Transcript Power Point Handouts

Session 6: Other Analysis Issues
In this session, we consider various analysis issues
that occur in practice:
•Incomplete Data:
–Subjects drop-out, do not complete study.
–Some missing data for completed subjects.
–Outcome=time for an event to occur, which does not
occur in some subjects.
•Repeated measurements on some or all subjects.
•Planning for making several comparisons.
Hypertension Randomized Trial
• Subjects randomized to one of 3 drugs for controlling
hypertension:
A: Carvedilol (new)
B: Nifedipinr (standard)
C: Atenolol (standard)
• Diastolic blood pressure (dbp) is measured at each of 6
visits:
Screen (week -1); Pre-trt (week 0); Post-trt weeks
2,4,6,8.
• Consider primary outcome = Pre-Week8 dbp change.
• Secondary outcomes include other changes and
patterns throughout the 8 weeks.
• Some subjects may miss some visits; others may "dropout" completely.
Pattern of Available dbp Data in HTN Trial
There was more drop-out under drug A:
Number of Subjects
Visit
A
B
C
----------------------Pre-Trt
100
93
95
2 Week
100
93
94
4 Week
94
91
94
6 Week
87
88
93
8 Week
83
84
91
% w/o 8 Week:
17%
10%
4%
p=0.01
• The primary analysis needs to account for differential
drop-out.
• Other analyses can examine reasons for drop-out.
• Consider drop-out rate itself as an outcome.
Possible Analyses for Pre-Week8 dbp Change
• Possible subject sets used in analyses:
– All randomized: Intention-to-Treat (ITT).
– Per-Protocol (meeting a compliance definition).
– Evaluated at 8 weeks.
• ITT outcome definitions for subjects with missing
8 week dbp:
– Use latest dbp as week8 dbp ("last value carried
forward")
– Define change=0.
– Use pre vs. week8 correlation among other subjects
(mixed model); assumes missing pattern is not
related to treatment.
Hypertension Trial Analyses Comparisons
Analysis I: ITT with Last Value Carried Forward N=288 Overall p=0.0490
Estimated Difference
p-value
95% CI
A-B
10.90-11.39 = -0.49
0.7070
-3.08 to 2.09
A-C
10.90-13.93 = -3.03
0.0211 -5.61 to -0.46
B-C
11.39-13.93 = -2.54
0.0582
-5.16 to 0.09
Analysis II: Exclude Drop Outs
Estimated Difference
A-B
11.98-11.22 = 0.77
A-C
11.98-13.70 = -1.72
B-C
11.22-13.70 = -2.48
p-value
0.5630
0.1860
0.0558
N=258
Overall p=0.1438
95% CI
-1.84 to 3.37
-4.27 to 0.83
-5.03 to 0.06
Analysis III: ITT with Drop Outs Assigned 0
N=288 Overall p=0.0209
Estimated Difference
p-value
95% CI
A-B
9.65 - 9.93 = -0.27
0.8296
-2.77 to 2.22
A-C
9.65 -12.86 = -3.21
0.0113
-5.69 to -0.73
B-C
9.93 -12.86 = -2.95
0.0230
-5.47 to -0.41
Secondary Analyses for HTN Trial
• The patterns of dbp over 8 weeks - rates of
change, e.g. - could be compared among drug
groups.
– Repeated measures analyses compare trends using
only subjects with dpb at every visit.
– Mixed models use all subjects with at least one visit.
• What is the normal range prior to drug treatment?
– Could use screen (week -1) or pre-trt (week 0) dbp.
– Mixed models use both sets, recognizing pairing by
subject.
Mixed Model Analyses
• Generalize usual t-test, ANOVA, ANOCOV (which
eliminate subjects with any missing data) when there is
partial (missing) outcomes for some subjects.
• Do not include subjects with missing independent
variables (such as a covariate in ANOCOV).
