EPICE-HIV: An Epidemiologic Cost-Effectiveness Model for HIV Treatment

Björn Vandewalle; Josep M. Llibre; Jean-Jacques Parienti; Andrew Ustianowski; Ricardo Camacho; Colette Smith; Alec Miners; Diana Ferreira; Jorge Félix

doi:10.1371/journal.pone.0149007

Abstract

The goal of this research was to establish a new and innovative framework for cost-effectiveness modeling of HIV-1 treatment, simultaneously considering both clinical and epidemiological outcomes. EPICE-HIV is a multi-paradigm model based on a within-host micro-simulation model for the disease progression of HIV-1 infected individuals and an agent-based sexual contact network (SCN) model for the transmission of HIV-1 infection. It includes HIV-1 viral dynamics, CD4⁺ T cell infection rates, and pharmacokinetics/pharmacodynamics modeling. Disease progression of HIV-1 infected individuals is driven by the interdependent changes in CD4⁺ T cell count, changes in plasma HIV-1 RNA, accumulation of resistance mutations and adherence to treatment. The two parts of the model are joined through a per-sexual-act and viral load dependent probability of disease transmission in HIV-discordant couples. Internal validity of the disease progression part of the model is assessed and external validity is demonstrated in comparison to the outcomes observed in the STaR randomized controlled clinical trial. We found that overall adherence to treatment and the resulting pattern of treatment interruptions are key drivers of HIV-1 treatment outcomes. Our model, though largely independent of efficacy data from RCT, was accurate in producing 96-week outcomes, qualitatively and quantitatively comparable to the ones observed in the STaR trial. We demonstrate that multi-paradigm micro-simulation modeling is a promising tool to generate evidence about optimal policy strategies in HIV-1 treatment, including treatment efficacy, HIV-1 transmission, and cost-effectiveness analysis.

Citation: Vandewalle B, Llibre JM, Parienti J-J, Ustianowski A, Camacho R, Smith C, et al. (2016) EPICE-HIV: An Epidemiologic Cost-Effectiveness Model for HIV Treatment. PLoS ONE 11(2): e0149007. https://doi.org/10.1371/journal.pone.0149007

Editor: Dimitrios Paraskevis, University of Athens, Medical School, GREECE

Received: August 6, 2015; Accepted: January 25, 2016; Published: February 12, 2016

Copyright: © 2016 Vandewalle et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: Aggregate results from the STAR trial have been presented by Cohen et al. (Cohen CJ, Wohl D, Arribas JR, Henry K, Van Lunzen J, Bloch M, et al. Week 48 results from a randomized clinical trial of rilpivirine/emtricitabine/tenofovir disoproxil fumarate vs. efavirenz/emtricitabine/tenofovir disoproxil fumarate in treatment-naive HIV-1-infected adults. Aids. 2014; 28:989-97 and Cohen C, Wohl C, Cavassini C, Henry K, Bloch M, Towner W, et al., editors. STaR Study: Single-Tablet Regimen Rilpivirine/Emtricitabine/Tenofovir DF Is Non-Inferior Compared to Efavirenz/Emtricitabine/Tenofovir DF and Improves Patient Reported Outcomes through Week 96. ICAAC; 2014 September 5–9, 2014; Washington DC, USA). Patient level data access was granted by Gilead for the purpose of the present analysis. Gilead's contact information for the data: filipa.aragao@gilead.com.

Funding: Gilead contracted with Exigo for the development of the model and its validation using STaR clinical trial data. Gilead also made STaR study data available for external model validation. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Exigo Consultores provided support in the form of salaries for authors BV, DF, JF, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the ‘author contributions’ section.

Competing interests: The authors have the following interests: Gilead contracted with Exigo for the development of the model and its validation using STaR clinical trial data. Gilead also made STaR study data available for external model validation. Björn Vandewalle, Diana Ferreira and Jorge Félix are employed by Exigo Consultores. There are no patents, products in development or marketed products to declare. This does not alter the authors' adherence to all the PLOS ONE policies on sharing data and materials, as detailed online in the guide for authors.

Introduction

As a result of the introduction of increasingly potent and safe anti-retroviral therapy (ART), over the last decade HIV-1 infection has largely become a manageable disease, with mortality rates approaching those of the general population in many countries [1–3]. Similar to other pharmaceutical drugs, before marketing authorization, efficacy and safety profiles of new anti-retroviral regimens are usually investigated exclusively in clinical trial settings.

