Joint analysis of PK and immunogenicity outcomes using factorization model − a powerful approach for PK similarity study

Biological products, whether they are innovator products or biosimilars, can incite an immunogenic response ensuing in the development of anti-drug antibodies (ADA). The presence of ADA's often affects the drug clearance, resulting in an increase in the variability of pharmacokinetic (PK) analysis and challenges in the design and analysis of PK similarity studies. Immunogenic response is a complex process which may be manifested by product and non-product-related factors. Potential imbalances in non-product-related factors between treatment groups may lead to differences in antibodies formation and thus in PK outcome. The current standard statistical approaches dismiss any associations between immunogenicity and PK outcomes. However, we consider PK and immunogenicity as the two correlated outcomes of the study treatment. In this research, we propose a factorization model for the simultaneous analysis of PK parameters (normal variable after taking log-transformation) and immunogenic response subgroup (binary variable). The central principle of the factorization model is to describe the likelihood function as the product of the marginal distribution of one outcome and the conditional distribution of the second outcome given the previous one. Factorization model captures the additional information contained in the correlation between the outcomes, it is more efficient than models that ignore potential dependencies between the outcomes. In our context, factorization model accounts for variability in PK data by considering the influence of immunogenicity. Based on our simulation studies, the factorization model provides more accurate and efficient estimates of the treatment effect in the PK data by taking into account the impact of immunogenicity. These findings are supported by two PK similarity clinical studies with a highly immunogenic biologic.