The Role of Exposure History on HIV Acquisition: Insights from Repeated Low-dose Challenge Studies

To assess the efficacy of HIV vaccine candidates or preventive treatment, many research groups have started to challenge monkeys repeatedly with low doses of the virus. Such challenge data provide a unique opportunity to assess the importance of exposure history for the acquisition of the infection. I developed stochastic models to analyze previously published challenge data. In the mathematical models, I allowed for variation of the animals' susceptibility to infection across challenge repeats, or across animals. In none of the studies I analyzed, I found evidence for an immunizing effect of non-infecting challenges, and in most studies, there is no evidence for variation in the susceptibilities to the challenges across animals. A notable exception was a challenge experiment by Letvin et al. Sci Translat Med (2011) conducted with the strain SIVsmE660. The challenge data of this experiment showed significant susceptibility variation from animal-to-animal, which is consistent with previously established genetic differences between the involved animals. For the studies which did not show significant immunizing effects and susceptibility differences, I conducted a power analysis and could thus exclude a very strong immunization effect for some of the studies. These findings validate the assumption that non-infecting challenges do not immunize an animal — an assumption that is central in the argument that repeated low-dose challenge experiments increase the statistical power of preclinical HIV vaccine trials. They are also relevant for our understanding of the role of exposure history for HIV acquisition and forecasting the epidemiological spread of HIV.

regoes12pcb-package regoes12pcb-package Supplementary online material accompanying Regoes RR, PLoS Comp Biol (2012) Description This package contains the repeated low-dose challenge data, likelihood and power analysis functions used in Regoes RR, PLoS Comp Biol (2012).

Details
This material is provided mostly for the sake of transparency. The functions were developed for the specific research questions and datasets that I analyzed in Regoes RR, PLoS Comp Biol (2012). They may not work beyond this restricted field of application.
I tried to document the functions as well as I could. However, documentation is only rudimentary, and will remain so because the package will not be updated.
For a summary of the data included in this package see rldc.data.
For a summary of the likelihood functions see likelihoods.regoes12pcb See power.analysis for documentation of the power analysis function.

Author(s)
Roland R Regoes <roland.regoes@env.ethz.ch> The package is not maintained. It is provided as supplementary online material to the paper Regoes RR, PLoS Comp Biol (2012).

References
Regoes RR (2012 fit.function Fitting various models to repeated low dose challenge data.

Description
Function that fits the geometric, immune priming, or heterogeneous susceptibility model to repeated low dose challenge data. This function was used in Regoes RR, PLoS Comp Biol (2012).
CI.type character string indicating the type of confidence interval to calculate. Possibilities are "profile.ll" (the appropriate method), or the over-confident "fisher.info".

Value
Named vector with log.likelihood, parameter estimates, and upper and lower bounds of their 95% confidence intervals.

Note
Do not forget to load the dataset to be fitted, e.g. data(wilson06jv).

likelihoods.regoes12pcb
Author ( Arguments p.inf scalar between 0 and 1 denoting the infection probability (geometric infection model), or the mean infection probability (heterogeneous susceptibility model).
p.inf1 scalar between 0 and 1 denoting the initial infection probability in the immune priming models.
p.inf2 scalar between 0 and 1 denoting the infection probability after the the lth challenge. power.analysis power.analysis Power to detect immunization or variation in susceptibility across animals in repeated low-dose challenge data.

Description
This function estimates the statistical power to detect immunization effects or heterogeneous susceptibility in repeated low-dose challenge data. It was used in Regoes RR, PLoS Comp Biol ( n.animals number of animals in the experiment.
n.chall.max integer vector of length n.animals containing the maximum number of challenges applied to each animal.
model.1 character string defining the first model to fit. Possible are "geometric", "immunization", or "frailty2". The first model is compared to the fit of the second model by a likelihood ratio test.
model.2 character string defining the second model to fit. Possible are "geometric", "immunization", or "frailty2". The first model is compared to the fit of the second model by a likelihood ratio test.
output.fits logical. If TRUE fits are returned. Only for diagnostic purposes and low n.expt. output.not.converged logical. If TRUE prints data and fit details of non-converged fits. Only for diagnostic purposes.
output.dots logical. If TRUE the function prints "*" for experiments that establish a significant difference between the fits of model.1 and model.2, "." if there is no significant difference, and "x" or "?" if there were convergence problems.

Value
Returns a list with the power estimate and the fraction of fits of the second model that converged. If output.fits=TRUE the fits are also returned.

References
Regoes RR (2012). The role of exposure history on HIV acquisition: insights from repeated lowdose challenge studies. PLoS Comp Biol.

See Also
The in silico repeated low-dose challenge data are generated with the function sim.rldc.
p.inf1 scalar between 0 and 1 denoting the initial infection probability in the immune priming models.
p.inf2 scalar between 0 and 1 denoting the infection probability after the the lth challenge.
l integer indicating the number of challenges after which susceptibility jumps from p.inf1 to p.inf2. Only relevant for the jump variant of the immune priming model. output.nuisance.par logical. If set to TRUE, the value of nuisance parameter maximizing the profile likelihood is returned also.

Value
The value of the log profile likelihood, or, if output.nuisance.par==TRUE a list with likelihood and nuisance parameter.

Format
Data frames with the following columns: Treatment a factor with only one level control.
AnimalID unique identifier of each animal challenges.received a numeric vector indicating the number of challenges received by each animal.
infected a logical vector indicating the final infection status of each animal

Details
The data were collected from the publications cited below, and analyzed in Regoes RR (2012) PLoS Comp Biol.
In some instances, tables with the data were available in the printed versions of the articles. In most cases, however, the data were read off from Kaplan-Meier curves in the papers or their accompanying supplementary material in combination with information in the text.
The data from Hansen et al, Nat Med (2009), were read off the virus load time courses in their Figure 4c. From that Figure, virus loads profiles from 15 control monkeys can be identified. This is inconsistent with the statements of the authors that there were 16 control monkeys. Although I asked the authors about this multiple times they did not clarify this inconsistency.

Description
Function that generates repeated low dose challenge data according to the geometric, immune priming, or heterogeneous susceptibility models defined in Regoes RR, PLoS Comp Biol (2012). n.chall.max integer vector of length n.animals containing the maximum number of challenges applied to each animal.
model.pars appropriately named vector with the parameters of the true model. E.g. for model.true = "immunization" we need model.pars = c(p.inf1 = 0.8, p.inf2 = 0.2). The names of model.pars can be seen in the likelihoods.regoes12pcb. print.comments logical. If TRUE model and parameter info printed in the beginning of the output.