title: Some extensions in continuous models for immunological correlates of protection.
abstract: BACKGROUND
  A 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.
  
  
  METHODS
  Some 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.
  
  
  RESULTS
  Alternative 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.
  
  
  CONCLUSIONS
  The 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.
authors.affiliation: Sanofi Pasteur, Swiftwater, PA, 18370, USA. adunning@alumni.washington.edu.
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Dunning
authors.affiliation: Virginia Tech, Blacksburg, VA, USA. jen.kensler@gmail.com.|Present address: Shell Global Solutions, Houston, TX, 77082, USA. jen.kensler@gmail.com.
authors.forename: Jennifer
authors.initials: J
authors.lastname: Kensler
authors.affiliation: Sanofi Pasteur, Lyon Cedex, 69367, France. laurent.coudeville@sanofipasteur.com.
authors.forename: Laurent
authors.initials: L
authors.lastname: Coudeville
authors.affiliation: Sanofi Pasteur, Marcy l'Étoile, 69280, France. fabrice.bailleux@sanofipasteur.com.
authors.forename: Fabrice
authors.initials: F
authors.lastname: Bailleux
mesh_terms: D006801:Humans; D007109:Immunity; D007118:Immunoassay; D016015:Logistic Models; D018448:Models, Immunological