Global Test Statistic to Assess a Treatment Effect on Multiple Outcomes

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Global Test Statistic to Assess a Treatment
Effect on Multiple Outcomes

• Mei Lu, Ph.D.
• Dept. of Biostatistics Research Epidemiology

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Outline

• -Motivations
• -Quasi-likelihood vs. likelihood estimation
• -Working correlation matrix
• -Applications
• -Summary

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Motivation NINDS t-PA Stroke Trials

• National Institute of Neurological Disorders and
  Stroke (NINDS), NIH
• Coordinating Center at Henry Ford Health System
  for data collection, management, and analysis
• 8 clinical centers participated and 43 hospitals
  involved in patients enrollments (USA)

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Trial Design/Treatment

• Design
• Phase II/III, double-blind, and
  placebo-controlled
• - Stratified randomization by time, 0-90 and
  91-180 minutes of the stroke onset, and by
  clinical centers
• Treatment of t-PA/Placebo
• Dose .9 mg/kg (estimated body wgt.)
• Max. dose 90mg, 10 bolus, remainder over 60
  minutes

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Trial Design/Endpoints

• Part 1 t-PA Activity (primary)
• Early clinical improvement at 24 hours after
  stroke
• Part 2 t-PA efficacy (primary)
• Hypothesis there is t-PA effect on stroke
  recovery at 3 months
• The stroke recovery is defined as a set of binary
  outcomes
• Barthel gt 95
• Rankin of 0 or 1 (no significant disability or
  symptoms)
• Glasgow of 1 (good recovery)
• NIHSS of 0 or 1

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Motivation Animal Stroke Model

• Design rats, subjected to stroke, received
  various doses of MSCs/PBS at 24h after stroke,
  and had the functional assessments completed at
  14 days after stroke.
• Hypothesis there is MSCs effect on stroke
  recovery
• The stroke recovery was measured from three
• functional tests and they have continues outcomes
• Adhesive-Removal patch test,
• Rotarod test and
• mNSS

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Correlated Outcomes

• Repeated measures/Cluster data same subject,
  same measure and successive times, or same
  subject with multiple endpoints

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Generalized linear model (GLM)
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Generalized Estimating Equations (GEE)

• , where V is a
  known function (working variance matrix) and ? is
  scale parameter (the over dispersion parameter)
• Quasi-score depends on Yi only through its mean
  and variance
• Yi are not necessary to be specified as normal

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GEE vs. GLM or MIXED in SAS

• vs. var(Yi)
• GLM or MIXED in SAS --- MLE assuming that Yi
  is normal
• GEE---Quasi LE (QLE) assuming that var(Yi)
  is function of ?i
• QLEMLE if only if V is the true covariance
  of Yi

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Correlation
For unit i
1. Independent Vi is diagonal 2. Exchangeable
All measurements on the same unit are equally
correlated 3. Unstructured correlation no
assumptions about the correlations
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Applications- Global test for a treatment effect
on multiple endpoints

• Design

Software Proc GENMOD SAS 9.0 or GEE Macro 2.0
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Properties of Global Test

• Calculate the global estimate (test statistic)
  assuming a common dose effect
• Take the correlation amount of the outcomes into
  account
• If global test is significant at 0.05 level,
  treatment effect can be evaluated on each single
  endpoint at level 0.05
• Power gt power of univariate test
• Pocock et al. Biometrics 1987

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Sample Size/Power Calculation

• The global test is more efficient than a single
  outcome if outcomes are correlated in the same
  direction (Legler et al., 1995) -Legler JM,
  Lefkopoulou M, Ryan L. Efficiency and power of
  tests for multiple binary outcomes. JASA 90430,
  680-693. 1995.
• Diggle, Liang and Zeger (1994) - Analysis of
  Longitudinal Data. Clarendon Press, Oxford.

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Global Test for NINDS t-PA Trials
Hypothesis there is a t-PA treatment effect on
stroke recovery, measured from four binary
outcomes Four (4) binary endpoints were collected
on each subject to measure the stroke recovery
with 312 patients in Part 2 and 291 in Part
1. Link function as logit and variance as
binominal with unspecified covariance structure
using GEE National Institute of Neurological
Disorders and Stroke rt-PA Stroke Study Group.
Tissue plasminogen activator for acute ischemic
stroke, New England Journal of Medicine, 333,
1581-1587 (1995).
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Global Test for Animal Stroke Model

• Hypothesis there is MSCs effect on stroke
  recovery, measured from three functional tests
  (continue outcomes), Adhesive-Removal patch test,
  Rotarod test and mNSS
• Rats, subjected to stroke, were randomized into
  one of three groups (0 MSCs/BPS, 1x106 MSCs and
  3x106 MSCs) at 24h after stroke
• -Lu M, Chen J, Lu D, Yi L, Mahmood A, Chopp M.
  Global test statistics for treatment effect of
  stroke and traumatic brain injury in rats with
  administration of bone marrow stromal cells. J
  Neurosci Methods 2003 128(1-2)183-190.

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Global Test for Animal Stroke Model

• Before conducting the global test, we need to do
  the following
• - Check the consistency of the outcome scoring
• Standardize the outcomes
• significant improvement on functional recovery
  compared to controls based on the global test
  p0.06, marginal differences on functional
  recovery between MSC dose 1 x 106 and 3 x 106

14 days after the treatment Adhesive-Removal (seconds) Mean Std Rotarod () Mean Std mNSS (score) Mean Std
Controls (n6) 86.3 28.0 68.8 16.1 7.3 0.8
1x106 MSCs (n6) 52.0 22.2 65.6 21.5 5.2 3.1
3x106 MSCs (n7) 33.6 15.8 73.5 18.3 4.6 1.8
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Summary

• Global test statistics can assess the common
  treatment effect on multiple correlated
  outcomes.
• Global test is an efficient test statistic
  when outcomes are consistent and correlated in a
  same direction. The less correlation, the more
  power, therefore the higher efficiency
• Before using the global test, check
  consistency of the outcomes and re-scaled
  outcomes if they are continuous.

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Summary

• GEE vs. GLM
• -use GLM when data are normal
• -GEE has a more robust estimation, when data are
  not normal
• Do not use GEE
• for conditional logistic regression (family data
  )
• If there is negative correlation among the
  outcomes (e.g.,30? or more)