# Viral load CD4 cells and antibodies

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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
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
Notice at the Cambridge University Computer Centre ‘Surgery’, 1970.
The standard model

CD4
Time                         Time
Antibodies

Acute phase ~ weeks
Final phase ~ months
Interested in the long
chronic phase ~ 10 yrs
Time
Virions/mL   Viral load and CD4 cell counts

CD4 cells/mL
Orange Farm, South Africa. (Auvert et al. PLOS Medicine, 2005)
Viral load and CD4 cell counts
10,000

1000

100
Virions/mL

10

1

0.1

0.01

CD4 cells/mL
Orange Farm, South Africa. (Auvert et al. PLOS Medicine, 2005)
CD4 cell count decline for different viral loads

150

100

50
CD4 slope/mL/year

0

-50

-100

-150

-200

-250

-300
0.001   0.01   0.1      1         10   100   1000
Virions/μL
Rodriguez et al. Jama, 2006.
Antibody concentration and CD4 cell counts
 Up to 2000
CD4 cells /mL

Optical density  log(antibody concentration)

ZVITAMBO (Hargrove, pers. comm.)
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 distribution: Young men in Orange Farm, South Africa
Frequency

0.01   0.1     1           10                100             1000        10,000
Orange Farm, South Africa. (Auvert et al. PLOS Medicine 2005)
CD4 cell counts in HIV-positive and HIV-negative people

Orange Farm, South Africa. (Auvert et al. PLOS Medicine 2005); Zambia (Kelly et al. Acta Tropica 2002)
Log antibody distribution: Harare
Frequency

Optical density i.e. ln(antibody concentration)
Combine the individual decline with
the initial distribution
2000                        Assume that survival is
CD4
independent of the
CD4 cells/ml

initial value of the CD4
1000                        cell count

500

HIV–
0               10                   20
Survival Time (years)
Assume that survival is
CD4                             independent of the
initial value of the CD4
cell count

Time
CD4 in HIV–

CD4 cell counts in HIV-positive and HIV-negative people

Orange Farm, South Africa. (Auvert et al. PLOS Medicine 2005); Zambia (Kelly et al. Acta Tropica 2002)
Distribution of CD4 cell count decline
250

200
Number of people

150

100

50

0
-50                            0         50          100           150      200   250
Decline in CD4 cell counts/mL/yr
Survival of young men in Orange Farm, South Africa?
Survival (yrs) = 42.2 – 6.5log10(VL/mL)

30
Frequency

20

Weibull survival

10

0
0        5      10      15             20             25             30             35
Time years
Orange Farm, South Africa. (Auvert et al. PLOS Medicine 2005)
So we need to explain why:

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:

V  a1 eb1C

4. Antibody concentration declines exponentially with CD4:

A  a2 eb2 C
Survival against age at HIV seroconversion

1.0
Proportion surviving

0.8
2.5
0.6
10

0.4                                                             20
30
0.2                                                             40
70                60             50
0.0
0             5                        10                        15
Years since infection
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
Prevalence
Lusaka                   Incidence

Gauteng
Death

00
00                                  05
40                10

05

95
95         10
90
90                   40
Lusaka

Gauteng

```
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