# ParCI macro

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## Description

The ParCI macro computes one-sided multiplicity-adjusted confidence intervals (simultaneous confidence intervals) for the following parametric multiple testing procedures in one-sided hypothesis testing problems with a balanced one-way layout and equally weighted null hypotheses:

- Single-step Dunnett procedure.
- Step-down Dunnett procedure.

## 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 ParCI macro.

## Example

Using the parametric hypothesis testing problem used for illustrating the ParProc macro, consider a problem of testing three null hypotheses of no treatment effect for three dose-placebo comparisons in a confirmatory trial in patients with major depressive disorder. The primary efficacy endpoint is continuous (Montgomery-Asberg Depression Rating Scale total score) and can be assumed to be normally distributed. The null hypotheses of interest are defined as follows:

- Null hypothesis H1: No difference between Dose H and Placebo.
- Null hypothesis H2: No difference between Dose M and Placebo.
- Null hypothesis H3: No difference between Dose L and Placebo.

and assumed to be equally weighted. The mean treatment differences for the three dose-placebo comparisons are given by

- Null hypothesis H1 (Dose H versus Placebo): mean=2.3.
- Null hypothesis H2 (Dose M versus Placebo): mean=2.5.
- Null hypothesis H3 (Dose L versus Placebo): mean=1.9.

with the pooled standard deviation of 9.5. Further, the common sample size per arm is n=180. Based on this information, the t test statistics for the dose-placebo comparisons are given by

- Null hypothesis H1 (Dose H versus Placebo): t=2.297.
- Null hypothesis H2 (Dose M versus Placebo): t=2.497.
- Null hypothesis H3 (Dose L versus Placebo): t=1.897.

The test statistics follow a trivariate t distribution with 2*(n-1)=358 degrees of freedom.

The ParCI macro will be used to compute lower limits of one-sided simultaneous confidence intervals for the true mean treatment differences with a joint coverage probability of 97.5% based on the two parametric procedures (single-step and step-down Dunnett procedures). The trial parameters passed to the macro include the test statistics (T variable), sample mean treatment differences (EST variable) and pooled standard error (SE variable):

data example; input t est sd; se=sd*sqrt(2/180); datalines; 2.297 2.3 9.5 2.497 2.5 9.5 1.897 1.9 9.5 ;

The pooled standard error is computed after the INPUT step based on the pooled standard deviation and common sample size. It is worth noting that neither parametric procedure takes into account the ordering of the p-values in the EXAMPLE data set.

The list of arguments for the ParCI macro is similar to that of the PvalCI macro:

- Name of the data set with the trial parameters (IN argument).
- Common sample size per arm (N argument).
- Joint coverage probability of one-sided simultaneous confidence intervals (COVPROB argument).
- Name of the data set with one-sided simultaneous confidence intervals (OUT argument).

The following call is used to compute lower limits of one-sided simultaneous confidence intervals for the true mean treatment differences in the major depressive disorder trial:

%parci(in=example,n=180,covprob=0.975,out=adjci);

The ADJCI data set contains lower limits of one-sided simultaneous confidence intervals for the single-step and step-down Dunnett procedures as well as univariate confidence intervals:

proc print data=adjci noobs label; format est se univariate dunnett stepdunnett 6.2; var test est se univariate dunnett stepdunnett; run;

The lower limits are given by:

Single- Step- Standard step down Test Mean error Univariate Dunnett Dunnett 1 2.30 1.00 0.33 -0.06 0.00 2 2.50 1.00 0.53 0.14 0.00 3 1.90 1.00 -0.07 -0.46 -0.07

The lower limits of one-sided simultaneous confidence intervals for the single-step and step-down Dunnett procedures are consistent with the adjusted p-values computed by the ParProc macro, i.e., a lower limit is greater or equal to 0 if and only if the corresponding adjusted p-value is less than or equal to 0.025.

## Other procedures

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