Most current clinical trials on HIV-1 ART follow a predefined schedule of follow-up visits rarely spaced more than 2 to 3 months apart, with quite rapid confirmation of virologic failure and drug withdrawal after initial detection [4–7]. Common clinical trial efficacy endpoints and their algorithms (e.g. the percentage of virologically suppressed patients at a certain time window, determined by the FDA Snapshot algorithm) are crucially dependent on these pre-specified follow-up protocols [4, 5, 7, 8]. International HIV-1 treatment guidelines, however, suggest follow-up visits for plasma HIV-1 RNA viral load assessment every 3 to 6 months (with more frequent monitoring only at the start of ART) and confirmation of virologic failure 1 to 2 months later [9]. Moreover, in clinical practice, much heterogeneity tends to be observed with respect to the monitoring of ART, and subjects on stable and suppressive regimens are commonly seen every 6 months [10, 11].

Despite efforts to raise patient´s adherence [12–16], in clinical practice it continues to be lower in comparison to clinical trials [17, 18]. For many patients it may be quite difficult to maintain a high level of adherence, necessary to achieve durable viral suppression, over the life-time course of a chronic disease [19–23]. Suboptimal adherence not only limits the effectiveness of therapy in terms of viral suppression, but also facilitates the replication and selection of resistant mutant viral strains, often limiting subsequent ART options [24, 25]. HIV resistance drug resistance has further become a relevant public health issue, as HIV-1 resistance mutations can be transmitted to other individuals [26].

Due to the heterogeneity observed in real-life monitoring schedules and adherence patterns, basing cost-effectiveness models for HIV-1 treatment mainly on the efficacy observed in clinical trials has the potential of leading to biased estimates of true effectiveness. Moreover, for drugs whose public use has only recently been authorized, little to no data might be available from observational studies, further restricting modeling options.

State of the art cohort and micro-simulation cost-effectiveness models for HIV-1 treatment typically focus on clinical outcomes such as viral suppression, life expectancy, causes of death, opportunistic infections and time on treatment [27–31]. Many of these models lack the ability of quantifying the impact of different treatment regimens and adherence behavior on the transmission of HIV-1 and HIV-1 drug resistance [27–31].

Some models that include transition modules tend to do so in a mostly deterministic, non-dynamic nature, making use of systems of ordinary differential equations. These models are capable of distinguishing between different populations (uninfected, infected, heterosexual, homosexual, injection drug users), linking them through pathway-dependent infection rates, but lack the ability to capture important population behavioral heterogeneity [27, 29, 31].

In this paper, we present EPICE-HIV, an epidemiologic cost-effectiveness model for HIV-1 treatment, designed to produce qualitatively and quantitatively credible results without overly depending on outcomes of clinical trials and observational studies. EPICE-HIV is a multi-paradigm model based on a within-host micro-simulation for the disease progression of HIV-1 infected individuals and an agent-based sexual contact network (SCN) model for the transmission of HIV-1 infection (transmission module). The two parts of the model are joined through a per-sexual-act, plasma HIV-1 RNA viral load dependent probability of HIV-1 transmission in serodiscordant couples and a CD4⁺ T cell count dependent mortality rate.

Since the algorithm driving the HIV-1 transmission module has been described and validated previously in the context of sexually transmitted diseases [32], this paper will focus on the within-host model of EPICE-HIV, in which disease progression is driven by adherence to ART and the interdependent changes in CD4⁺ T cell counts and plasma HIV-1 RNA levels. For validation purposes, a simulation study was set up to investigate the effectiveness of once daily treatment with rilpivirine 25mg (RPV), emtricitabine 200mg (FTC) and tenofovir DF 245mg (TDF) as initial ART, mimicking the conditions and population of the STaR study [5, 33].

Material and Methods

In the within-host model (Fig 1), adherence to the ART regimen of primary interest is modeled using a binary autoregressive model, assuming adherence on any given day is conditional on adherence on the previous day. A per-drug, one-compartment, pharmacokinetics model (PK) followed by a pharmacodynamics model (PD), link adherence to a progressive HIV-1 dynamics model (HIV-D) generating time dependent plasma concentrations of free virus and uninfected and infected CD4⁺ T cells. Treatment regimens of secondary interest are modeled connecting a previously published discrete event simulation (DES) model for HIV-1 treatment [34] to the HIV-D model.

