ram c. tiwari associate director office of biostatistics, cder, fda [email protected]

Ram C. Tiwari Associate Director Office of Biostatistics, CDER, FDA [email protected]

Disclaimer This presentation reflects the views of the author and should not be construed to represent FDAs views or policies. Benefit-risk Assessment2

Outline Introduction Commonly-used Benefit-risk (BR) measures Methodology BR measures based on Global benefit-risk (GBR) scores and a new measure Bayesian approaches Power prior Illustration and simulation study Future work Benefit-risk Assessment4

Introduction The benefit-risk assessment is the basis of regulatory decisions in the pre- market and post market review process. The evaluation of benefit and risk faces several challenges. Benefit-risk Assessment5

Commonly used B-R measures Various measures have been proposed to assess benefit and risk simultaneously: Q-TWiST by Gelbert et al. (1989) Ratio of benefit and risk by Payne (1975) The Number Needed to Treat and the Number Needed to Harm by Holden et al. (2003) Global Benefit Risk (GBR) scores by Chuang-Stein et al. (1991) Benefit-risk Assessment6

BR categories A five-category multinomial random variable to capture the benefit and risk of a drug product on each individual simultaneously: BenefitNo benefit No AECategory 1Category 3 AECategory 2Category 4 withdrawal Category 5 Table 1: Possible outcomes of a clinical trial with binary response data Benefit-risk Assessment7

Example: Hydromorphone Data was provided by Jonathan Norton. Benefit-risk Assessment8

GBR scores Benefit-risk Assessment9

Methodology: BR measures BR measures based on the global scores proposed by Chuang-Stein et al. BR measures based on the global scores are for each arm (treatment and comparator) separately. BR_Linear can take a continuous value on a scale of -4 to 4 (inclusive). Benefit-risk Assessment10

Methodology: New BR measure A new indicator based measure is proposed: BR_Indicator compares two arms simultaneously. It takes a integer value between -6 to 6 (inclusive). Benefit-risk Assessment11

Methodology: Dirichlet prior Dirichlet distribution is used as the conjugate prior for multinomial distribution, and the posterior distribution of the five-category random variable is derived at each visit using sequentially updated posterior as a prior. Benefit-risk Assessment12

Methodology: Sequential Updating Sequential updating of the posteriors are given by: The posterior mean (i.e., Bayes estimate) and 95% credible interval for each of the four measures are obtained using a Markov chain Monte Carlo (MCMC) technique. Benefit-risk Assessment13

Methodology: Decision Rules For a BR measure, If the credible interval include the value zero, the benefit does not outweigh the risk; If the lower bound of the credible interval is greater than zero, the benefit outweighs the risk; If the upper bound of the credible interval is less than zero, the risk outweighs the benefit. Benefit-risk Assessment14

Methodology: Power Prior Power prior (Ibrahim and Chen, 2000) is used through the likelihood function to discount the information from previous visits, and the posterior distribution of the five-category random variable is obtained using the Dirichlet prior for p and a Beta (1, 1) as a power prior for. Benefit-risk Assessment15

Methodology: Model Fit The model fit of the two models (with and without power prior) is assessed through the conditional predictive ordinate (CPO) and the logarithm of the pseudo-marginal likelihood (LPML). The larger the value of LPML, the better fit the model is. Here, n (i) is the data with n i removed. Benefit-risk Assessment16

Back to our example: Hydromorphone Benefit-risk Assessment17

Benefit-risk Assessment Illustration: Posterior Means and 95% Credible Intervals for BR_Linear Measure without power prior with power prior 18

Benefit-risk Assessment Illustration: Posterior Means and 95% Credible Intervals for BR_Indicator Measure without power prior with power prior 19

Benefit-risk Assessment a. The model without power prior b. The model with power prior Illustration: Results 20

Benefit-risk Assessment Illustration: Posterior Means and 95% Credible Intervals for Power Prior Parameter 21

Illustration: Model Fit LPML values TreatmentControl Model without power prior-14.230-14.209 Model with power prior-6.432-6.190 Benefit-risk Assessment22

Simulation study Correlated longitudinal multinomial data are simulated using the R package SimCorMultRes.R, which uses an underlying regression model to draw correlated ordinal response. Two scenarios are simulated: The treatment arm is similar to the control arm in terms of benefit-risk; The treatment arm is better than control arm in the sense that the benefit outweighs risk. Benefit-risk Assessment23

