Multiple test procedures and smile plots

Roger Newson

No 16, United Kingdom Stata Users' Group Meetings 2003 from Stata Users Group

Abstract: Scientists often have good reasons for wanting to calculate multiple confidence intervals and/or p-values, especially when scanning a genome. However, if we do this, then the probability of not observing at least one "significant" difference tends to fall, even if all null hypotheses are true. A skeptical public will rightly ask whether a difference is "significant" when considered as one of a large number of parameters estimated. This presentation demonstrates some solutions to this problem, using the unofficial Stata packages parmest and smileplot. The parmest package allows the calculation of Bonferroni-corrected or Sidak-corrected confidence intervals for multiple estimated parameters. The smileplot package contains two programs, multproc (which carries out multiple test procedures) and smileplot (which presents their results graphically by plotting the p-value on a reverse log scale on the vertical axis against the parameter estimate on the horizontal axis). A multiple test procedure takes, as input, a set of estimates and p-values, and rejects a subset (possibly empty) of the null hypotheses corresponding to these p-values. Multiple test procedures have traditionally controlled the family-wise error rate (FWER), typically enabling the user to be 95% confident that all the rejected null hypotheses are false, and that all the corresponding "discoveries" are real. The price of this confidence is that the power to detect a difference of a given size tends to zero as the number of measured parameters become large. Therefore, recent work has concentrated on procedures that control the false disco very rate (FDR), such as the Simes procedure and the Yekutieli-Benjamini procedure. FDR-controlling procedures attempt to control the number of false discoveries as a proportion of the number of true discoveries, typically enabling the user to be 95% confident that some of the discoveries are real, or 90% confident that most of the discoveries are real. This less stringent requirement causes power to "bottom out" at a non-zero level as the number of tests becomes large. The smileplot package offers a selection of multiple test procedures of both kinds.

Date: 2003-03-16
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