Uncertainty quantification in modeling HIV viral mechanics

Abstract

We consider an in-host model for HIV-1 infection dynamics developed and validated with patient data in earlier work [7]. We revisit the earlier model in light of progress over the last several years in understanding HIV-1 progression in humans. We then consider statistical models to describe the data and use these with residual plots in generalized least squares problems to develop accurate descriptions of the proper weights for the data. We use recent parameter subset selection techniques [5,6] to investigate the impact of estimated parameters on the corresponding selection scores. Bootstrapping and asymptotic theory are compared in the context of confidence intervals for the resulting parameter estimates.

Uncertainty quantification for a model of HIV-1 patient response to antiretroviral therapy interruptions

“…For these data points, the expectation maximization (EM) algorithm was applied in [1]. For this report, we chose to model the data for Patient 1 from Banks et al, because the mathematical model was very accurate for over four years (similar results for other patients are presented in [20] and confirm the findings summarized here). The EM data points for Patient 1 were combined with the uncensored data to form a data set that could be used for parameter estimation.…”

Model comparison tests to determine data information content

“…These known [6] statistically-based model comparison tests add to a growing list of tools including the parameter subset/parameter selectivity tools based on parameter sensitivity based scores [3], and other Fisher Information Matrix, Akaike Information Criteria based techniques [8, 11] that may be used to better understand information content in data sets.…”

“…A recent concrete example involves previous HIV models [1, 5] with 15 or more parameters to be estimated. In [3], using recently developed parameter selectivity tools [4] based on parameter sensitivity based scores, the authors showed that many of the parameters could not be estimated with any degree of reliability. Moreover, it was found that quantifiable uncertainty varies among patients depending upon the number of treatment interruptions (perturbations of therapy).…”

A dynamical modeling approach for analysis of longitudinal clinical trials in the presence of missing endpoints

“…It was found in [1] that this model has impressive predictive capability when comparing model simulations (with parameters estimated using only half of the longitudinal observations) to the corresponding full clinical data sets. This model was further validated in [2, 3]. We suggest this provides a sufficient rationale and support for use of this model to predict the missing endpoints and predict the final outcomes for our clinical trials.…”