Novel Statistical Approaches for Non-Normal Censored Immunological Data: Analysis of Cytokine and Gene Expression Data

Background: For several immune-mediated diseases, immunological analysis will become more complex in the future with datasets in which cytokine and gene expression data play a major role. These data have certain characteristics that require sophisticated statistical analysis such as strategies for non-normal distribution and censoring. Additionally, complex and multiple immunological relationships need to be adjusted for potential confounding and interaction effects. Objective: We aimed to introduce and apply different methods for statistical analysis of non-normal censored cytokine and gene expression data. Furthermore, we assessed the performance and accuracy of a novel regression approach in order to allow adjusting for covariates and potential confounding. Methods: For non-normally distributed censored data traditional means such as the Kaplan-Meier method or the generalized Wilcoxon test are described. In order to adjust for covariates the novel approach named Tobit regression on ranks was introduced. Its performance and accuracy for analysis of non-normal censored cytokine/gene expression data was evaluated by a simulation study and a statistical experiment applying permutation and bootstrapping. Results: If adjustment for covariates is not necessary traditional statistical methods are adequate for non-normal censored data. Comparable with these and appropriate if additional adjustment is required, Tobit regression on ranks is a valid method. Its power, type-I error rate and accuracy were comparable to the classical Tobit regression. Conclusion: Non-normally distributed censored immunological data require appropriate statistical methods. Tobit regression on ranks meets these requirements and can be used for adjustment for covariates and potential confounding in large and complex immunological datasets.