I would like to do a cross-sectional study, 1-year period prevalence) and have performed the univariate analysis for my variables (i.e. frequentist t-test (no assumption for equality of variance) and chi-square (no correction)), and have gotten very small p-values for most of the variables. I think it is largely due to the large sample size, ~46K (~21K for diseased and ~24K for non-diseased) – data obtained from registry. I understand that we should steer away from p-values and use 95% compatibility intervals. How is this typically presented in papers? Would it be mean difference (95% CI) for continuous and proportion difference (95% CI) for categorical? Any reference papers?

Should I looking into using Bayesian t-test and proportion test due to the large patient cohort? Subsequently, I would like to do a logistic regression, and may also use Bayesian method if I adopt it in univariate analysis.