Dmitrienko, A., Wiens, B.L., Tamhane, A.C., Wang, X. (2007). Tree-structured gatekeeping tests in clinical trials with hierarchically ordered multiple objectives. Statistics in Medicine. 26, 2465-2478.

Table 2 contains two minor typographical errors. First, the parallel rejection set of H41 is {H33} and, secondly, the adjusted p-values for the hypotheses H33 and H41 should be 0.030 and 0.867, respectively (this error does not affect the overall conclusion).

In order to compute multiplicity adjusted p-values in clinical trials with hierarchical objectives, one can invoke the TreeGatekeeper macro that implements tree gatekeeping procedures based on the Bonferroni test. The structure of this SAS macro is similar to that of the Gatekeeper macro described in Section 2.7 of Analysis of Clinical Trials Using SAS by Alex Dmitrienko, Geert Molenberghs, Christy Chuang-Stein and Walt Offen.

The TreeGatekeeper macro has the following two parameters:
- Dataset is the input data set with information about individual families of hypotheses (including the gatekeeper information, hypothesis weights and raw p-values).
- Outdata is the output data set with adjusted p-values.

The macro assumes that the input data set contains one record per individual hypothesis and includes the following variables:
- Family variable identifies the family index for each individual hypothesis (families are sequentially numbered).
- Weight variable specifies the relative importance of hypotheses within each family (the weights must be between 0 and 1 and must add up to 1 within each family).
- Raw_p variable contains the raw p-values for the individual hypotheses.
- Parallel variable is a sequence of indicator variables that define the parallel gatekeeping set for each hypothesis (with the exception of hypotheses in the first family). For example, parallel="001010000" means that the the parallel gatekeeping set for the current hypothesis includes the third and fifth hypotheses.
- Serial variable is a sequence of indicator variables that define the serial gatekeeping set for each hypothesis (with the exception of hypotheses in the first family). As in the case of parallel gatekeeping sets, serial="01100000" means that the the serial gatekeeping set for the current hypothesis includes the second and third hypotheses.

The first example in the paper deals with a clinical trial in patients with hypertension. This trial was conducted to compare an experimental drug to an active control with respect to four endpoints:
- Primary endpoint (P): Mean reduction in systolic blood pressure.
- Two secondary endpoints (S1 and S2): Mean reduction in diastolic blood pressure and proportion of patients with controlled systolic/diastolic blood pressure.
- Tertiary endpoint (T): Average blood pressure based on ambulatory blood pressure monitoring.

Download the SAS code for computing the multiplicity adjusted p-values in the hypertension clinical trial example (these adjusted p-values are displayed in Table 2).

The second example deals with a clinical trial in patients with Type II diabetes. The trial compares three doses of an experimental drug (Doses L, M and H) versus placebo (Plac). The efficacy profile of the drug was studied using three outcome variables:
- Primary endpoint (P): Hemoglobin A1c.
- Secondary endpoint (S1): Fasting serum glucose.
- Secondary endpoint (S2): HDL cholesterol.
The endpoints are examined at each of the three doses.

Download the SAS code for computing the multiplicity adjusted p-values in the diabetes clinical trial example (these adjusted p-values are displayed in Table 3).