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Multiple Endpoint Testing in Clinical Trials – Some Issues & Considerations. Mohammad Huque, Ph.D. Division of Biometrics III/Office of Biostatistics/OPaSS/CDER/FDA 2005 Industry/FDA Workshop, Washington. DC. Disclaimer.

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Multiple Endpoint Testing in Clinical Trials – Some Issues & Considerations

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Multiple endpoint testing in clinical trials some issues considerations l.jpg

Multiple Endpoint Testing in Clinical Trials – Some Issues & Considerations

Mohammad Huque, Ph.D.

Division of Biometrics III/Office of Biostatistics/OPaSS/CDER/FDA

2005 Industry/FDA Workshop, Washington. DC


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Disclaimer

  • Views expressed here is that of the presenter and not necessarily of the FDA


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Sources of Multiplicity in Clinical Trials

  • Multiple endpoints 

  • Multiple comparisons

  • Interim analysis

  • Subgroup analysis

  • Selection of covariates in an analysis model

  • Others


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OUTLINE

  • Type I error concept and type I error control when testing for multiple endpoints. Complexities?

  • Multiple endpoints are often triaged into primary, secondary and other types of endpoints. Reasons for doing so and how these endpoints are tested?

  • Sequential testing of endpoints - no alpha adjustment is needed. Issues and fixes?

  • Some trials require that 2 or more endpoints must show effects for clinical evidence. Reasons for doing so and consequences?

  • Composite endpoints. Underlying concepts and complexities?


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Trial has a single endpoint to test – type I and type II errors

  • Conduct a test for claiming that a new treatment is beneficial

  • α = Probability of the Type I error

  • β = Probability of the Type II error (power = 1- β )


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Trial has multiple endpoints to test

  • Consider a two arm superiority trial, a test treatment versus a control

    Endpoints: y1, y2, …, yK

    Multiple Null Hypotheses: F = {H01, H02, …, H0K}

    H0j: δj = 0, Haj δj ≠ 0, j =1, …, K


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Trial has multiple endpoints to test

  • Two scenarios:

    (A) In the family F all are true null hypotheses

    (B) Some may be true null hypotheses, and some may be false null hypotheses, but their true state are unknown.


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Testing under scenario (A)

  • Scenario (A) and the trial has 3 endpoints y1, y2, and y3

  • A test procedure can give type I error in multiple ways: (-, -, +), (-, +, -), (+, -, -), (-, +, +), (+, -, +), (+, +, -), (+, +, +). These are chance events because of multiplicity of tests when in fact there is no treatment benefit for any of the endpoint.

  • α0 = Pr {of at least one of these chance events | test procedure, H0}, H0= ∩H0j


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Testing under scenario (A)

  • α0is called global alpha (or overall alpha). Also, called the familywise type I error rate (FWER) under H0, where

  • H0= ∩H0j is the global null hypothesis.

  • A test procedure for testing H0 is called a global test procedure


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Global Test procedures

  • Useful for non-specific global claims. Difficulty in interpreting the result. Type I error rate can remain inflated for specific claims.

  • Examples: Simes test, O’Brien’s OLS/GLS tests, Hotelling’s T2 test (Sankoh et al, DIA Jr.,1999)


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Testing under scenario (B)

  • Some of the null hypotheses F = {H01, H02, …, H0K} may be true null hypotheses and some be false, but its not known which ones are which.

  • Question: Is there a treatment effect specifically for the endpoint y1?

  • For answering this question, the null hypothesis is not a single null hypothesis like a global null hypothesis, rather it is a class of null hypothesis configurations in which there is no treatment effect for y1, and all possible scenarios for treatment effects for the remaining endpoints y2, …, yK


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Testing under scenario (B)

  • Consider 3 endpoints y1, y2, and y3.

  • Question: Is there a treatment effect specifically for the endpoint y1?

  • Null hypothesis configurations F1for testing for treatment effect specifically for the endpoint y1:

    F1 = { (δ1 = 0, δ2 = 0, δ3 = 0),

    (δ1 = 0, δ2 = 0, δ3 ≠ 0),

    (δ1 = 0, δ2 ≠ 0, δ3 = 0),

    (δ1 = 0, δ2 ≠ 0, δ3 ≠ 0)}.


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Control of FWER(two types)

  • Weak control

    • Control FWER only under the global null configuration

  • Strong control

    • Control FWER under all null configurations

    • Specificity property -- useful for making specific claims.

    • Examples of methods: Bonferroni, Holm, Hochberg*, closed statistical tests, and other methods

      *with some caveats


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Triaging of multiple endpoints into meaningful families by trial objectives

1) Prospectively defined

2) FWE controlled

  • Two important families

Primary endpoints

Secondary endpoints

Exploratoryendpoints

(usually not prospectively defined)

  • Primary endpoints are primary focus of the trial. Their results determine

  • main benefits of he clinical trial’s intervention.