• Incorporate correlations among measurements
replicated on subjects or among sets of subjects:
– Find normal range for unteated dbp using both screen and
week0 dbp, which are correlated in subjects.
E.g., we want SD(among subjects), but SD of 2*100 = 2 dbp's in
each of 100 subjects includes SD(among subjects) & SD(within
subjects).
Mixed models will separate these SDs even when subjects have
varying # of measurements.
– "Nested" subjects. The HTN study actually had 29 centers.
Mixed models incorporate potential differences among centers,
and enable generalization to all recipients of the drugs, not just
in the chosen centers.
Multiple Analyses
• Often, several comparisons are made with the
same data.
• If each test declares significance when p<0.05,
the 1 of 20 comparisons are expected to be false
positives.
• Solution is to use smaller p-values for each test,
or adjust p-values for the number and type of
tests.
• Two major issues:
– All pairwise comparisons of several groups ("multiple
comparisons").
– Comparison of groups several times sequentially
throughout the study, as more subjects complete
(interim analyses).
Multiple Comparisons
• Specify prior to study (in protocol) comparisons to be made.
In HTN study, only A vs. B and A vs. C, since B & C are current
standard of care?
• If all three pairwise comparisons (A-C, A-B, A-C) are to be made:
Analysis I: ITT with Last Value Carried Forward
A-B
A-C
B-C
Individual Comparisons
p-value
95% CI
0.7070
-3.08 to 2.09
0.0211
-5.61 to -0.46
0.0582
-5.16 to 0.09
Tukey-Adj'd Comparisons
p-value
95% CI
0.9250
-3.59 to 2.60
0.0548
-6.11 to 0.05
0.1399
-5.68 to 0.61
Interim Analyses
• Often, comparison of groups will be made several times
sequentially throughout the study, as more subjects
complete the study.
• These comparisons are usually made by an independent
Data and Safety Monitoring Board (DSMB) and results
are not revealed to the investigators or the public.
• The purpose is usually to decide whether to end the trial
early due to efficacy or inferiority of a test treatment
(treatment A in the HTN study).
• As with multiple comparisons, adjustment needs to be
made for examining the same data repeatedly.
• Interim analyses incorporate the fact that these multiple
looks are made at the data.
• Sometimes an interim analysis requires stronger
evidence of efficacy than inferiority early in the study.
Overall P<0.05 is maintained at study completion. An
example (not for HTN study) illustrates this situation.
Example of Interim Analysis Stopping Guidelines
Stopping Boundaries
Figure: Group sequential
boundaries set at overall
0.05 level of significance.
Benefit
4
Z-Value
2
Crossing upper boundary
= benefit; crossing lower
boundary = harm.
0
-2
Z-value = standardized
treatment - placebo
difference in outcome.
Harm
-4
10
20
30
40
50
60
70
80
90
Number of Subjects
Criteria for Harm
Criteria for Benefit
Analysis
Number of
Subjects
Interim#1
20
-2.368
0.0089
4.332
0.000007
0.009
Interim#2
50
-2.276
0.0114
2.606
0.00458
0.016
Final
80
-2.276
0.0114
1.985
0.0236
0.035
Lower
Boundary
Nominal
Alpha
Upper
Boundary
Nominal
Alpha
Combined
Nominal Alpha
Time-to-Event or Survival Analysis
• Suppose that, in HTN study, outcome = time until dbp < K, for some
K.
• Each subject is observed for 8*7 = 56 days (or longer, in practice,
due to continuous enrollment and a fixed termination date).
• Possible data:
Subject: 1
Days to dbp<K: 26
2
52
3
>56
4
40
5
>28
6 7
45 29
8
9 10
>56 >56 19
• Subjects 3,5,8,9 have "censored time".
• If there are no censored time, mean or median time can be used.
• Note that dropped subjects preclude just finding % with time < some
time t.
• Use survivial analysis methods with censored time:
– Uses variable time for different subjects.
– Can compare rates of events per time.
– Can compare Prob[Time > t] among groups for any time t.