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# Statistics for Clinical Trials in Neurotherapeutics - PowerPoint PPT Presentation

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

### Funding:

NIA Resource Center on Minority Aging

5 P30 AG21677

NINDS Parkinson’s Disease Statistical Center

U01NS043127 and U01NS43128

### 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

+

)

s

4(Z

Z

2

2

a

b

=

2n

d

2

• 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

### Analysis

• Parametric?

• Normal

• Binomial

• Nonparmetric?

• Ranked

100

### Sample Size

Sample size to detect effect of size

observed in NINDS t-PA Stroke Trial

Barthel:

• Non-parametric N = 507

• Binary N = 335

Rankin:

• Non-parametric N = 394

• Binary N = 286

### Multiple Comparisons

• Different questions, can argue

• Effect on blood pressure

• Effect on quality of life

• All pair-wise comparisons or

multiple measures of same

• 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

### Randomization

• 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”

5.0

3.0

2.0

-2.0

-3.0

-5.0

Reject Ho

• O’Brien-Fleming

• Pocock

• Peto

Continue

Fail to Reject Ho

0

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

### Imputation

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

• Imputation may or may not be ITT.

### Optimal Approach

MAKE IMPUTATION UNECESSARY!

### 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

• Why?

• How?

### 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

### 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)

### References

• 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.

### Completers

• 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