  • Secondary endpoints by themselves generally not sufficient for characterizing

  • treatment benefit. Generally, tested for statistical significance for extended

  • indication and labeling after the primary objectives of the trial are met.


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Statistical methods

  • Prospective alpha allocation schemes (PAAS) – Moyé (2000)

    • Spend alpha1 for the primary endpoints and the remaining alpha for the secondary endpoints - FWER is controlled


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Statistical methods

  • Parallel gatekeeping strategies for clinical trials –

    • Dmitrienko-Offen-Westfall (SM 2003)

    • Chen-Luo-Capizzi (SM 2005)

  • Allows testing of secondary endpoints when at least one of the primary endpoints exhibits a statistically significant result

  • These methods controls FWER for both the primary and secondary endpoints in the strong sense.


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Sequential testing of multiple endpoints

  • A fixed sequence approach allows testing of each of the k null hypotheses at the same significance level of α without any adjustment, as long as the null hypotheses to be tested are hierarchically ordered and are tested in a pre-defined sequential order.

  • Hierarchical ordering of null hypotheses can be achieved, for example, by their clinical relevance.


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Sequential testing of multiple endpoints

For this fixed-sequence approach, however,

there are two caveats:

  • Pre-specification of the testing sequence

  • No further testing once the sequence breaks

  • Problem: when the sequence breaks and the next p-value is extreme (e.g., p1= 0.50, p2= 0.001)


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A flexible fixed-sequence approach

Test H(02) at

Level α

H(01) is rejected

Test H(01) at

Level α1

Test H(02) at

Level γ

H(01) is rejected

e.g., α1 = 0.04, α = 0.05, γ = 0.0104, ρ = 0

(γ = 0.0214, ρ = 0.8)


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Example: flexible fixed-sequence method


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Some trials require that 2 or more endpoints must show effects

Examples:

  • Alzheimer trial

    • (win on ADAS-Cognitive Sub-scale) and (win on Clinician’s Interview Based Impression of Change)

  • Many other examples (PhRMA draft paper)

    Main Reason:

  • Clinical expectations of the desired clinical benefit

    (concept beyond statistics)


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Adjustments in the Type I error rate - Some wining criterion require adjustments and some don’t

Adjustment by Sidak’s method on accounting for correlation

Note: Which method to use depends on on the clinical decision rule set in advance


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Power ComparisonCase of K=2 endpoints:


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Loss in Power when win in all endpointsK=# of endpoints


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Sample Size Increase (1) When Win in All K Endpoints Compared to Single Endpoint Case

Alpha = 0.025 (1-sided), Power = 0.90

Correlation K = 2K=3K=4

0.0 22.8% 35.9% 45.0%

0.3 21.1 33.1 41.2

0.4 20.2 31.7 39.7

0.5 19.1 29.8 37.3

0.6 17.7 27.5 34.4

0.7 15.9 24.6 30.7

0.8 13.5 20.8 25.8

0.9 10.0 15.3 18.9

(1)Calculations using mutivariate normal distribution of the test statistics comparing active treatment versus placebo for a 2-arm trial, assuming same delta/sigma for all K endpoints


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Composite Endpoints

Two types -

  • Total score or index based on a rating scale, e.g., HAMD totals in depression trials, ACR20/ACR70 in rheumatoid arthritis trials

    Issues: validity and reliability


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Composite Endpoints

Another Type

  • Composite endpoint is defined in terms of the time to the first “event”, where event is one of several possible event types

    LIFE study: Composite of cardiovascular death, stroke and myocardial infraction events.


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Composite Endpoint Issues

Life Study

The Composite endpoint was significantly positive. However, analysis of the first events by individual components and sub-composite endpoints indicate overall composite result mainly due to reduction in fatal and non-fatal stroke.

Issue:

How to interpret composite endpoint results? How to characterize benefits in terms of the component endpoints?


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Extent of multiplicity adjustments between endpoints

correlation

high

Practically no adjustments

Small

adjustments

Good case

for combining

endpoints

Large

adjustments

low

high

low

Homogeneity of treatment effects across endpoints


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Concluding Remarks

  • For endpoint specific claims – strong control of the type I error is needed

  • Parallel gate-keeping strategies can be used for the primary and secondary endpoint claims

  • Flexible sequential test procedure can be used to gain power of the test

  • There is a scientific basis when a reasonable clinical decision rule asks for statistically significant efficacy results in more than 1 endpoint – issue of loss of power?

  • When 4 or more endpoints included as primary (e.g., arthritis trials), and homogeneity of treatment effects acress endpoints is expected - a composite or responder endpoint approach will be effective.


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