Viral load, CD4 cell counts and antibodies: What do we know and what does it all mean? Brian...
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Transcript of Viral load, CD4 cell counts and antibodies: What do we know and what does it all mean? Brian...
Viral load, CD4 cell counts and antibodies:What do we know and what does it all mean?
Brian Williams, SACEMA, November 2007
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.
Vira
l loa
d
CD
4
Ant
ibod
ies
Time
Time
Time
The standard model
Acute phase ~ weeksFinal phase ~ months
Interested in the long chronic phase ~ 10 yrs
CD4 cells/L
Vir
ion
s/m
L
Orange Farm, South Africa. (Auvert et al. PLOS Medicine, 2005)
Viral load and CD4 cell counts
10,000
1000
100
10
1
0.1
0.01
CD4 cells/L
Vir
ion
s/L
Orange Farm, South Africa. (Auvert et al. PLOS Medicine, 2005)
Viral load and CD4 cell counts
Virions/μL
CD
4 s
lop
e/L
/ye
ar150
100
50
0
-50
-100
-150
-200
-250
-3000.001 0.01 0.1 1 10 100 1000
Rodriguez et al. Jama, 2006.
CD4 cell count decline for different viral loads
Optical density log(antibody concentration)
CD
4 c
ells
/L
Antibody concentration and CD4 cell counts
ZVITAMBO (Hargrove, pers. comm.)
Up to 2000
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
Viral load/L
Fre
que
ncy
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
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
Combine the individual decline with the initial distribution
0 10 20 Time (years)
500
1000
2000
CD
4 ce
lls/
l
Assume that survival is independent of the initial value of the CD4 cell count
HIV–
Survival
CD4
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
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
0
50
100
150
200
250
-50 0 50 100 150 200 250
Decline in CD4 cell counts/mL/yr
Nu
mb
er
of
pe
op
le
Distribution of CD4 cell count decline
0
10
20
30
0 5 10 15 20 25 30 35
Time years
Fre
que
ncy
Orange Farm, South Africa. (Auvert et al. PLOS Medicine 2005)
Survival of young men in Orange Farm, South Africa?
Survival (yrs) = 42.2 – 6.5log10(VL/L)
Viral load
Weibull survival
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:
11 e b CV a
22 e b CA a
So we need to explain why:
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15
2.5
10
20
30
40
5070 60
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 11311137