1. Viral load, CD4 cell counts and antibodies: What do we know and what does it all mean? Brian Williams, SACEMA, November 2007

2. We have not succeeded in answering all your problems. The answers we have found only serve to raise a whole set of new questions. In some ways we feel that we are as confused as ever but we believe that we are confused on a higher level and about more important things. Notice at the Cambridge University Computer Centre ‘Surgery’, 1970.

3. Viral load CD4 Antibodies Time The standard model Acute phase ~ weeks Final phase ~ months Interested in the long chronic phase ~ 10 yrs

4. CD4 cells/  L Virions/mL Orange Farm, South Africa. (Auvert et al. PLOS Medicine, 2005) Viral load and CD4 cell counts

5. 10,000 1000 100 10 1 0.1 0.01 CD4 cells/  L Virions/  L Orange Farm, South Africa. (Auvert et al. PLOS Medicine, 2005) Viral load and CD4 cell counts

6. Virions/μL CD4 slope/  L/year 150 100 50 0 -50 -100 -150 -200 -250 -300 0.001 0.01 0.1 1 10 100 1000 Rodriguez et al. Jama, 2006. CD4 cell count decline for different viral loads

7. Optical density  log(antibody concentration) CD4 cells /  L Antibody concentration and CD4 cell counts ZVITAMBO (Hargrove, pers. comm.)  Up to 2000

8. Quite solid relationships buried in a vast amount of noise... 1. What does the underlying relationship imply? 2. Where does the noise come from? Problem: We have lots of cross-sectional data but little time series data

9. Viral load/  L Frequency 0.01 0.1 1 10 100 1000 10,000 Orange Farm, South Africa. (Auvert et al. PLOS Medicine 2005) Viral load distribution: Young men in Orange Farm, South Africa

10. Orange Farm, South Africa. (Auvert et al. PLOS Medicine 2005); Zambia (Kelly et al. Acta Tropica 2002) CD4 cell counts in HIV-positive and HIV-negative people

11. Optical density i.e. ln(antibody concentration) Frequency Log antibody distribution: Harare

12. Combine the individual decline with the initial distribution 0 10 20 Time (years) 500 1000 2000 CD4 cells/  l Assume that survival is independent of the initial value of the CD4 cell count HIV– Survival CD4

13. Log(Initial viral load) sets survival CD4 in HIV– CD4 Time Assume that survival is independent of the initial value of the CD4 cell count

14. Orange Farm, South Africa. (Auvert et al. PLOS Medicine 2005); Zambia (Kelly et al. Acta Tropica 2002) CD4 cell counts in HIV-positive and HIV-negative people

15. Distribution of CD4 cell count decline

16. Time years Frequency Orange Farm, South Africa. (Auvert et al. PLOS Medicine 2005) Survival of young men in Orange Farm, South Africa? Survival (yrs) = 42.2 – 6.5  log 10 (VL/  L) Viral load Weibull survival

17. 1. Survival is (almost) independent of initial CD4 cell count 2. Survival is (entirely) determined by log(set-point viral load) 3. Viral load declines exponentially with CD4: 4. Antibody concentration declines exponentially with CD4: So we need to explain why:

18. Years since infection Proportion surviving Survival against age at HIV seroconversion Time from HIV-1 seroconversion to AIDS and death before widespread use of highly-active anti- retroviral therapy A collaborative re-analysis. Cascade Collaboration. Lancet 2001:355 1131  1137

19. Lusaka Gauteng Incidence Prevalence Death 90 95 00 05 10 40 90 95 00 05 10 40

20. Lusaka Gauteng