Some extensions in continuous models for immunological correlates of protection

Abstract

BackgroundA scaled logit model has previously been proposed to quantify the relationship between an immunological assay and protection from disease, and has been applied in a number of settings. The probability of disease was modelled as a function of the probability of exposure, which was assumed to be fixed, and of protection, which was assumed to increase smoothly with the value of the assay.MethodsSome extensions are here investigated. Alternative functions to represent the protection curve are explored, applications to case-cohort designs are evaluated, and approaches to variance estimation compared. The steepness of the protection curve must sometimes be bounded to achieve convergence and methods for doing so are outlined. Criteria for evaluating the fit of models are proposed and approaches to assessing the utility of results suggested. Models are evaluated by application to sixteen datasets from vaccine clinical trials.ResultsAlternative protection curve functions improved model evaluation criteria for every dataset. Standard errors based on the observed information were found to be unreliable; bootstrap estimates of precision were to be preferred. In most instances, case-cohort designs resulted in little loss of precision. Some results achieved suggested measures for utility.ConclusionsThe original scaled logit model can be improved upon. Evaluation criteria permit well-fitting models and useful results to be identified. The proposed methods provide a comprehensive set of tools for quantifying the relationship between immunological assays and protection from disease.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-015-0096-9) contains supplementary material, which is available to authorized users.

Correlates of Protection against Influenza in the Elderly: Results from an Influenza Vaccine Efficacy Trial

“…Protection curves estimating the level of protection at each assay titer were calculated using the scaled logit model and extensions, which incorporate both protection related to assay titer and exposure ( 29 , 30 ). Goodness-of-fit of models were assessed by the method of Hosmer and Lemeshow ( 31 ); models with goodness of fit less than 0.5 were considered unreliable and results were not reported.…”

Assessing correlates of protection in vaccine trials: statistical solutions in the context of high vaccine efficacy

“…We can see that the scaled logistic model is slightly conservative. Standard errors of this model should be computed by bootstrap [27].…”

“…Rare events data obtained in high VE trials make it challenging for statisticians to apply classical methods used for CoP assessment due to the lack of available information. These include ML estimators, where bias, infinite estimates, multicollinearity and convergence issues can arise and negatively impact Prentice criteria and meta-analytic frameworks commonly used to assess vaccine CoPs, as shown in this paper [24, 26, 27].…”

“…The number of additional parameters should be small to avoid overfitting. Other models with flexible link functions have also been proposed that can be used within the Prentice framework [26, 27]. Model selection can be done using the Akaike Information Criterion (AIC) approach.…”

“…When the number of events is small, this model can encounter issues due to lack of fit, leading to erroneous conclusions. To solve the problem of lack of fit, flexible link functions [25–27], could be used within Prentice framework. In this paper, we consider the classical logistic models with flexible (non-linear) effect of the surrogate …”