Statistical and mathematical modelling of HIV and AIDS, effect of reverse transcriptase inhibitors and causal inference for HIV mortality.

Abstract

The HIV and AIDS epidemic has remained one of the leading causes of death in the world and

has been destructive in Africa with Sub-Saharan Africa remaining the epidemiological locus of

the epidemic. HIV and AIDS hinders development by erasing decades of health, economic and

social progress, reducing life expectancy by years and deepening poverty [57].The most urgent

public-health problem globally is to devise effective strategies to minimize the destruction caused

by the HIV and AIDS epidemic. Due to the problems caused by HIV and AIDS, well defined

endpoints to evaluate treatment benefits are needed. The surrogate and true endpoints for a

disease need to be specified. The purpose of a surrogate endpoint is to draw conclusions about

the effect of intervention on true endpoint without having to observe the true endpoint. It is

of great importance to understand the surrogate validation methods. At present the question

remains as to whether CD4 count and viral load are good surrogate markers for death in HIV or

there are some better surrogate markers. This dissertation was undertaken to obtain some clarity

on this question by adopting a mathematical model for HIV at immune system level and the

impact of treatment in the form of reverse transcriptase inhibitors (RTIs). For an understanding

of HIV, the dissertation begins with the description of the human immune system, HIV virion

structure, HIV disease progression and HIV drugs. Then a review of an existing mathematical

model follows, analyses and simulations of this model are done. These gave an insight into the

dynamics of the CD4 count, viral load and HIV therapy. Thereafter surrogate marker validation

methods followed. Finally generalized estimating equations (GEEs) approach was used to analyse

real data for HIV positive individuals, from the Centre for the AIDS Programme of Research

in South Africa (CAPRISA). Numerical simulations for the HIV dynamic model with treatment

suggest that the higher the treatment efficacy, the lower the infected cells are left in the body.

The infected cells are suppressed to a lower threshold value but they do not completely disappear,

as long as the treatment is not 100% efficacious. Further numerical simulations suggest that it

is advantageous to have a low proportion of infectious virions (ω) at an individual level because

the individual would produce few infectious virions to infect healthy cells. Statistical analysis

model using GEEs suggest that CD4 count< 200 and viral load are highly associated with death,

meaning that they are good surrogate markers for death. An interesting finding from the analysis

of this particular data from CAPRISA was that low CD4 count and high viral loads as surrogates

for HIV survival act independently/additively. The interaction effect was found to be insignificant.

Individual characteristics or factors that were found to be significantly associated with HIV related

death are weight, CD4 count< 200 and viral load.