1 METHODS FOR DETERMINING SIMILARITY OF EXPOSURE-RESPONSE BETWEEN PEDIATRIC AND ADULT POPULATIONS Stella G. Machado, Ph.D. Quantitative Methods and Research Staff Office of Biostatistics/OPASS/CDER/FDA CLINICAL PHARMACOLOGY SUBCOMMITTEE MEETING NOV 2003

2 ACKNOWLEDGEMENTS Substantial contribution from my colleague Meiyu Shen ideas from Yi Tsong, James Hung, Donald Schuirmann, Scott Patterson, Walter Hauck and Sharon Anderson, Peter Lee, C. Naito, K. Akihiro, and many others.

3 INTRODUCTION General method described for comparing PK/PD response curves in 2 populations: –Pediatric versus Adult populations –Other population groups, eg, ethnic region, gender Exposure: dose, AUC, Cmin, etc Response: biomarkers, clinical endpoints

4 BRIDGING PK/PD STUDIES Goal is to evaluate similarity in PK/PD relationships in Adult (original) and Pediatric (new) Populations –Conclude similarity similarity with some dose regimen modification lack of similarity Absence of precise guidance as to how this should be done Exploratory, not confirmatory, approaches needed

5 DRUG X Scatter plot of Y vs. C for 2 populations How to establish similarity?

6 DRUG X: New and Original populations: PD vs. PK

7 STEPS IN THE STATISTICAL APPROACH Suppose data from Original and New Populations: –original (adult): n 0 patients, measure Y and C –new population (pediatrics): n 1 patients, measure Y and C –concentration measurements generally different, unless data from concentration controlled trial

8 STEPS IN THE STATISTICAL APPROACH PK/PD response curves: –to establish similarity, need to compare the average shapes of response curves, taking account variability –response curve Y depends on exposure C, and unknown parameters  : Y = f(C,  ) may have different parameters  in the two populations

9 DRUG X: PK/PD scatter plot with loess fits

10 STEPS IN THE STATISTICAL APPROACH assess similarity between responses at all concentrations likely to be encountered distance between the curves – shape comparison account for variability of the response need “Equivalence” type approach, not hypothesis tests showing that the responses are not significantly different

11 HYPOTHETICAL:SIMPLEST SITUATION focus on single exposure C Reduces to usual equivalence-type analysis approach Response metric of interest for comparison could be: –average response at every exposure C –combination of average and variance of response at each C: like FDA-PBE or Kullback-Liebler distance metrics or –whole distribution at each C – Kolmogorov-Smirnov generalization Choose here to look at average response

12 All C’s identical, continued Usual equivalence-type analysis: –can define “similarity” to be requirement that the average responses in the 2 populations, at the same C, are closely similar: –choose “goalposts” L and U, eg 80% to 125% –calculate 95% confidence interval for ratio of average responses (  1 /  0 ) (  = mean or average response)

13 All C’s identical, continued If 95% confidence interval of ratio  1 /  0 falls entirely within interval (L, U), then null hypothesis of lack of equivalence is rejected. This corresponds to “simultaneous two one-sided test procedure for equivalence”, carried out at level  = Proposal: use confidence intervals to measure “similarity” and to quantify what was actually determined from data in the 2 populations

14 Estimation of 95% confidence interval for ratio  1 /  0 some work required - methods in literature easier: use bootstrap method from observations, or computer simulation for decision-making, can make useful statements, such as, for example, –“the average response to concentration C in the New Population is about 93% of that in the Original Population, and we are 95% confident that the ratio of the averages lies between 83% and 105%”

15 SITUATION: MANY VALUES OF C First approach: –Categorize values of C into intervals: (C 1, C 2 ), (C 2, C 3 ), (C 3, C 4 ), etc –For each interval, (C i, C i+1 ), estimate 95% confidence intervals for  1i /  0i and interpret. –Interpret responses graphically, for all categories of C.

16 Drug X: 95% CI’s for ratios  1 /  0 for concentrations: 0, 0-40, 40-60, 60-80, >80

17 Comment on Graph ratios trend upwards from 1.0 as C increases: New population has greater average response than Original population upper limits of 95% CI’s exceed 1.25 for all exposures

18 SITUATION: MANY VALUES OF C Second approach: model-based. Fit models:  0 (C) = f(C,  0 )  1 (C) = f(C,  1 ) Estimate the unknown parameters:  ’s, variances. Use fitted model to simulate  0 (C),  1 (C), for as many values of C as desired: estimate the ratios of the average responses:  1 (C)/  0 (C) estimate 95% CI’s from percentiles of ratios

19 EXAMPLE: Drug X Response transformed by square root to stabilize the variance Linear models were fitted separately for the two populations sqrt(response) = a + b * Conc+  For each C, 5000 pairs of studies were generated  5000 estimates of  1 /  0, and percentiles

20 DRUG X: 95% CI’s for ratios  1 /  0 for concentrations: 0, 20,50,70,90 via model-based method

21 DRUG X: COMPARISON OF 2 APPROACHES 95% CI’s for  1 /  0 from Categorized C’s (1st in pair) and Model-based method (2nd in pair)

22 Comparison of approaches model based method: – less influenced by outliers – generally greater precision – both useful

23 DESIGN CONSIDERATIONS for studies in New Population based on parameter estimates from Original Population and any prior information from New Population include doses likely to produce C’s in the whole range of interest perform simulations to assess robustness to model assumptions, variability of parameter estimates, choice of doses, to determine required number of patients needed in new population

24 OCNCLUDING REMARKS efficacy vs. safety proposed method for quantifying the similarity between Original and New Populations over whole range of concentrations likely to be encountered applies to data from trials with different designs usual goalposts such as (0.8, 1.25) may not be meaningful for the drug (therapeutic range) and disease - interpretation of how much similarity is needed requires medical input.