1. 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

2. Pre- and post-HAART CD4 counts: UK data40 30
SQRT (CD4) 20 10 -5 5
Time before (−ve) and after (+ve) HAART initiation (years)

3. 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)

4. Uncertainty in seroconversion date: relationship to pre-treatment viral load (VL)6 4
Log10(viral load in copies /mL) 2 2 4 6
Time from estimated date of seroconversion (years)

5. Uncertainty in seroconversion date: relationship to pre-treatment viral load (VL)
Taken from Pantazis et al. (2005)

6. 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 pre-treatment 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 pre-treatment biomarker data.

7. 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:
pre-treatment CD4 counts
pre-treatment VL measurements
post-treatment CD4 counts
Estimation conducted using ADMB.

8. 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

9. Estimated transition from early to late treatment response

10. 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
months
1 year

11. Predictions from fitted model (2/2)
Time from seroconversion to treatment initiation:
Immediate
3 months
1 year
Pre-treatment viral load:
············ low (2.5th centile)
median (50th centile)
high (97.5th centile)
Baseline CD4: 350 cells/μL

12. 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.