Transcript Accounting for uncertainty in the timing of

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
•
•
•
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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