# Chain macro

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## Description

The Chain macro computes multiplicity-adjusted p-values for the nonparametric chain procedure in general hypothesis testing problems.

## General reference

Dmitrienko, A., Bretz, F., Westfall, P.H., Troendle, J., Wiens, B.L., Tamhane, A.C., Hsu, J.C. (2009). Multiple testing methodology. Multiple Testing Problems in Pharmaceutical Statistics. Dmitrienko, A., Tamhane, A.C., Bretz, F. (editors). Chapman and Hall/CRC Press, New York.

## Download

Download Chain macro.

## Example

Consider a confirmatory clinical trial which was conducted to study the efficacy profile of a novel treatment in a schizophrenia population compared to a placebo. The sponsor's plan was to test the treatment in the general patient population (all-comers population) and simultaneously in two important subgroups defined by a phenotypic characteristic (Subpopulation 1) and by a genotypic classifier (Subpopulation 2). The three null hypotheses tested in the trial were:

- Null hypothesis H1: No difference between Treatment and Placebo in the general patient population.
- Null hypothesis H2: No difference between Treatment and Placebo in Subpopulation 1.
- Null hypothesis H3: No difference between Treatment and Placebo in Subpopulation 2.

The following hypothesis hypothesis weights were chosen by the sponsor to account for the importance of achieving a significant treatment effect in the general patient population and classifier-based subgroup (Subpopulation 2):

- Null hypothesis H1: weight=0.50.
- Null hypothesis H2: weight=0.20.
- Null hypothesis H3: weight=0.30.

The sponsor is interested in performing the chain procedure to control the familywise Type I error rate with respect to all three primary tests. The serial chain procedure uses the following transition parameters:

- g12=0.5 (fraction of alpha transferred from H1 to H2).
- g13=0.5 (fraction of alpha transferred from H1 to H3).
- g23=1.0 (fraction of alpha transferred from H2 to H3).

All other transition parameters are set to 0.

The one-sided p-values for the three primary tests were given by:

- Null hypothesis H1: p=0.0061.
- Null hypothesis H2: p=0.0233.
- Null hypothesis H3: p=0.0098.

The p-values and other procedure parameters are included in a data set:

data example; input raw_p weight g1-g3; datalines; 0.0061 0.3333 0.0 0.5 0.5 0.0233 0.3333 0.0 0.0 1.0 0.0098 0.3334 0.0 0.0 0.0 ;

and the Chain macro is called as follows:

%chain(in=example,out=adjp);

The ChainSer macro generates the ADJP data set with multiplicity-adjusted p-values for the three primary null hypotheses:

proc print data=adjp noobs label; format raw chain 6.4; var test raw chain; run;

The multiplicity-adjusted p-values for the chain procedure are listed below:

Test Raw Chain 1 0.0061 0.0183 2 0.0233 0.0466 3 0.0098 0.0196

The chain procedure thus finds the following significant effects in the schizophrenia trial at a one-sided α=0.025:

- Treatment versus Placebo in the general patient population, adjusted p=0.0183.
- Treatment versus Placebo in Subpopulation 2, adjusted p=0.0196.

## Other procedures

To find out more about software implementation of other multiple testing procedures and gatekeeping procedures, see Software.