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Statistics for Clinical Trials in Neurotherapeutics. Barbara C. Tilley, Ph.D. Medical University of South Carolina. Funding:. NIA Resource Center on Minority Aging 5 P30 AG21677. NINDS Parkinson’s Disease Statistical Center U01NS043127 and U01NS43128. Sample Size.

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Statistics for Clinical Trials in Neurotherapeutics

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Statistics for Clinical Trials in Neurotherapeutics

Barbara C. Tilley, Ph.D.

Medical University of South Carolina


NIA Resource Center on Minority Aging

5 P30 AG21677

NINDS Parkinson’s Disease Statistical Center

U01NS043127 and U01NS43128

Sample Size

Issues in Neurotherapeutics

  • What is the outcome?

  • How will this be measured

    • One or many measures of outcome?

  • How will you analyze the data?

  • (Nquery $700, STPLAN free, etc.)

Sample Size: Putting it all together

Continuous (Normal) Distribution

Need all but one: , , 2, , N

Z = 1.96 (2 sided, 0.05);

Z = 1.645 (always one-sided, 0.05,

95% power)

 = difference between means

2= pooled variance














Adjusting for Drop-outs/Drop-ins

  • 10% dropout, increasing sample size by 10% is not enough

  • Use: 1/(1-R)2

    Friedman, Furburg, DeMets

Sample Size for Multiple Primary Outcomes

  • Choose largest

    sample size for any

    single outcome.

  • If multiple aims, use

    largest sample size for

    any aim.

Sample Size: Food for Thought

  • Is detectable difference biologically/clinically meaningful?

  • Is sample size too small to be believable? WHERE DID YOU GET the estimate????

  • Report power (for design), not conditional power for negative study.

Sample Size: Keeping It Small

  • Study continuous outcome

    (if variability does not increase)

    • Updrs Score rather “above or below cut-point”

  • Study surrogate outcome where

    effect is large

    • Rankin at 3 months rather than stroke mortality

  • Reduce variability (ANCOVA, training, equipment, choosing model)

Sample Size: Keeping It Small

  • Difference between two means = 1

  • Standard deviation = 2;

    N = 64/group

  • Standard deviation = 1;

    N = 17/group


  • Parametric?

    • Normal

    • Binomial

  • Nonparmetric?

    • Ranked

Distribution of Barthel Index


Sample Size

Sample size to detect effect of size

observed in NINDS t-PA Stroke Trial


  • Non-parametric N = 507

  • Binary N = 335


  • Non-parametric N = 394

  • Binary N = 286

Multiple Comparisons

  • Different questions, can argue

    no adjustment (O’Brien, 1983)

    • Effect on blood pressure

    • Effect on quality of life

  • All pair-wise comparisons or

    multiple measures of same

    outcome, adjust

    • Pairwise comparisons of

      Drugs A, B, C (same outcome)

Multiple Comparisons

  • Bonferroni (or less conservative Simes, or Hockberg)

    • /#tests = 0.05/5 = 0.01

    • Sample size, use adjusted 

  • ANOVA methods – Tukey’s, etc.

    • Sample size for ANOVA

Bonferroni for Different Primary Outcomes, Same Construct

  • All outcomes measure same construct

    • Stroke recovery

    • PD progression

  • May lack power when most measures of efficacy are improved, but no single measure is overwhelmingly so.

  • Problem exacerbated when outcomes are highly correlated.

Use Global Tests When:

  • No one outcome sufficient or desirable

  • Outcome is difficult to measure and combination of correlated outcomes useful

Properties of Global Test

  • If all outcome measures perfectly correlated,

    • test statistic, p-value same as for single (univariate) test

    • power = power of univariate test

  • Assumes common dose effect

  • Power increases as correlation among outcomes decreases

O’Brien’s Non-parametric Procedure (Biomet., 1984)

  • Separately rank each outcome in the two treatment groups combined.

  • Sum ranks for each subject.

  • Compare mean ranks in the two treatment groups using

    • Wilcoxon or t-test

    • ANOVA if more than two treatments

Sample Size forGlobal Test

  • Use largest sample size for single outcome

NINDS t-PA Stroke Trial Binary Outcomes (Part II)

NINDS t-PA Trial Observed Agreement & Correlations for Binary Outcomes



  • Stratification

    • Age, prior stroke, years with PD, site

    • Greatest gain if N < 20

    • Too many strata, difficult to balance

      • 3 age x 2 years with PD x gender = 12

  • Blocking – balance number in each treatment group

    • Important if number expected per site is small

  • Minimization

    • Can be complicated to implement, cause delays

Interim Analyses

  • Who?

  • Why?

  • When?

  • How?

Stopping “Guidelines”







Reject Ho

  • O’Brien-Fleming

  • Pocock

  • Peto


Fail to Reject Ho


Standard Normal Statistic (Zi)

Reject Ho

# Looks

1 2 3 4 5

Intent-to-Treat (ITT)

Intent-to-treat means analyzing

ALL patients as randomized.

  • Patients lost to follow-up (LTF)

  • Patients who do not adhere to treatment

  • Patients who were randomized and did not receive treatment

  • Patients incorrectly randomized


  • Definition - replacing a value for those lost to follow-up or not adhering.

  • Imputation may or may not be ITT.

Optimal Approach


Optimal Approach Continued

  • Make follow-up a high priority

  • Monitor follow-up closely

  • Build in patient incentives

    • “gifts” for patients (t-shirts, mugs, etc.)

