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Table 2 Summary of the 6 studies which present novel methods to estimate the CoC timing

From: HIV continuum of care: expanding scope beyond a cross-sectional view to include time analysis: a systematic review

Article

Time-related Method

Lee H et al. AIDS, 2018 [19]

The authors presented the dynamic patterns of care and retention using multistate methodology (Method described in: Lee H, et al., A state transition framework for patient-level modeling of engagement and retention in HIV care using longitudinal cohort data. Statistics in Medicine, 2017). After defining the CoC states, the transition probabilities between them were estimated using multinomial regression. Then, state membership (i.e. the probability of being in a state) was estimated as a function of the transition probabilities up to this state. In cases where endogeneous covariates had to be taken into account, e.g.disease markers, a joint model of the distribution of the covariate and of the state transition processes was applied to predict state membership probabilities.

Lesko CR et al. AIDS, 2016 [20] and Desir FA et al. Clin Infect Dis, 2019 [21]

In this article, the non-parametric estimates of the cumulative incidence were used. The investigators follow a method (described in: Cole SR, Lau B, Eron JJ, et al. Estimation of the standardized risk difference and ratio in a competing risks framework: application to injection drug use and progression to AIDS after initiation of antiretroviral therapy. Am J Epidemiol. 2015; 181 (4):238–45) for the estimation of risk based directly on the survival function. Rather than estimating hazards and hazard ratios, the method proposed the application of censoring and exposure weights to the Nelson-Aalen estimate of the cumulative incidence function.

Reyes-Uruena JM et al. BMJ Open, 2018 [22]

To estimate the annual incidence and the time of infection, the authors used the ECDC Modelling tool. The method is based on a multistate back-calculation model that estimates HIV annual incidence along the size of the undiagnosed population, using data on reported HIV and AIDS cases, and information on CD4 count at the time of diagnosis

Robertson MM et al. Clin Infect Dis, 2019 [23]

In this article the estimation of the time of infection was based on the CD4 cell count at diagnosis and the CD4 decline rate estimated by previous studies on seroconverters.

Supervie V et al. J Acquir Immune Defic Syndr, 2016 [24]

To estimate both the HIV incidence and the distribution of times from infection to diagnosis, the authors fitted a back-calculation model to the annual number of new HIV diagnoses (Ndawinz JD, Costagliola D, Supervie V. New method for estimating HIV incidence and time from infection to diagnosis using HIV surveillance data: results for France. AIDS. 2011;25:1905–1913). Nonparametric estimates of the cumulative distribution function for each stage were produced, accounting for censoring. Using the inversion method (Nonparametric Estimates of Cumulative Distribution Functions and Their Inverses. Available at: http://fr.mathworks.com/help/stats/examples/nonparametric-estimates-of-cumulative-distribution-functionsand-their-inverses.html?refresh=true), 10,000 random values for each time interval were generated. The estimated time intervals were summarised as means, medians and interquartile ranges.