Sequential analysis in clinical trials and epidemiological studies

1
Sequential analysis in clinical trials and
epidemiological studies

• Ingeborg van der Tweel
• Centre for Biostatistics
• Utrecht University
• 25-11-2004

2
Sequential methods in statistics

• the whole of life is sequential,
• for our future actions are conditioned
• to some extent by our past experience
• (Wetherill and Glazebrook, 1986)

3
Outline

• Sequential analysis in
• clinical trials
• epidemiological studies
• quality control
• safety monitoring

4
Clinical Trial

• recruitment and inclusion sequentially
• ?
• response available sequentially
• ?
• analysis sequentially

5
Interim analysis

• after each new response or group of responses
• an interim analysis is performed
• ?
• enough evidence to stop the trial
• or
• continue the trial
• ? continuous sequential or group sequential
  analysis

6
Why interim analyses?

• Ethics superiority of a treatment
• Safety inferiority of a treatment /
• toxicity of a treatment
• Economy costly therapy
• no clinically relevant difference in
  effect between treatments

7
ICH E9 (International guideline)Statistical
principles for clinical trials

• 4.5
• The goal of an interim analysis is to stop the
  trial early
• if the superiority of the treatment under
  study is clearly established,
• if the demonstration of a relevant treatment
  difference has become unlikely or
• if unacceptable adverse effects are apparent.

8
Effect of interim analyses

• total significance
• number of analyses level ?
• 1 0.05
• 2 0.08
• 3 0.11
• 4 0.13
• 5 0.14
• 10 0.19

9
Effect of interim analyses

• The more often one analyses the accumulating
  data, the greater the chance of eventually and
  wrongly detecting a difference, and thus drawing
  incorrect conclusions from the trial.
• Increase in overall significance level ?
• decrease in nominal significance level ?
• per interim analysis

10
Critical Z values per interim analysis (overall
?0.05)



. Pocock ---- Haybittle-Peto ___ OBrien-Fleming
11
RST vs boundaries

• Repeated Significance Tests (Pocock, OBF, HP)
• fixed number and timing of the
• interim analyses
• More flexible (alpha-spending function) design
• by Lan DeMets
• Most flexible is the boundaries approach
• (Wald, Whitehead)

12
A. Wald (1947)

• Sequential Probability Ratio Test (SPRT)

• stop and reject H0 as soon as Ln ? A A
  (1-?)/?
• stop and accept H0 as soon as Ln ? B B ?/ (1-
  ?)
• continue as long as B lt Ln lt A

13
A (hypothetical) example

• Cross-over trial on treatment of hypertension
• standard treatment S and new treatment N
• probability of superiority of N over S ? 0.7
• under H0 ? 0.5
• one-sided ? 0.05 power 1- ? 0.80

14
A (hypothetical) example
15

A (hypothetical) example


after n13 patients H0 can be accepted
16
J. Whitehead (University of Reading, UK)

• flexible boundaries approach
• continuous and group sequential testing
• SPRT, TT, . (one- and two-sided)
• outcome dichotomous, Normal, survival,
• H0 ? 0 vs H1 ? ? ?R
• test statistics V (amount of information)
• and Z (effect size)

17
The (hypothetical) example

• Z Y n?0 observed expected
• Y number of preferences for N
• n total number of patients with a preference
• ?0 probability of a preference for N under H0
• Z Y n/2 under H0
• V n ?0(1- ?0) n/4 under H0
• ?R log(OR) log(0.7x0.5)/(0.3x0.5) 0.847

18
The (hypothetical) example a (truncated) SPRT
after n13 patients H0 can be accepted
19
The (hypothetical) example a triangular test
(TT)
after n14 patients H0 can be accepted
20
Important

• on average, less observations necessary to come
  to a decision with the same type I and type II
  errors
• ? sample size is not fixed beforehand, but
  stochastic

21
An example

• Amyotrophic Lateral Sclerosis (ALS)
• progressive weakness in skeletal muscles leading
  to death due to respiratory failure
• 50 of the patients do not survive 3 years
• no medical treatment available yet
• Trial to compare placebo to dietary supplement
• possible positive effect on muscle strength

22
ALS-example (continued)

• death from any cause, tracheostomy and persistent
  assisted ventilation were considered events for
  survival analysis
• cumulative survival after 16 months
• with placebo 60
• with dietary supplement ? 80
• one-sided ?0.05 power 1-?0.90
• fixed total number of events ? 56
• fixed total number of patients ? 190

23
ALS-example (continued)

• Fixed sample analysis can not take place before
  all patients are included, followed-up and
  analyzed.
• Total duration
• duration of the inclusion period
• 16 months after inclusion of the last patient

24
ALS-example (continued)

• Ethical considerations
• minimize the burden for ALS-patients
• total trial duration as short as possible
• number of included patients as small as possible
• Enough evidence? ?STOP

25
ALS-example (continued)

• Hazard Ratio log(0.8) / log(0.6) 0.437
• ?R -log(HR) 0.828
• Z observed number of events in the control
  group
• expected number of events under H0
• V ? (number of events)/4 (11 randomisation)
• Z²/V logrank test statistic

26
ALS-example (continued)
27
ALS-example (continued)

• Lower boundary was crossed after 34 events in 164
  included patients ? accept H0
• Eventually 175 patients included
• placebo 30 / 87 died
• supplement 28 / 88 died
• Adjusted HR 0.78 (95 CI 0.47 1.48)
• No real gain in number of patients,
• but in follow-up time