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Fig 1. Diagram of the within-host model for disease progression of HIV-1 infected individuals.

For the treatment regimen of primary interest (blue diagram), the adherence model dictates the daily intake of ART. Through a pharmacokinetic (PK) and pharmacodynamic (PD) model, the plasma drug concentration and drug effect are determined. Drug effect influences the inter-dependent and time-evolving plasma HIV-1 RNA level and CD4+ T cell count in the basic HIV-1 dynamics model (HIV-D). For treatment regimens of secondary interest (orange diagram), a discrete event simulation model (DES) determines the plasma HIV-1 RNA level over time. Using the dynamics of the HIV-D model, CD4+ T cell counts are updated accordingly.

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Basic HIV-1 Dynamics Model

The HIV-D model consists of four populations: uninfected CD4⁺ T cells (T₁), productively infected activated CD4⁺ T cells (T₂), latently infected resting CD4⁺ T cells (L) and HIV-1 virions (V) [35]. Initially, only uninfected target CD4⁺ T cells (T₁) and HIV-1 virions (V) are present in the system (Table 1).

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Table 1. Basic HIV-D model populations and initial values [35].

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HIV-1 virions can infect target CD4⁺ T cells, a process modeled through a commonly used “mass-action” term , with the target CD4⁺ T cell infection-rate by free virus. Upon infection, a small fraction α_L of CD4⁺ T cells will result in latently infected CD4⁺ T cells (L), not actively producing HIV-1 virions. The remaining fraction of infections results in productively infected CD4⁺ T cells (T₂). Latently infected CD4⁺ T cells are activated into productively infected cells at a constant rate α_L.

All cells have a finite lifespan, determined by death-rates and δ_L for uninfected, productively infected and latently infected CD4⁺ T cells, respectively. For HIV-1 virions, the death-rate is given by δ_V. Source rates of uninfected CD4⁺ T cells () and HIV-1 virions (f_pp_vT₂), drug potency (ε) and persistent low level viremia (V_Min) are discussed further on in this section.

The following system of ordinary differential equations, of which a graphical illustration is given in Fig 2, represents the resulting rate of change in the concentration of cells for each of the four modelled populations: (1)

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Fig 2. Stock and flow diagram of the basic HIV-1 dynamics model, modified from Rong et al [35].

Uninfected CD4+ T cells (T₁) are produced at a rate . Infected CD4+ T cells are produced at a rate , following mass-action kinetics between free virions (V) and uninfected CD4+ T cells. A small fraction α_L of infections results in latently infected resting CD4+ T cells (L). The remaining fraction results in productively infected activated CD4+ T cells (T₂). Latently infected CD4+ T cells are activated into productively infected cells at a constant rate a_L. Free virions are produced by productively infected CD4+ T cells at a rate f_pp_vT₂.

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Disease Progression.

During the first stage of HIV-1 infection (acute infection), in the absence of treatment, large amounts of virus are being produced, destroying CD4⁺ T cells in the process. As a result, CD4⁺ T cell counts drop rapidly and viral load levels spike. At the end of this stage CD4⁺ T cell counts begin to increase, but do not return to pre-infection levels. At the same time, plasma viral loads drop back down and settle into a viral set-point after a couple of months, remaining at more stable levels thereafter. HIV-1 infection then moves into a clinical latency stage, in which HIV-1 continues reproducing, but at much lower levels than during the acute stage. This stage, though very variable, typically lasts about 8–10 years and is characterized by a slow depletion of CD4⁺ T cells and late stage increase in plasma viral load [36–38].

Over time the efficiency in viral production increases due to different factors, including the progressive loss by the immune system of the ability to contain viral production. In the model, this is implemented by applying a time-dependent replication increase factor (f_p) to the initial viral production rate (p_v) of productively infected CD4⁺ T cells (T₂) [39]. Furthermore, since HIV-1 infection is known to eventually exhaust the body’s capacity to produce new uninfected CD4⁺ T cells, a time-dependent capacity reduction factor (f_s) is also applied to the base CD4⁺ T cell source rate () [39].

Both adjustment factors (f_p and f_s) depend on a measure for the total viral burden accumulated over time since the start of infection, as (2) where Q represents a Weibull cumulative distribution function on the viral burden V_b, the area under the curve of the time evolving virion concentration V with respect to reference value V_ref [39]: (3)

The effect of specific incumbent period determinants that may affect disease progression (e.g. age at infection, the presence of other sexually transmitted diseases) have not been included in the current paper and will be addressed in future work.

