Evaluation of surrogacy in the multi-trial setting based on information theory: an extension to ordinal outcomes

Informed decision-making: Statistical methodology for surrogacy evaluation and its role in licensing and reimbursement assessments

The desire, by patients and society, for faster access to therapies has driven a long tradition of the use of surrogate endpoints in the evaluation of pharmaceuticals and, more recently, biologics and other innovative medical technologies. The consequent need for statistical validation of potential surrogate outcome measures is a prime example on the theme of statistical support for decision-making in health technology assessment (HTA). Following the pioneering methodology based on hypothesis testing that Prentice presented in 1989, a host of further methods, both frequentist and Bayesian, have been developed to enable the value of a putative surrogate outcome to be determined. This rich methodological seam has generated practical methods for surrogate evaluation, the most recent of which are based on the principles of information theory and bring together ideas from the causal effects and causal association paradigms. Following our synopsis of statistical methods, we then consider how regulatory authorities (on licensing) and payer and HTA agencies (on reimbursement) use clinical trial evidence based on surrogate outcomes. We review existing HTA surrogate outcome evaluative frameworks. We conclude with recommendations for further steps: (1) prioritisation by regulators and payers of the application of formal surrogate outcome evaluative frameworks, (2) application of formal Bayesian decision-analytic methods to support reimbursement decisions, and (3) greater utilization of conditional surrogate-based licensing and reimbursement approvals, with subsequent reassessment of treatments in confirmatory trials based on final patient-relevant outcomes.

Evaluation of Surrogate Endpoints Using Information-Theoretic Measure of Association Based on Havrda and Charvat Entropy

Surrogate endpoints have been used to assess the efficacy of a treatment and can potentially reduce the duration and/or number of required patients for clinical trials. Using information theory, Alonso et al. (2007) proposed a unified framework based on Shannon entropy, a new definition of surrogacy that departed from the hypothesis testing framework. In this paper, a new family of surrogacy measures under Havrda and Charvat (H-C) entropy is derived which contains Alonso’s definition as a particular case. Furthermore, we extend our approach to a new model based on the information-theoretic measure of association for a longitudinally collected continuous surrogate endpoint for a binary clinical endpoint of a clinical trial using H-C entropy. The new model is illustrated through the analysis of data from a completed clinical trial. It demonstrates advantages of H-C entropy-based surrogacy measures in the evaluation of scheduling longitudinal biomarker visits for a phase 2 randomized controlled clinical trial for treatment of multiple sclerosis.

Separation and the information theory surrogate evaluation approach: A penalised likelihood solution

Surrogate evaluation is an important topic in clinical trials research, the use of a surrogate in place of a primary endpoint of interest is a common occurrence but also a contentious issue that is much debated. Statistical techniques to assess potential surrogates are closely scrutinised by the research community given the complexities of such an assessment. One such technique is the information theory surrogate evaluation approach which is well-established, practical and theoretically sound. In the context of discrete outcomes, we investigated issues of bias due to inefficiency, overfitting and separation (sparse data) that have not been recognised or addressed previously. The most serious cause of bias is separation in trial information. We outline the concerns surrounding this bias and conduct a simulation study to investigate whether a penalised likelihood technique provides an appropriate solution. We found that removing trials with separation from surrogacy evaluation resulted in a large amount of discarded data. Conversely, the penalised likelihood technique allows retention of all trial information and enables precise and reliable surrogate estimation. The information theory approach is a critical tool for conducting surrogate evaluation. This work strengthens the practical application of the information theory approach, allowing analyses to be adapted or the results summarised with appropriate caution to mitigate the biases highlighted. This is especially true where separation occurs. The adoption of the penalised likelihood technique into information theory surrogate evaluation is a useful addition that solves an issue likely to arise frequently in the context of categorical endpoints.