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Statistical Communications in Infectious Diseases

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Estimating Trends in Incidence, Time-to-Diagnosis and Undiagnosed Prevalence using a CD4-based Bayesian Back-calculation

Paul J. Birrell
  • MRC Biostatistics Unit
/ Tim R. Chadborn
  • Health Protection Agency
/ O. Noel Gill
  • Health Protection Agency
/ Valerie C. Delpech
  • Health Protection Agency
/ Daniela De Angelis
  • MRC Biostatistics Unit and Health Protection Agency
Published Online: 2012-11-09 | DOI: https://doi.org/10.1515/1948-4690.1055


There has been much recent speculation regarding the potential for HIV test-and-treat strategies to provide control of the HIV endemic. In the UK, despite advanced HIV surveillance and the implementation of a number of testing initiatives and attempts to widen access to antiretroviral drugs, the number of new diagnoses persists at a high level having risen considerably over the course of the last ten years. The extent to which this high level of diagnosis is attributable to levels of HIV transmission or improved rates of testing and diagnosis is unclear. To disentangle these competing factors, we use a Bayesian back-calculation based on HIV and AIDS diagnosis data augmented by observed CD4 count levels at diagnosis. The CD4 count acts as a prognostic marker indicative of the time-since-infection for any new diagnosis. In addition to estimating time-dependent rates of infection and diagnosis, we exploit the model structure to estimate posterior distributions for a number of key epidemiological quantities such as trends in the time-to-diagnosis and the time-since infection distributions as well as the prevalence of undiagnosed infection. These quantities are stratified by CD4 count where possible. The proposed methodology is applied to HIV/AIDS surveillance data from England & Wales uncovering a decreasing trend in the time to diagnosis and stable levels of incidence in recent years.

Keywords: back-calculation; Bayesian inference; multi-state; incidence; diagnosis; undiagnosed prevalence

Published Online: 2012-11-09

Citation Information: Statistical Communications in Infectious Diseases. Volume 4, Issue 1, ISSN (Online) 1948-4690, DOI: https://doi.org/10.1515/1948-4690.1055, November 2012

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