    • free parking, meal ticket

    • Transportation

  • Follow even those off treatment

Hypertension Detection and Follow-up Program/MRFIT

  • Outcome was mortality

  • HDFP 21/10,940

  • MRFIT 30/12,866

  • Used Death Index, Social Security, detectives

NINDS t-PA Stroke Trial

  • Four 3-month outcomes

    • Barthel,NIHSS,GOS, Rankin

  • NINDS Project Officer pushed for complete ascertainment

  • Study staff made house calls, searched medical records

  • 5/612 (<1%) lost to follow-up on at least one of the four outcome measures

  • Used worst value possible

NET-PD Futility StudiesLTF for 1-year outcome(Used worst outcome in assigned group)

  • FS-1 3/200

    • Creatine 2

    • Minocycline 0

    • Placebo 1

  • FS-2 4/213

    • GPI 3

    • CoQ10 1

    • Placebo 0

Handling Missing Values

  • Why?

  • How?

When Data Are Missing:Common Approaches

Subgroup Analyses (Sub-set)

  • Pre-specified based on rationale

    • NINDS t-PA Stroke Trial

      • Those randomized 0-90 minutes and 91-180 minutes from stroke onset

  • Post-hoc in the presence of interaction

    • (Yusuf, 1991)

Subgroup Analyses

  • The more subgroups examined, the more likely analyses will lead to finding a difference by chance alone.

    • 10 mutually exclusive subgroups;

    • 20% chance that in one group the treatment will be better than control and that the converse will be true in another

Example of Interaction (Effect Modification)

Example of Interaction(Effect Modification)

Lack of Interaction

Trial of Org10172 for Stroke (TOAST) Trial

N = 379(M) 238 (F) N=372(M) 239 (F)

Test for interaction p = 0.251

Pooled AnalysisCarotid Endarterectomy

Rothwell, 2004 NASCET &ECST

N (men) 4175 N(women) 1718 Test for interaction p = 0.007 (Cox model)

Pooled Analysis ECASS, Atlantis, NINDSKent 2005

N (men) 4175 N(women) 1718 Test for interaction p = 0.04 (logistic model)


  • Rubin, DB. More powerful randomization-based p-values in double blind trials with non-compliance. Statistics in Medicine (1998) 17:317-385.

  • Little R, Yau L. Intent-to-treat analysis for longitudinal studies with drop-outs. Biometrics (1996) 52:1324-1333.

  • NINDS t-PA Stroke Trial Study Group. Tissue Plasminogen Activator for Acute Stroke (1995) 333:1581-1587.

  • Curb JD, et al. Ascertainment of vital status through the national death index and social security administration. A J Epi (1985)121:754-766.

  • Multiple Risk Factor Intervention Trial Research Group. Multiple risk factor intervention trial: risk factor changes and mortality results. JAMA (1982) 248:1466-77.

EXTRA slides not presented


  • Retain only those patients who remain on treatment

  • Was used frequently in past in trials in rheumatoid arthritis

  • Not intent-to-treat

  • Obvious potential for bias

    • patients not responding to treatment drop-out

Last Observation Carried Forward

  • For those missing a final value, use most recent previous observation.

  • Potential for bias in disease with downward course

Worst case

  • Replace missing values with worst outcome

    • assumes that those who are lost to follow-up were not successfully treated

    • generally variance is not inflated

    • could inflate or deflate differences

Best Case/Worst Case

  • Replace missing values in treatment group by worst outcome and missing values in comparison group with best outcome.

    • Rarely used

    • Generally overly conservative as both treatment and placebo group drop-out for lack of efficacy.

Missing at Random

  • Drop-out at time t does not depend on unobserved outcomes at times t’> t, after conditioning on data up to time t.

  • Example:

    • a patient misses follow-up visit because she is not feeling well (small TIA’s) then has a major stroke a week later.

Missing at random

  • Ignore missing values

  • In survival analyses, censor at date of last follow-up

  • Use generalized estimating equations

  • Difficulties in assessing missing at random

  • Rarely is this assumption expected

Rubin’s Approach for Non-Compliance

  • Assume assignment to treatment (T) or control (C) has no effect on outcome for non-complying patients.

  • Model compliance status under the null hypothesis (no effect on outcome)

  • Compute average effect of assignment to T versus C for subset of T compliers.

Rubin’s Approach Continued

  • Few studies have “pure” non-compliers.

  • Pure non-compliers

    • those refusing surgery in surgical trial

    • those refusing medication after randomization

  • If patients take some medication, there may be carryover treatment effects

Little’s Approach to Imputation

  • Uses multiple imputation for patients who are missing information based on actual dose after drop-out if known or assumption.

  • Accounts for uncertainty in parameter estimates.

    • Model parameters drawn from posterior distn’, then missing values drawn from predictive distn’ conditional on drawn parameters.

Geller, et al

  • Raynaud’s Treatment Study

  • Model missing values using patient covariates at baseline to identify similar patient(s) with follow-up (neighbor)

  • Weights neighbor, sets weight for missing patient to zero

  • (Propensity Score)

Sample Size for Composite Favorable Outcome*

LTF Groups And Imputation Methods


Variables in The Imputation Model

Baseline risk factorsAgeNo College Education Low or High ETOH Consumption Sedentary life style Hx Diabetes Hx Cardiac Disease Hx Diabetes and Hx Stroke Hx Diabetes and Glasgow <5

Among the 12 group 3 patients: Primary endpoints imputed for 2 patients Event-free follow-up imputed for 10 patients

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