analysis of complex statistical models using MCMC techniques. We have been careful to apply only the models that WinBugs handles thus avoiding possibly spurious results with untested models as one is so warned.