THE ROLE OF SUBGROUPS IN CLINICAL TRIALS

1
THE ROLE OF SUBGROUPS IN CLINICAL TRIALS

• Ralph B. DAgostino, Sr., PhD
• Boston University
• September 13, 2005

2
OUTLINE

• Clinical trial scenarios for subgroup (subset)
  analysis
• Illustrations of possible outcomes
• GOOD and PROBLEMATIC PRACTICES
• Role of formal Interaction Test
• Statistical properties of analyses
• Closing Comments

3
POSSIBLE SCENARIOS FOR SUBSET ANALYSIS

• Primary Hypothesis is for an overall
  statistically significant effect (All data
  combined) If Yes
• Subgroups examined for consistency
• Special subgroups examined for additional effect
• Latter two activities are secondary analyses
• Primary Hypothesis anticipates subgroup effect
• Subgroups examined for equal effect to justify
  pooling and an overall analysis

4
Primary Hypothesis is for an overall
statistically significant effect

• Primary hypothesis is that two treatments are
  significantly different
• If yes to above, concern then is that this should
  be consistently seen in all relevant subgroups
  (THIS IS A SECONDARY ANALYSIS)

5
OVERALL TEST IS SIGNIFICANT
6
GOOD T 1 better than T 2 Events Plots over Study
Time
1.00
TREATMENT 1
.75
TREATMENT 2
30.0
. 50

.25
-
0.0
0
0.5
1.0
1.5
2.0
2.5
3.0
Time from randomization in years
7
Overall
Males females
Gender
lt 65
Age
gt65
Note Many subgroups may not show statistical
significance, but do show consistentcy
Previous Condition
yes
no
Hazard Ratio
0.1
10
1
1 better 2 better
8
Overall
Males females
Gender
lt 65
Age
gt65
Years with Condition
yes
no
Location X
Special subgroup
NO
YES
Hazard Ratio
0.1
10
1
1 better 2 better
9
21
10
Relative Risk Reduction by Qualifying Condition

• IS n 6431
• MI n 6302
• PAD n 6452
• Total n 19185
• 30 20 10 0 10 20
• Clopidogrel Better Aspirin Better

11
OVERALL TEST IS NOT SIGNIFICANT

• TECHNICALLY YOU CANNOT GO BEYOND THIS WITH ANY
  STATISTICAL STATEMENTS
• USEFUL TO LOOK AT SUBSETS AS EXPLORATORY ANALYSIS
  (NOT EVEN APPROPRIATE TO CALL IT A SECONDARY
  ANALYSIS)

12
PROBLEM T1 not better Events Plots over Study
Time
1.00
TREATMENT 1
.75
TREATMENT 2
30.0
. 50

.25
-
0.0
0
0.5
1.0
1.5
2.0
2.5
3.0
Time from randomization in years
13
Overall
Males females
Gender
lt 65
Age
gt65
Note Only age gt 65 is significant. Do we
believe it?
Previous Condition
yes
no
Hazard Ratio
0.1
10
1
1 better 2 better
14
Overall
Males females
Gender
lt 65
Age
gt65
Years with Condition
yes
no
Location X
Location is significant. Was it pre-specified
as primary? No
NO
YES
Hazard Ratio
0.1
10
1
1 better 2 better
15
Primary Hypothesis anticipates possible subgroup
effect

• Subgroups identified by pre-randomization or
  post-randomization stratification
• Subgroups tests for equal vs. unequal effect.
  This is done formally by INTERACTION TEST
• Procedure
• If significant interaction, do not pool and test
  groups
• If no significant interaction pool
• May need to add variable in analysis for groups

16
Primary Hypothesis anticipates subgroup effect
(continue)

• INTERACTION TEST may be avoided and subgroups can
  be tests separately with control of error rates
• For example, if there are two groups then each
  can be tested at 0.025 level of significance
• For example, groups can be tested sequentially
  with error rate control

17
Location X YES
1.00
TREATMENT 1
.75
TREATMENT 2
30.0
. 50

.25
-
0.0
0
0.5
1.0
1.5
2.0
2.5
3.0
Time from randomization in years
18
Location X NO
1.00
TREATMENT 1
.75
TREATMENT 2
30.0
. 50

.25
-
0.0
0
0.5
1.0
1.5
2.0
2.5
3.0
Time from randomization in years
19
Overall

Location X
Location Interaction of location is
significant Do not pool
NO
YES
Hazard Ratio
0.1
10
1
1 better 2 better
20
Statistical properties of analysesOverall test

• If Primary hypothesis of overall significance is
  satisfied
• Then as secondary analyses we can examine
  subgroups and control error rates (that is, can
  control chance of identifying falsely significant
  subgroups) for specified subgroups
• If number of subgroups is unspecified, then
  analysis is exploratory even here

21
Statistical properties of analysesOverall test
(continue)

• If Primary hypothesis of overall significance is
  not met (that is, we do not achieve statistical
  significance), then we cannot control error rate
  (falsely identifying significant subsets). We
  have used alpha on overall test

22
Primary hypothesis anticipates subgroup
differences

• Level of significance is chance of rejecting at
  least one false null hypothesis and it can be
  controlled.
• If there are potentially k subgroups this error
  rate may be as high as k(0.05) if each subgroup
  is tested at 0.05 level of significance.
• With k2, 0.10 k3, 0.15, k5, 0.25

23
Closing Comments

• Error rates (level of significance) can be
  controlled even for looking at subgroups if
  structure of statistical approach is clearly
  stated.
• We must not confuse test for subgroups stated in
  a pre-specified manner from post hoc
  identification and tests