Given a set samples e.g. n=1000 patients, 500 cases and 500 controls, but only 30% men and 1% smokers, the proposal to take heterogeneity into account would be to use bootrapping b=100, and subselect 100 samples each b to repeat the statistical test. So the result of the combined p-value takes into account the probability of the sample being selected given the frequency of the covariate.
How to combine p-values? How to vizualize results?
For each bootstrap sample, statistical tests are conducted and p-values are obtained, which can then be combined using methods such as Fisher's combined probability test to consider the probability of sample selection. Visualization of the results can be achieved through boxplots and density plots of the p-values, or performance metrics if predictive modeling is involved. To address sample heterogeneity in differential expression analysis, bootstrap resampling is used to create multiple subsamples, maintaining the proportion of covariates like gender and smoking status.
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