Statistical analysis of highly skewed immune response data

Abstract

This paper considers methods of statistical analysis for highly skewed immune response data. Observations from population studies of immunological variables are rarely normally distributed between individuals; typically the distribution shows extreme levels of skewness. In some situations, skewness remains considerable even after transforming the data. Using resampling techniques, applied to several actual datasets of ELISA assay data, we consider the robustness of normal parametric methods, e.g. t tests and linear regression. Despite the skewness of the transformed data, we demonstrate that such methods are quite robust depending on the number of observations, type of analysis and severity of skewness. We also illustrate how bootstrap resampling can be used to provide a valid alternative method of analysis that can be used either for checking normal parametric analysis or as a direct method of analysis. We illustrate this combined approach by analysing real data to test for association between human serum antibodies to malaria merozoite surface proteins, MSP1 and MSP2, and resistance to clinical malaria, and confirm the protective effect of antibodies to MSP1 and demonstrated a similar protective effect for some antibodies to MSP2.