Drug Potency.

Anti-retroviral drugs within different classes (nucleoside reverse transcriptase inhibitors (NRTI), non-nucleoside reverse transcriptase inhibitors (NNRTI), protease inhibitors (PI), etc.) act on different points in the complex viral replication process in CD4⁺ T cells. In order not to overly complicate the HIV-D model, an overall effect of ART on plasma CD4⁺ T cell and HIV-1 virion concentrations was assumed. This overall drug effect or drug potency ε represents the percentage of new cell infections inhibited and acts upon the mass-action term by reducing the rate at which uninfected target CD4⁺ T cells are infected by free virus [35].

The analysis of viral decay following initiation of ART shows that plasma HIV-1 RNA levels typically decline in three distinct phases [35]. In the model, to simulate the second phase decay, a population of latently infected CD4⁺ T cells was considered, with a much lower decay rate than the productively infected CD4⁺ T cells.

Persistent Low Level Viremia.

Studies with especially sensitive assays [40] have demonstrated that the second phase decay typically brings plasma viral loads down to a new quasi-steady state below the 50 plasma HIV-1 RNA copies/mL threshold, with an average of persistent low level viremia of around 3 copies/mL [41]. This could reflect the release of viruses from other stable reservoirs, potentially outside of the plasma, which are unaffected by treatment intensification. To accomplish a persistent low level of viremia in the model, an extra term δ_VV_min was added to the rate of change in concentration of virions, representing the potential inflow of free viruses from external reservoirs.

The level of persistent low viremia correlates well with pre-therapy plasma HIV-1 RNA levels, more than with specific treatment regimens, even though some reports have linked PI with higher rates of low level viremia than NNRTI [42]. Moreover, longitudinal analysis revealed no significant decline in the level of persistent viremia over time (60–110 weeks), while on suppressive ART. As a result of this, the HIV-D model assumes that the level of persistent low-viremia under ART (represented by the parameter V_min) remains constant over time and depends only on pre-therapy plasma HIV-1 RNA levels, through a log-normal model fitted to data presented in Maldarelli et al. (2007) [41]. The results of this analysis are presented in Table 2 and show a highly significant effect of pre-therapy plasma HIV-1 RNA levels (log₁₀ copies/mL) on persistent low-level viremia.

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Table 2. Log-normal model parameter estimates for on-therapy plasma HIV-1 RNA levels as a function of baseline pre-therapy plasma HIV-1 RNA levels.

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Between-Patient Variability.

Between-patient variability in cell concentrations in plasma has been introduced by exploiting the stable-state solution of the untreated (ε = 0), disease progression free (f_p = 1 and f_s = 1) system of ordinary differential equations. For untreated individuals, the contribution of the latently infected CD4⁺ T cell population to plasma HIV-1 RNA levels is negligible. Ignoring the presence of latently infected CD4⁺ T cells, two key parameters of the HIV-D model, the HIV-1 infection rate of CD4⁺ T cells () and the viral production rate (p_V), can be written as a function of the stable-state plasma concentrations of target CD4⁺ T cells () and HIV-1 virions (), as (4)

Both productively infected activated and latently infected resting CD4⁺ T cells represent only a residual fraction of the total CD4⁺ T cell population. As a result, the total CD4⁺ T cell plasma concentration (T) can be approximated by the target CD4⁺ T cell population (T ≅ T₁). Between-patient variability in plasma cell concentrations over time can then be controlled by allowing for variability in model parameters and p_V, substituting the desired viral set-point HIV-1 virion (V_s) and total CD4⁺ T cell (T_s) concentrations for and in the equations above.

Model Parameters.

All base parameters relevant to the HIV-D model can be found in Table 3. Most parameters were initially taken from the literature [35, 39, 43]. Some were recalibrated to suit the purpose of modeling HIV-1 disease progression.

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Table 3. Parameter values used in the basic HIV-D model.

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Many different values can be found in the literature for the viral production rate (p_V) and the HIV-1 infection rate of CD4⁺ T cells (). For the base-case examples, presented throughout the paper, the viral production rate (p_V) was fixed [35]. The HIV-1 infection rate () was calibrated, from within a realistic range of values [35], as for stable-state CD4⁺ T cells count and HIV-1 viral load to present suitable values (Fig 3). In the section on between-patient variability, it has been explained how these two parameters can be varied to introduce variability in stable-state CD4⁺ T cell counts and HIV-1 viral loads for different patients.

