Confidence regions for multiple outcomes, effect modifiers, and other multiple comparisons

Epidemiologists are sometimes interested in estimating multiple parameters. In this context, confidence intervals are not guaranteed to provide simultaneous coverage of more than one parameter. In other words, confidence intervals understate the uncertainty due to random error in these cases. This understated uncertainty can lead to a false sense of precision in the results, potentially leading to irreproducible results or misinformed decisions. To address this challenge, one can use confidence bands, an extension of confidence intervals to multiple parameters. We illustrate the use of confidence bands in three case studies: estimation of multiple causal effects, effect measure modification by a binary variable, and effect measure modification by a continuous variable. Each example uses publicly available data and is accompanied by SAS, R, and Python code. The type of confidence region reported by epidemiologists should depend on whether scientific interest is in one or multiple parameters. For multiple parameters, like in cases where multiple actions or outcomes, effect measure modification, dose-response, or other functions are of interest, sup-t confidence bands are preferred due to their statistical properties, computational simplicity, and ease of presentation.