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

Optical density i.e. ln(antibody concentration)

Fre

que

ncy

Log antibody distribution: Harare

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

Lusaka

Gauteng

Incidence

Prevalence

Death

9095

00

05

10

4090

95

0005

1040

Lusaka

Gauteng