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Fig 3. Evolution of plasma HIV-1 RNA levels and CD4+ T cell counts in an untreated subject.

Left: Plasma HIV-1 RNA levels as a function of time, simulated by the HIV-D model accounting for disease progression. Right: corresponding CD4⁺ T cell counts. The model simulates the 3 typical stages of HIV-1 infection: acute infection, clinical latency and AIDS phase. Dashed grey lines represent the HIV-D model without disease progression, the stable-state solution of which is exploited to introduce between-patient variability in plasma cell concentrations.

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The remaining parameters that were subject to recalibration are related to the HIV-1 disease progression module. The conceptual model for disease progression was taken from a paper on co-infection with HIV-1 and tuberculosis, based on a different HIV-1 dynamics model [39]. Recalibration of the model parameters was necessary to result in a realistic CD4+ T cell decline and HIV-1 viral load increase over time (Fig 3 in the results section).

Disease Monitoring.

Not all individuals in the simulated population are forced to perform regular HIV-1 testing. For those that do, HIV-1 testing is assumed to follow a Poisson process, with exponential times between consecutive tests. Upon being diagnosed, a fraction of infected individuals may choose not to seek treatment. For those who do seek treatment, regular medical visits are programmed in which CD4⁺ T cell counts and plasma HIV-1 RNA levels are monitored until a patient is considered eligible for treatment (e.g.: CD4⁺ T cell count below 500 or 350 cells/mm³ [9, 44]).

The model is completely flexible with respect to disease monitoring parameters, making it possible to investigate the effect on results of different hypotheses in terms of patients’ willingness to test, willingness to be treated, monitoring frequency and treatment eligibility.

Primary Treatment Regimen Model

Adherence to Therapy.

A quantitative relationship can be observed between the duration of the longer treatment interruption and the average adherence level [45], in which treatment interruptions of 30 or more days are not unusual for patients with an average adherence between 40% and 60%. Furthermore, there is a differential impact of adherence and treatment interruptions on the risk of virologic rebound (> 400 plasma HIV-1 RNA copies/mL) when comparing NNRTI- based ART to ritonavir-boosted (PI/r) based ART [45]. For NNRTI, due to their long terminal pharmacokinetic tail, at low-to-moderate adherence levels, sustained treatment interruptions pose a greater risk of virologic rebound than a comparable number of interspersed missed doses. On the other hand, PI/r average adherence rather than consecutive missed doses is found to be associated with virologic rebound. In raltegravir-based regimens longer treatment interruption and average adherence were both independently associated with virological failure [46]. Lastly, and most importantly, the quantitative relationship between the longer treatment interruption and the average adherence level seems to depend little on specific treatment regimens [45].

The correct modeling of the daily adherence process, in order to capture the delicate relationship between treatment interruptions and average adherence, is of utmost importance. Assuming adherence is a memoryless process may be misleading because the probability of a treatment interruption of 30 or more days, related to an average adherence of 50%, is almost non-existing. As such, in EPICE-HIV, adherence is modeled using a binary autoregressive model, assuming adherence on any given day is a random process, conditional on adherence on the previous day.

It depends on two key parameters: the probability of taking drugs on the current day, given drugs were skipped the previous day (p₁₀) or not (p₁₁). For each individual in the simulated population, an expected average adherence level (α_Adh) is sampled from a pre-defined empirical or theoretical population-level distribution. Given this adherence level, the parameters p₁₀ and p₁₁ are then determined randomly for each individual as (5)

Here, p₁₀ is sampled from one of two possible continuous uniform distributions, conditional on the expected average adherence level being inferior or superior to 80%. The uniform distributions were calibrated as to result in a qualitatively representative simulated relationship between the longer treatment interruption and average adherence [45]. No formal calibration techniques were used. p₁₁ Is determined as a function of p₁₀ and α_Adh to ensure that the adherence level of each individual converges over time to the pre-specified average adherence level α_Adh.

PK/PD Modeling.

