Attach importance of the bootstrap t-test against Student's t-test in clinical epidemiology: A demonstrative comparison using COVID-19 as an example

Student's t-test is valid for statistical inference under the normality assumption or asymptotically. Although the bootstrap t-test was proposed in 1993, it is seldom adopted in medical research. We aim to demonstrate that the bootstrap t-test outperforms Student's t-test under normality in data. Using random data samples from normal distributions, we evaluated the testing performance, in terms of true positive rate (TPR)and false positive rate (FPR), and diagnostic abilities, in terms of the area under curve (AUC), of the bootstrap t-test and Student's t-test. We explore the AUC of both tests with varying sample size and coefficient of variation (CV). We compare the testing outcomes using the COVID-19 serial interval data in Shenzhen and Hong Kong, China, for demonstration. With fixed TPR, the bootstrap t-test maintained the equivalent accuracy in TPR, but significantly improved the TNR from the Student's t-test. With varying TPR, the diagnostic ability of bootstrap t-test outperformed or equivalently performed as Student's t-test in terms of AUC. The equivalent performances are possible but rarely occur in practice. We find that the bootstrap t-test outperforms by successfully the difference in COVID-19 serial interval, which is defined as the time interval between consecutive transmission generations, due to sex and nonpharmaceutical interventions against the Student's t-test. We demonstrated that the bootstrap t-test outperforms Student's t-test, and it is recommended to replace Student's t-test in medical data analysis regardless sample size.