Multiple-reactivation model

This repository contains jupyter notebooks, Stan models and data used in our PLOS Computational Biology paper

van Dorp CH et al. (2020) Models of SIV rebound after treatment interruption that involve multiple reactivation events. PLoS Comput Biol 16(10): e1008241.

To use the code, simply clone the repository

$ git clone https://github.com/lanl/multiple-reactivation-model.git

The model is described in full detail in the paper. In short, we present a refinement of a model developed by Pinkevych et al. and Hill et al. for SIV and HIV rebound after treatment interruption, that takes the effect of multiple reativation events into account. We derive a parameteric probability density function for the time to viral rebound, and implement this in the Stan programming language. We fit the model to data from SIV infected and very early treated macaques, published by Whitney et al. (2014), and (2018).

This repository contains scripts to fit a number of HIV and SIV viral rebound models to viral load data from treatment interruption experiments and acute infections. The scripts generate parameter estimates of the viral growth rate after rebound and the recrudescence rate after treatment interruption. The models are implemented in the probabilistic programming language Stan, and formulated in a Bayesian framework. In particular, we implemented our multiple-reactivation model, which is a refinement of a model for viral rebound developed by Pinkevych et al. and Hill et al.

In addition to the Stan models, we provide Jupyter notebooks that guide the user through the process of the parsing of the data, compiling and running the Stan models, extracting estimates from the resulting chain and making figures of these results. The notebooks can also be used for a more theoretical analysis of the mutliple-reactivation model. A number of functions to simulate viral rebound trajectories is bundled in the included python module mrmpytools. This simulator can also be used for sensitivity analyses, which we demonstrate in one of the notebooks. The repository contains a data set from SIV infected macaques that we used to test our model.

Dependencies

Make sure the following python packages are installed

pystan
scipy
numpy
matplotlib

Which can be installed with e.g.

$ pip install pystan

For using the notebooks, Jupyter is required. Installation instructions can be found here. The code is only tested on Ubuntu 18.01, Python version 3.6.9 (pystan version 2.19), but should also work on Mac OSX and Windows 10.

Data

The data folder contains the timeseries used in the analysis. The data has been described by Whitney et al. in two publications

Whitney et al. Rapid seeding of the viral reservoir prior to SIV viraemia in rhesus monkeys. Nature, 512(7512):74-77, Aug 2014.

Whitney et al. Prevention of SIVmac251 reservoir seeding in rhesus monkeys by early antiretroviral therapy. Nat. Commun., 9(1):5429, 12 2018.

The data is separated into two csv files, containing rebound timeseries and acute infection timeseries respectively.

rebound-data-long.csv Viral load measurements after treatment interruption
acute-data-long.csv Viral load measurements during acute infection

Notebooks

The following jupyter notebooks can be found in the notebooks folder:

VLProcessSimulations.ipynb Simulate trajectories and first passage times of the viral load process. These are used to make Figure 1 and 2 of the paper and Figure S3, S4, S5 and S6 of the Supplementary Information.
ParseData.ipynb This notebook is used to load the viral load data into a python dictionary. This dictionary is "pickled" into a file that can be loaded into the other notebooks for further analysis.
FitStanModels.ipynb In this notebook, we fit the Stan models to the VL time series. We then make Figure 3 of the paper and Supplementary Figure S1 and S2.
FitAcuteStanModel.ipynb In this notebook, we fit a Stan models to the acute VL time series.
ReboundTimeVarianceAnalysis.ipynb What percentage of the variance of the rebound time is due to the first recrudescence event, and when do other reactivations become important. This notebook is used to make Figure 4.
SensitivityAnalyses.ipynb How sensitive is the model to misspecification? Look at the effect of a misspecified initial viral load and intra-host variation of the exponential growth rate. Create Figure 5.

Stan models

For more information on the Stan programming language, see the Stan website. In the folder stan-models the following files can be found

logistic-rebound-model-multiple-reactiv-II.stan is the main model, implementing the stochastic multiple-reactivation model in Stan.
logistic-rebound-model-single-reactiv.stan This is the simple single-reactivation model.
logistic-rebound-model-multiple-reactiv-CD.stan This is Pinkevych's approximation of the multiple-reactivation model implemented in Stan.
logistic-acute-model.stan Simple logistic growth model to fit the acute infection data and estimate growth rates.
expon-rebound-model-multiple-reactiv-II-Gsp.stan Simplified model with exponential growth instead of logistic growth and no random effects.

Python module

The Python module mrmpytools contains common functions used in the notebooks. To get access to this module from a Jupyter notebook in the notebooks folder, add the parent directory to the path with

import sys
sys.path.append("..") ## or the location of the mrmpytools module

Then import elements from this module. For instance

import mrmpytools.utilities as util
x1, x2 = util.unzip([('a', 1), ('b', 2)]) ## should be ['a', 'b'], [1, 2]

The folder mrmpytools contains the following files

plots.py Some plotting functions.
pystantools.py Some functions for compiling and analyzing Stan models.
stats.pyImplements the rebound time distribution and many other functions.
wkb.py Functions used for the WKB approximation
simulations.py Simulates the viral load process.
definitions.py Define constants used throughout the project.
utilities.py Some auxiliary functions used throughout the project.

copyright 2020. Triad National Security, LLC. All rights reserved. This program was produced under U.S. Government contract 89233218CNA000001 for Los Alamos National Laboratory (LANL), which is operated by Triad National Security, LLC for the U.S. Department of Energy/National Nuclear Security Administration. All rights in the program are reserved by Triad National Security, LLC, and the U.S. Department of Energy/National Nuclear Security Administration. The Government is granted for itself and others acting on its behalf a nonexclusive, paid-up, irrevocable worldwide license in this material to reproduce, prepare derivative works, distribute copies to the public, perform publicly and display publicly, and to permit others to do so.