Testing For Group Differences in Proteomics Data with Left Censored Data and a Limited Sample Size

Abstract

This research study aims to assess how a specific treatment influences the levels of three proteins when left-censored observations are present in a limited sample size. The dataset contained paired data gathered from 20 subjects categorized into 4 groups with increasing dosages, collected before and after administrating the treatment. The primary objective of this study is to evaluate whether there is an increase in response with increasing dosage for each of the proteins. To check the adherence of data to standard distribution, Cumulative Distribution Function (CDF) plots were used. To obtain summary statistics, Regression on Order Statistics (ROS), Maximum Likelihood Estimate (MLE) and Kaplan-Meier (KM) methods were utilized. ROS assumed to be the estimate that generally works well for the dataset as KM was unable to estimate the median for highly censored data and MLE produced unrealistic values for mean in some cases. Various matched paired tests were used to assess differences between before treatment and after treatment. The censored sign test, censored sign rank test, Peto Prentice test, and censored paired test all produced consistent conclusions across different alternative hypotheses, confirming higher protein concentrations after treatment. To evaluate mean differences, censored ANOVA, permutation tests, Peto Peto test, and Kruskal Wallis test were employed. No method demonstrated clear superiority over others. Jonckheere Terpstra test revealed the presence of group trend across increasing dosages. Multiple detection limits did not significantly impact the conclusions drawn from the study, and their consideration did not pose additional burdens. In conclusion, the treatment had a significant effect on protein levels, with dose variations influencing the outcome.