Statistical challenges in the evaluation of surrogate endpoints in randomized trials

Abstract

The validation of surrogate endpoints has been studied by Prentice, who presented a definition as well as a set of criteria that are equivalent if the surrogate and true endpoints are binary. Freedman et al. supplemented these criteria with the so-called proportion explained. Buyse and Molenberghs proposed to replace the proportion explained by two quantities: (1) the relative effect, linking the effect of treatment on both endpoints, and (2) the adjusted association, an individual-level measure of agreement between both endpoints. In a multiunit setting, these quantities can be generalized to a trial-level measure of surrogacy and an individual-level measure of surrogacy. In this paper, we argue that such a multiunit approach should be adopted because it overcomes difficulties that necessarily surround validation efforts based on a single trial. These difficulties are highlighted.

The Mediation Formula: A Guide to the Assessment of Causal Pathways in Nonlinear Models

“…as is normally assumed in the mediation literature (Prentice, 1989;Freedman et al, 1992;MacKinnon and Dwyer, 1993;Fleming and DeMets, 1996;Molenberghs et al, 2002;MacKinnon et al, 2007b). In particular, the mediated fractions 1 − DE/T E, and IE/T E may differ substantially from the fractions γ xz γ zy /(γ xy + γ xz γ zy ), 1 − γ xy /β xy , or γ xz γ zy /β xy that have been proposed to evaluate mediation effects by traditional methods.…”

“…17), with Y regressed on both X and Z. 9 When generalized to nonlinear systems, however, these two strategies yield conflicting results (MacKinnon and Dwyer, 1993;MacKinnon et al, 2007b) and much controversy has developed as to which strategy should be used in assessing the size of mediation effects (MacKinnon and Dwyer, 1993;Freedman et al, 1992;Molenberghs et al, 2002;MacKinnon et al, 2007b;Glynn, 2009;Green et al, 2010).…”

Time and PSA threshold model prognosticates long-term overall and disease-specific survival in prostate cancer patients as early as 3 months after external beam radiation therapy

“…In the interim, the clinical usefulness of the proposed model may actually be further explored as it has been suggested that the satisfaction of rigorous criteria as suggested by Prentice 22 is not required in order for a model to serve as a surrogate in applications other than phase III trials. 14,[23][24][25][26] According to previously published findings and the present analysis, time and PSA threshold modeling appears to be a valid response-to-treatment metric, prognosticating not only bRFS, but also the ultimate outcome measures DSS and OS, as early as 3 months following external beam radiation therapy for prostate cancer. Validation of conclusions derived from this large single-institution prostatic carcinoma follow-up database in an independent population will be required to establish the model as a response-to-treatment metric which may assist clinicians in determining which patients should be considered for early adjuvant therapy.…”

Simplified modeling strategies for surrogate validation with multivariate failure-time data

“…The adjusted association carries over when data are available on several randomized trials, while the RE can be extended to a trial-level measure of agreement between the effects of treatment of both endpoints. Molenberghs et al (2002) and Alonso et al (2004) pointed out serious issues surrounding the Prentice-Freedman framework. It has been asserted that the criteria set out by Prentice are too stringent (Fleming and DeMets, 1996) and neither necessary nor sufficient for his definition to be fulfilled, except in the special case of binary outcomes (Buyse and Molenberghs, 1998).…”