Scenario 1: Treatment benefit does not outweigh risk compared to control Scenario 2: Treatment benefit outweighs risk compared to control Benefit-risk Assessment Simulation study: Scenarios 24

Treatment benefit does not outweigh risk compared to control Benefit-risk Assessment a. The model without power prior b. The model with power prior Simulation study: Scenario 1 25

Treatment benefit outweighs risk compared to control Benefit-risk Assessment a. The model without power prior b. The model with power prior Simulation study: Scenario 2 26

Scenario 1: Treatment benefit does not outweigh risk compared to control Scenario 2: Treatment benefit outweighs risk compared to control Benefit-risk Assessment Simulation study: Results 27

Benefit-risk Assessment Simulation study: Model Fit LPML values TreatmentControl Scenario 1: Model without power prior-23.536-23.354 Model with power prior-8.472-7.667 Scenario 2: Model without power prior-27.099-21.840 Model with power prior-8.532-8.393 28

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Future work in BR assessment Frequentist approaches: Bootstrap approach General linear mixed model (GLMM) approach Other Bayesian approaches: Normal priors Dirichlet process Benefit-risk Assessment30

Bootstrap Approach Approximate underlying distribution using the empirical distribution of the observed data; Resample from the original dataset; Calculate the estimates and confidence intervals (CIs) of the BR measures based on the bootstrap samples; Percentile bootstrap CIs; Basic bootstrap CIs; Studentized bootstrap CIs; Bias-Corrected and Accelerated CIs. Apply the decision rules. Benefit-risk Assessment31

Bootstrap Approach-Results Benefit-risk Assessment32

General linear mixed model (GLMM) approach Within each arm (T or C), the i th subject falls in the j th category (vs. the first category) at k th visit can be modeled as, where, 0 is the baseline effect assumed common across all categories, j is the category effect, and k is the longitudinal effect at k th visit, with and,. Benefit-risk Assessment33

GLMM approach Note that different variance-covariance structures can be used for ( 1, 2, 8 ), to model the longitudinal trend. Compound-symmetry Power covariance structure Unstructured covariance structure The estimates of the confidence intervals of the global measures can be derived from Monte Carlo samples, and the decision rules can be determined based on the confidence intervals. Benefit-risk Assessment34

General linear mixed model approach-Results Benefit-risk Assessment35

Bayesian approaches with GLMM ( 0, j ; j=1,,5)~ independent Normal with means 0 and large variances; Variance parameters~ IG Dirichlet Process Approach: Let 0 to depend on subjects, that is, assume that 0i |G ~ iid G, with G~ DP(M, G0), M>0 concentration parameter and G0 a baseline distribution such as a normal with mean 0 and large variance. j ; j=1,,5 are independent normal with means 0, and large variances. The posterior distributions of the probability and the global measures can be derived, and the decision rules can be determined based on the credible intervals. Benefit-risk Assessment36

Discussion Quantitative measure of benefit and risk is an important aspect in the drug evaluation process. The Bayesian method is a natural method for longitudinal data by sequentially updating the prior; Power prior can be used to discount information from previous visits. Frequentist approaches such as bootstrapping method and general linear mixed model can be applied for benefit risk assessment. Continuous research in longitudinal assessment of drug benefit-risk is warranted. Benefit-risk Assessment37

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Selected References Gelber RD, Gelman RS, Goldhirsch A. A quality-of-life oriented endpoint for comparing treatments. Biometrics. 1989;45:781-795 Payne JT, Loken MK. A survey of the benefits and risks in the practices of radiology. CRC Crit Rev Clin Radiol Nucl Med. 1975; 6:425-475 Holden WL, Juhaeri J, Dai W. Benefit-Risk Analysis: A Proposal Using Quantitative Methods, Pharmacoepidemiology and Drug Safety. 2003; 12, 611616. 154 Chuang-Stein C, Mohberg NR, Sinkula MS. Three measures for simultaneously evaluating benefits and risks using categorical data from clinical trials. Statistics in Medicine. 1991; 10:1349-1359. Norton, JD. A Longitudinal Model and Graphic for Benefit-risk Analysis, with Case Study. Drug Information Journal. 2011; 45: 741-747. Ibrahim, JG, Chen, MH. Power Prior Distributions for Regression Models. Statistical Science. 2000; 15: 46-60. Benefit-risk Assessment39

Benefit-risk Assessment Q & A 40

ram c. tiwari associate director office of biostatistics, cder, fda [email protected]

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