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Accounting for uncertainty in the timing of seroconversion in combined models for pre- and post-treatment CD4 counts in HIV-patients Oliver Stirrup, Andrew Copas and Ab Babiker MRC Clinical Trials Unit at UCL, UCL, London @ISCB Birmingham 24th August 2016 MRC Clinical Trials Unit at UCL Pre- and post-HAART CD4 counts: UK data SQRT (CD4) 40 30 20 10 -5 0 5 Time before (−ve) and after (+ve) HAART initiation (years) MRC Clinical Trials Unit at UCL Maximum likelihood estimation (MLE) • MLE requires optimisation of likelihood function that involves integration over an unobserved latent variable ‘u’, representing the underlying true value of the biomarker at treatment initiation. • Limited software options, but can be achieved using: Described in Stirrup et al. (in press, BMC Medical Research Methodology) MRC Clinical Trials Unit at UCL Log10(viral load in copies /mL) Uncertainty in seroconversion date: relationship to pre-treatment viral load (VL) 6 4 2 0 0 2 4 6 MRC Clinical Trials Unit at UCL Time from estimated date of seroconversion (years) Uncertainty in seroconversion date: relationship to pre-treatment viral load (VL) Taken from Pantazis et al. (2005) MRC Clinical Trials Unit at UCL Extensions to combined model • MLE requires optimisation of likelihood function that involves integration over true date of seroconversion for each patient and a random intercept term for pretreatment viral load, as well as the latent variable representing true CD4 value at treatment initiation: Follows work by Sommen et al. and Drylewicz et al. on pretreatment biomarker data. MRC Clinical Trials Unit at UCL Dataset for analysis • Analysis is conducted using data from the CASCADE international cohort collaboration (Concerted Action on SeroConversion to AIDS and Death in Europe), with up to 3 years between –ve and +ve HIV tests. • Includes all patients with estimated date of seroconversion during or after 2003 (up to March 2014) who are recorded initiating HAART. • Analysis includes 7789 patients, with: 39 854 pre-treatment CD4 counts 36 808 pre-treatment VL measurements 61 057 post-treatment CD4 counts • Estimation conducted using ADMB. MRC Clinical Trials Unit at UCL Uncertainty in seroconversion date: distribution of possible ‘true’ dates Probability mass or density functions for true seroconversion date of patient with 1 year between –ve and +ve tests: ‘Fixed’ mid-point assumption Uniform between –ve and +ve tests Beta(6,6) between –ve and +ve tests MRC Clinical Trials Unit at UCL Estimated transition from early to late treatment response MRC Clinical Trials Unit at UCL Predictions from fitted model (1/2) ‘True’ baseline CD4 count at HAART initiation: 200 cells/μL 350 cells/μL 500 cells/μL Time from seroconversion to treatment initiation: ············ Immediate - - - - - 3 months 1 year MRC Clinical Trials Unit at UCL Predictions from fitted model (2/2) Time from seroconversion to treatment initiation: Immediate 3 months Pre-treatment viral load: ············ low (2.5th centile) - - - - - median (50th centile) high (97.5th centile) 1 year Baseline CD4: 350 cells/μL MRC Clinical Trials Unit at UCL References • • • • Stirrup OT, Babiker AG and Copas AJ. Combined models for pre- and post-treatment longitudinal biomarker data: an application to CD4 counts in HIV-patients. BMC Medical Research Methodology (in press). Pantazis N, Touloumi G, Walker AS and Babiker AG. Bivariate modelling of longitudinal measurements of two human immunodeficiency type 1 disease progression markers in the presence of informative drop-outs. Journal of the Royal Statistical Society: Series C (Applied Statistics) 2005; 54: 405–423. Sommen C, Commenges D, Vu SL, Meyer L, and Alioum A. Estimation of the distribution of infection times using longitudinal serological markers of HIV: implications for the estimation of HIV incidence. Biometrics 2011; 67: 467–475. Drylewicz J, Guedj J, Commenges D, and Thiébaut R. Modeling the dynamics of biomarkers during primary HIV infection taking into account the uncertainty of infection date. The Annals of Applied Statistics 2010; 4: 1847–1870. MRC Clinical Trials Unit at UCL