Viral load, CD4 cell counts and antibodies: What do we know and what does it all mean?
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Viral load, CD4 cell counts and antibodies:What do we know and what does it all mean?
Brian Williams, SACEMA, November 2007
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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.
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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
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CD4 cells/L
Vir
ion
s/m
L
Orange Farm, South Africa. (Auvert et al. PLOS Medicine, 2005)
Viral load and CD4 cell counts
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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
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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
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Optical density log(antibody concentration)
CD
4 c
ells
/L
Antibody concentration and CD4 cell counts
ZVITAMBO (Hargrove, pers. comm.)
Up to 2000
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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
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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
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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
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Optical density i.e. ln(antibody concentration)
Fre
que
ncy
Log antibody distribution: Harare
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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
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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
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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
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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
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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
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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:
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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
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Lusaka
Gauteng
Incidence
Prevalence
Death
9095
00
05
10
4090
95
0005
1040
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Lusaka
Gauteng
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