Discussion of presentations Issues 1. imbalanced sample size 2 Discussion of presentations Issues 1. imbalanced sample size 2. estimate of reference variance for margin 3. adjusted for correlated lots 4. equivalence test of effect size instead 5. Comparability 6. tier 2 – What to propose for k? - it is more a statistical scale instead of a statistical test

Tsong and Dong’s presentation on Sample Size Imbalance Adjustment Method B: when the sample size ratio > 1.5 Use all the reference sample to estimate μR and σR; Use nR* = Min(1.5×nT, nR) to compute the CI. Satterthwaite approximation is recommended for CI computation. DIA/FDA Stat Forum 2016

III. Sample Size Imbalance Adjustment Statistical properties of Method B Decision Rule: conclude stat. Equivalence in means if T1 > t1-α, df* and T2 < -t1-α, df* . Power: p(u1,u2)~bivariate t(df*,df*, θ1, θ2,1) DIA/FDA Stat Forum 2016

III. Sample Size Imbalance Adjustment Method B: Type I error rate vs. SS Ratio the type I error rate is a monotone function of the sample size ratio for given variance. More specifically, the type I error rate is more conservative if the sample size ratio (imbalance) is large. DIA/FDA Stat Forum 2016

III. Sample Size Imbalance Adjustment Method B: Power Comparison(σT = σR) the type I error rate is a monotone function of the sample size ratio for given variance. More specifically, the type I error rate is more conservative if the sample size ratio (imbalance) is large. DIA/FDA Stat Forum 2016

  Use nR*=min(1.5nT,nR) Power Type I Error  

Very similar results But the issues are The need of information of biosimilar product There is no blindness or randomization of the study No control of change design through interim analysis Power rewarding based on product of extremely large sample size

II. Estimated vs. fixed equivalence margin Guidance will only focus on fixed margin Estimation margin but test as fixed will inflate type I error rate and reduce power Alternative approaches are in in the process of research and evaluation Generalized confidence interval of effect size approach has been proposed

III. Correlation between lots Tsong’s presentation on adjustment of lot correlation Parameters of a population may be estimated unbiasedly if the sample is taken randomly and representatively Which means every member of the population should have the same chance to be sampled Or randomly sample clusters before members but each clusters should represent the population The practical analytical population may consists of clusters do not represent the population And the random sample are taken from clusters only available during the study time In conclusion, study sample define a population which is a population ℙ generalized from the sample

Practical sampling design of analytical biosimilarity assessment

True batch population and sample defined population

Out of 30 data set we examined, 70% of data set has observed reference variability is larger than the biosimilar variability

Population, sample defined population ℙ, random sample and correlated samples Given the fact that there is no formula, example or knowledge of how the correlation is calculated, or how large it is based on the data available to the biosimilar sponsor, the adjustment proposed by researcher or sponsor becomes unrealistic Under the assumption that such knowledge is available, we conducted a research and found the conventional t-test used for equivalence assessment inflates type I error rate and lowers power (Shen, Wang (2016), to submit to JBS) 2016 MBSW

90% CI 4. Equiv. test of effect size Is [1-(confidence level)]/2 = type I error rate of two one-sided test? Is such a test monotone from -∞ to 0? Tsong’s presentation “hypothesis testing and confidence interval – where is the duality?

5. Comparability Comparability is to demonstrate the consistency of the same product before and after some change to its manufacturing process Equivalence test of means before and after change(s) Profile comparison – multivariate equivalence Normal vs. non-normal, parametric vs. nonparametric, equal vs. unequal variance – small sample problem Dissolution profile comparison Model dependent vs. model independent methods SK (saranadasa & krishnamoorthy (2015)) using mean difference at all time point IUT using non-constant margin at each time point Parallelism testing