Using Mixture of Normal Distributions to Detect Treatment Effects when the Frequentist Method Fails

Abstract

Background: Results from a clinical trial can either support the efficacy and safety of a new compound or fail to provide such evidence. One reason for ‘non[1]positive’ result is due to the underlying assumption of normality and homogeneity of variances, which are quite often violated when analyzing data from clinical trials, despite randomization. A question of interest is can we obtain more informative results when using mixture of normal distributions or linear models (MLMs) in such cases.\n\n Introduction: MLM can be used when traditional methods fail. MLMs “search” within the variability in data to identify components or subgroups of individuals (also known as latent classes) who have common intercepts and common slopes of change in a variable/endpoint of interest but whose intercepts and slopes are different from other subsets of patients. Thus, MLMs can be used to identify subgroups of patients exhibiting differential response to treatment within each treatment arm. The purpose of our study was to examine the usefulness of using MLM in such circumstances.\n\nMethods: Data of 155 subjects taken from a Multicenter, randomized, double blind, placebo controlled trial that evaluated the efficacy of Cpn10, administered twice weekly subcutaneously to treat Rheumatoid Arthritis was taken to evaluate the usefulness of MLM. The primary efficacy measure ACR20 was analyzed using a 3-step process: first, MLM was used to estimate RA duration using a 3-component model. The second step took the results of the first step to inform the logistic model and its analyses. Model was fitted with an intercept, MLM components, treatment arm, RA duration (linear and quadratic), dose response (modeled as an interaction effect), age and baseline weight. LOCF was used to impute for missing data. Data was analyzed using MLM and SAS v 9.0.\n\nResults: The model was a good fit to the data with a likelihood ratio significant at p=0.026, and a significant increase in the -2log L. We also observed low p-values for those variables that were non normal. Overall and for the 75 mg dose, Cpn 10 was efficacious relative to placebo, p<0.050. We also observed that dose response was significant at p><0.15\n\nConclusion: The use of MLM adds value because it can be used to understand the disease experience or the value of treatment when traditional statistical methods cannot.\n\nKey words: Mixture of linear models, normality, entropy.