1. Subhead Calibri 14pt, White
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution
Subhead Calibri 14pt, White
T. Wu, Z. Geng, S. Mukhopadhyay, Y.Gu

2. Disclosure
The support of this presentation was provided by AbbVie. AbbVie participated in the review and approval of the content. Tianshuang Wu, Ziqian Geng, Saurabh Mukhopadhyay, and Yihua Gu are employees of AbbVie, Inc.
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution JSM Aug 1st

3. Outline Motivation Introduction Simulation Application Summary
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution JSM Aug 1st

4. Motivation

5. Motivation
Key efficacy objective often comprises multiple primary and secondary endpoints in clinical trials.
UltIMMa-1&2 (Risankizumab): 2 primary, 15 secondary
Solo-1&2 (Dupilumab): 2 primary, 15 secondary
VOYAGE-1 (Guselkumab): 1 primary, 13 secondary
VOYAGE-2 (Guselkumab): 1 primary, 12 secondary
The optimal success of a trial often require simultaneous achievement of multiple endpoints, especially when the drug is not the first MOA coming into the market
UltiMMa-1&2 (risankizumab): American Academy of Dermatology Annual Meeting, February 2018, San Diego, CA, United States
Solo-1 & 2 (dupilumab): NE.L. Simpson, Engl J Med. DOI: /NEJMoa
VOYAGE-1 &2 (Guselkumab): Blauvelt et al. Journal of American Academy of Dermatology. Vol 76, Issue 3, Page
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution JSM Aug 1st

6. Motivation
Traditional sample size calculation treats endpoints as independent
Based on the assumption of response rates or means, generate n copy of random numbers.
Average the rejection frequency as an estimation of power.
For POS calculation, the posterior distributions of endpoints are also assumed to be independent.
Underestimate overall power/POS
Overestimate the sample size
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution JSM Aug 1st

7. Introduction

8. Introduction – our method
Estimates the correlation coefficient from historical data
Incorporates the correlations among endpoints in the Truncated Multi-Variate Correlated Normal Distribution
Utilizes the correlation matrix for both power and POS estimation
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution JSM Aug 1st

9. Procedure Power estimation: POS estimation:
For a given sample size, n, generate a large number of sets of ‘study data’ from a multi-variate truncated normal distribution with assumed means and variance matrix.
Average their rejection frequencies as an estimation of power.
Increase n until meeting the desired power.
POS estimation:
For a given sample size, n, generate a large number of sets of ‘underlying parameters’ from a multi-variate truncated normal distribution with assumed means and variance matrix.
Calculate power for each ‘underlying parameter’ using the technique above.
Average the power as an estimation of POS.
Increase n until meeting the desired POS.
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution JSM Aug 1st

10. Simulation

11. A naïve scenario
For simplicity we used compound symmetry structure for the assumption of endpoints. The common correlation coefficient would be denoted as 𝜌.
We performed simulation on the case of 2, 3, 4, 6 and 10 endpoints. For each case, the value of ρ=0 (independent), 0.1, 0.25 (represent weak correlation), 0.5 and 0.75 (represent strong correlation).
The number shown above the bars is the number of subjects per arm to achieve 80% power (to meet all endpoints simultaneously with 2-sided α=0.05).
The true response rate of treatment and competitor are assume to be 75% and 50%, regardless of how many endpoints we are considering.
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution JSM Aug 1st

12. Sample Size Reduction
10 percent sample size saving under moderate correlation coefficient (rho=0.5).
Note: in general, the larger the correlations are, the more sample size reduction would be expected.
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution JSM Aug 1st

13. Application

14. Application
The example below was modified from an actual randomized active comparator study.
The endpoints and the assumptions of response rates were:
Endpoint 1 (75% vs 57%)
Endpoint 2 (81% vs 56%)
Endpoint 3 (85% vs 62%)
Endpoint 4 (58% vs 38%)
The common correlation is estimated based on historical data
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution JSM Aug 1st

15. Application and expansion
To achieve 80% power, the sample size was 125 per arm utilizing the correlations, and 135 per arm under the independence assumption.
Given that the sample size in Phase 2 study was 60 per arm, 135 per arm would have a POS of 58% utilizing the correlations, and 46% under independence assumption.
In order to achieve 70% POS, we need 185 subjects per arm. The number would be 250 if we assume independence.
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution JSM Aug 1st

16. Summary

17. Summary
Traditional way of calculating sample size for achieving many endpoints overestimates the sample size.
Considering correlation will reduce the sample size, especially when the target is POS.
In practice, to be conservative we can use a ‘less correlated’ assumption.
Estimating Probability of Simultaneous Success with Multiple Endpoints Using Truncated Multi-Variate Correlated Normal Distribution JSM Aug 1st