28
Epidemiological studies

• Why a sequential analysis?
• efficiency and economical aspects
• quality control
• savings in money, time, biological samples,
  ...
• screening of new hypotheses

29
Epidemiological studies

• the DOM project a breast cancer screening
  programme in Utrecht and surroundings
• biological material stored in a biobank
• regional cancer registration ? cases
• large number of interesting hypotheses
• vs
• limited number and amount of biological samples
• ? efficient statistical methods needed

30
data OL vd Hel et al (1998)
11 matching
13 matching
cohort-nested case-control study relating
exposure to the MTHFR-gene to the occurrence of
rectal cancer (2?0.05, power 1-?0.80, ?R0.5)
31
data OL vd Hel et al (2002)
non-hierarchical GxE-interaction, breast
cancer P(G)0.30, P(E)0.30, 2?0.05, 1-?0.80,
OR2 Nfixed 308, Nseq 5x44 220 ? 29 gain
32
data OL vd Hel et al (2002)
hierarchical GxE-interaction breast cancer
P(G)0.30, P(E)0.30, 2?0.05, 1-?0.80,
OR2 Nfixed 674, Nseq 9x44 396 ? 41 gain
33
Quality control

• MR de Leval et al.
• Analysis of a cluster of surgical failures
• J Thorac Cardiovasc Surg (1994)107914-924
• 104 neonatal arterial switch operations for
  transposition of the great arteries
• 1 in the first 52 patients
• then nrs 53, 55, 59, 63, 64, 67, 68
• H0 p0.02 versus H1 p0.05
• ? 0.05, power 0.80

34
Quality control(MR de Leval et al (1994))

35
Safety monitoring

• Example
• RCT in head injury
• active drug vs placebo
• evaluation of functional status after 6 months
• safety monitoring of mortality within 21 days
• placebo 21-day mortality rate 0.35
• If exp. 21-day mortality rate is larger than
  0.52,
• it is undesirable to continue the trial

36
Safety monitoring

• cum. nr of patients
• date of interim active placebo
• died entered died entered
• 07/02/1994 0 16 4 14
• 27/04/1994 1 33 7 27
• 09/05/1994 4 49 12 44
• 26/08/1994 6 64 14 58
• 30/11/1994 8 76 17 77
• 05/05/1995 14 118 26 117
• 28/06/1995 18 139 27 134
• 04/08/1995 20 153 28 150
• 21/11/1995 29 190 38 184
• 17/05/1996 33 230 43 223

37
Safety monitoring
38
Newer statistical methods

• W.G. Cochran (1959)
• In the sequential trial, at the beginning the
  doctor is forced to make decisions about the
  desired sensitivity of the trial which he can
  dodge in the fixed-size trial.
• But to make an intelligent choice of the number
  of patients in a fixed-size trial, the same
  questions, or similar ones must be answered.
• When sequential trials are better explained and
  better understood, they should not be any harder
  than fixed-size trials.
• In Quantitative methods in human pharmacology and
  therapeutics, ed D.R. Laurence, pp 119-143,
  London Pergamon.

39
Conclusion

• Sequential design and analysis
• of clinical trials and epidemiological studies
• could be considered more often for
• ethical reasons
• superiority or inferiority of a treatment
• toxicity
• efficiency and economical reasons
• quality control
• savings in money, time, biological samples,
  ...
• screening of new hypotheses

40
PEST 4.4 (2004)
41
Some literature

• Lewis JA.
• Statistical principles for clinical trials (ICH
  E9).
• An introductory note on an international
  guideline.
• Stat in Med 1999 (18) 1903-1942
• Whitehead J.
• The design and analysis of sequential clinical
  trials.
• Chichester Wiley 1997 (rev. 2nd ed.)
• PEST 4.4 Operating Manual. MPS Research Unit.
• Reading the University of Reading 2004
• Wetherill GB, Glazebrook KD.
• Sequential methods in statistics, 3d ed.
• London Chapman and Hall, 1986.

42
Some literature

• Todd S, Whitehead A, Stallard N, Whitehead J.
• Interim analyses and sequential designs in phase
  III studies.
• Br J Clin Pharmacol 2001 (51) 394-399
• Van der Tweel I, Schipper M.
• Sequentiële analysen in klinisch en
  epidemiologisch onderzoek.
• NTvG 2002 (146) 2348-2352 (in Dutch)
• Groeneveld GJ, Veldink JH, Van der Tweel I, ,
  van den Berg LH.
• A randomized sequential trial of creatine in
  amyotrophic lateral sclerosis. Ann Neurol 2003
  (53) 437-445
• Van der Tweel I.
• Application and efficiency of sequential tests
  in matched case-control studies. PhD thesis.
  Utrecht University. March 2nd, 2004
• Baksh M.F.
• Sequential tests of association with
  applications in genetic epidemiology. PhD thesis.
  University of Reading. 2002

43
Some literature

• Baksh MF, Todd S, Whitehead J, Lucini MM.
• Design considerations in the sequential analysis
  of matched case-control data.
• Stat in Med (2004) to appear
• Van der Tweel I, Schipper M.
• Sequential tests for gene-environment
  interactions in matched case-control studies.
• Stat in Med (2004) to appear