Session 6: Other Analysis Issues

1
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.
• Outcometime for an event to occur, which does
  not occur in some subjects.
• Repeated measurements on some or all subjects.
• Planning for making several comparisons.

2
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
  "drop-out" completely.

3
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
  p0.01
• 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.

4
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 change0.
• Use pre vs. week8 correlation among other
  subjects (mixed model) assumes missing pattern
  is not related to treatment.

5
Hypertension Trial Analyses Comparisons

• Analysis I ITT with Last Value Carried Forward
  N288 Overall p0.0490
• 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
  N258 Overall p0.1438
• Estimated Difference p-value
  95 CI
• A - B 11.98-11.22 0.77 0.5630
  -1.84 to 3.37
• A - C 11.98-13.70 -1.72 0.1860
  -4.27 to 0.83
• B - C 11.22-13.70 -2.48 0.0558
  -5.03 to 0.06
• Analysis III ITT with Drop Outs Assigned 0
  N288 Overall p0.0209
• 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

6
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.

7
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 2100 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.

8
Multiple Analyses

• Often, several comparisons are made with the same
  data.
• If each test declares significance when plt0.05,
  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).

9
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
• Individual Comparisons
  Tukey-Adj'd Comparisons
• p-value 95 CI
  p-value 95 CI
• A - B 0.7070 -3.08 to 2.09
  0.9250 -3.59 to 2.60
• A - C 0.0211 -5.61 to -0.46
  0.0548 -6.11 to 0.05
• B - C 0.0582 -5.16 to 0.09
  0.1399 -5.68 to 0.61

10
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 Plt0.05 is maintained at study
  completion. An example (not for HTN study)
  illustrates this situation.

11
Example of Interim Analysis Stopping Guidelines
Figure Group sequential boundaries set at
overall 0.05 level of significance. Crossing
upper boundary benefit crossing lower boundary
harm. Z-value standardized treatment -
placebo difference in outcome.

12
Time-to-Event or Survival Analysis

• Suppose that, in HTN study, outcome time until
  dbp lt K, for some K.
• Each subject is observed for 87 56 days (or
  longer, in practice, due to continuous enrollment
  and a fixed termination date).
• Possible data
• Subject 1 2 3
  4 5 6 7 8 9 10
• Days to dbpltK 26 52 gt56 40 gt28
  45 29 gt56 gt56 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 lt 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 ProbTime gt t among groups for any
  time t.