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
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.
                       The standard model
Viral load




                               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
                               Viral load/mL
                                   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–

              Log(Initial viral load) sets survival
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
                                                           Viral load

                                                           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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