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Background  Minimisation of the delay to diagnosis is critical to achieving optimal outcomes for HIV patients and to limiting the potential for further onward infections. However, investigation of diagnosis delay is hampered by the fact that in most newly diagnosed patients the exact timing of infection cannot be determined and so inferences must be drawn from biomarker data.    Methods  We develop a Bayesian statistical model to evaluate delay-to-diagnosis distributions in HIV patients without known infection date, based on viral sequence genetic diversity and longitudinal viral load and CD4 count data. The delay to diagnosis is treated as a random variable for each patient and their biomarker data are modelled relative to the true time elapsed since infection, with this dependence used to obtain a posterior distribution for the delay to diagnosis. Data from a national seroconverter cohort with infection date known to within ± 6 months, linked to a database of viral sequences, are used to calibrate the model parameters. An exponential survival model is implemented that allows general inferences regarding diagnosis delay and pooling of information across groups of patients. If diagnoses are only observed within a given window period, then it is necessary to also model incidence as a function of time; we suggest a pragmatic approach to this problem when dealing with data from an established epidemic. The model developed is used to investigate delay-to-diagnosis distributions in men who have sex with men diagnosed with HIV in London in the period 2009–2013 with unknown date of infection.    Results  Cross-validation and simulation analyses indicate that the models developed provide more accurate information regarding the timing of infection than does CD4 count-based estimation. Delay-to-diagnosis distributions were estimated in the London cohort, and substantial differences were observed according to ethnicity.    Conclusion  The combination of all available biomarker data with pooled estimation of the distribution of diagnosis-delays allows for more precise prediction of the true timing of infection in individual patients, and the models developed also provide useful population-level information.    Electronic supplementary material  The online version of this article (10.1186/s12874-018-0522-x) contains supplementary material, which is available to authorized users.

Estimation of delay to diagnosis and incidence in HIV using indirect evidence of infection dates