Some Tests, Confidence Limits and Tolerance Limits for Assessing Biosimilarity

Abstract

Biosimilars or follow-on biologics are defined as biological medicinal products that are expected to be similar to a licensed biological product. The standard proce- dures for assessing bioequivalence may not be applicable in establishing biosimilarity due to the complexity of the protein structure. In particular, any criterion based on only the means will ignore the possible difference in variability between the test and reference products. Nevertheless, average biosimilarity is clearly a minimum requirement in the process of biosimilarity assessment, and some procedures are already available in the literature for testing average biosimilarity. However, these test procedures are not accurate in terms of maintaining the type I error probability. This will clearly impact the power, and hence the sample size. Thus two aspects of biosimilarity testing are investigated in the thesis, in the context of normally distributed responses: (i) the development of accurate tests for assessing average biosimilarity, and (ii) the development of alternative criteria that incorporate the variances, along with accurate test procedures for the alternative criteria. In addi- tion, biosimilarity assessment based on binary responses is also investigated. The issue of average biosimilarity investigated is in the context of a three-arm parallel design. For testing the relevant interval hypotheses, a very accurate test is derived using the novel concept of a generalized pivotal quantity. A desirable feature of his test procedure is that it is valid and applicable without the restrictive assumption of equal variances for the responses from the test and reference formu- lations. Sample size determination is also addressed, so that the test will guarantee a specified power. In short, this work has resulted in an accurate test for average biosimilarity. In the context of biosimilarity assessment, it is well known that the possibility of higher variability for the test drug could lead to lower efficacy, or potential safety risks for some patients. As a result, the need for statistical criteria that incorporate the variance is very important. In the thesis, we have explored the development of alternative criteria using the concept of tolerance limits. A tolerance limit naturally takes into account possible differences between the means, as well as the possibility of a larger variance for the test drug. We have constructed an upper tolerance limit for the absolute difference between the responses from the test drug and reference drug. It is shown that such an upper tolerance limit is an increasing function of the absolute difference between the means, and is also an increasing function of the variance of the test drug. The techniques employed in the development of the tolerance limit include parametric and non-parametric bootstrap along with non- parametric tolerance limit computation. Numerical results are reported to show the accuracy of the tolerance limit in terms of meeting the coverage probability requirement. The final topic investigated in the thesis is on the assessment of biosimilarity when the responses are binary. It is assumed that the data are generated using a parallel line assay consisting of two dose-response trials, one for the biosimilar product and one for the reference product, each with several dose levels. Logistic regression models are assumed for the probability of a positive response. A three step approach is used to conclude biosimilarity: (i) test whether the slope parameters are equal; if so (ii) test if the common slope parameter is significantly different from zero; if so, (iii) test if the relative potency parameter is inside a pre-specified interval. These problems have been addressed in the literature and approximate procedures have been developed for (i), (ii) and (iii) using asymptotic normality of the maximum likelihood estimators. We have followed a fiducial approach for testing the hypotheses in (i), (ii) and (iii), and the accuracy of the proposed fiducial approach is numerically verified. Throughout the thesis, the methodologies are illustrated with examples. Fur- thermore, R codes are available for their implementation.