Normalized drug concentrations C_n(t) = C(t)/IC₅₀ (with C(t) the drug concentration and IC₅₀ the 50% inhibitory concentration against wild-type virus) are modeled as a function of time as in [47] using the impulsive differential equation: (6)

Normalized concentration C_n(t) is assumed to increase instantaneously by a single amount (C_n,sd) every time-point τ_i (for i = 1,2, …) a dose is taken, while in between doses C_n(t) decays exponentially with a certain rate w_C. For most commercially available antiretroviral drugs, values are available for their 50% inhibitory concentration (IC₅₀), plasma half-life (t_1/2), required dosing interval (δτ = τ_i+1−τ_i) and related maximum concentration (C_max). These values allow for w_C and C_n,sd to be determined as follows: (7)

The drug-potency ε_wt against wild-type HIV-1 virus for a given drug is modeled as a function of its normalized concentration using a Hill type dose-response curve [48]: (8) representing the fraction of new infections unaffected by the drug. A logarithmic measure of inhibition F_wt can be defined from this equation, as (9)

The slope parameter m of the linearized dose-response curve has greatly been ignored when describing the antiviral activity of therapy in HIV-1 infection, but is of great importance to determine inhibition at clinical drug concentrations (C_n ≫ 1) [49].

For combination therapy, drug potency interaction effects can readily be modeled, starting from the individual normalized drug concentrations, through Loewe additivity or Bliss independence [49]. Loewe additivity assumes drugs have similar mechanisms or compete for the same binding site. For a three-drug version of the Loewe additivity model, drug potency ε_wt,L can be described by the equation: (10)

Bliss independence assumes independent action between drugs, such that the combined effect ε_wt,B of triple combination therapy can be written as the product of the fractions unaffected by each individual drug: (11)

It predicts higher inhibition than Loewe additivity, especially at clinical drug concentrations. Inhibition less than the Loewe prediction represents antagonism, whereas a combined effect significantly greater than the Bliss prediction represents synergy.

The inhibitory effect of drug combinations are characterized on a spectrum defined by two states, independent inhibition (Bliss independence) and competitive binding (Loewe additivity), with synergistic and antagonistic interactions at either extreme [49], as (12) where F_wt,DI, F_wt,L and F_wt,B follow the definition of the previously introduced logarithmic measure of inhibition. Here, DI represents an index that quantifies the degree of independence, with DI = 0 corresponding to Loewe additivity and DI = 1 to Bliss independence.

The inhibitory potential at clinical drug concentrations for pairwise and triple combinations of 19 commonly used antiretrovirals were analyzed, allowing for quantitative comparison of antiviral activity of different drug regimens at expected plasma concentrations [49]. The results of this analysis in terms of DI index estimates can be used to determine the combined inhibition effect of different drug regimens in the spectrum defined by Bliss independence and Loewe additivity.

A summary of key PK/PD modeling quantities can be found in Table 4.

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Table 4. Key PK/PD modeling quantities.

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Disease Monitoring.

Viral suppression is checked for the first time at 1–2 months for a patient starting a new ART and every 4–6 months thereafter, following international treatment guidelines [9, 44]. If HIV-1 viral load is suppressed (<50 plasma RNA copies/mL), regular medical follow-up visits are programmed for plasma HIV-1 RNA and CD4⁺ T cell count monitoring. If on any of these medical visits plasma HIV-1 RNA is no longer suppressed, a confirmation visit is scheduled (e.g. one month after [9]). If plasma HIV-1 RNA continues non-suppressed, the patient is defined as having a virologic failure and moves to a subsequent treatment line. If plasma HIV-1 RNA is suppressed again, the patient maintains its current treatment regimen and returns to regular medical follow-up visits. Any time during the treatment, a patient can switch a regimen due to adverse events or other non-virologic reasons. Time to event distributions are considered for these regimen switches.

Costs.

Daily costs for each of the components in the modeled ART are quantified independently and accumulated continuously (dependent on adherence) for ART cost identification purposes. For non-ART costs (e.g. non-ART medication, examinations and laboratory tests) the model follows the same rules as for secondary treatment regimens discussed below. The same holds for the simulation of hospitalizations and corresponding costs.

Secondary Treatment Regimens Model

Suppressive Therapy.

Modeling of suppressive therapy for regimens of secondary interest is based on an adaptation of a DES-based cost-effectiveness model [34]. Conditional on a number of patient-specific characteristics (age, gender, regimen characteristics, resistance level, etc.) the time to the occurrence of 5 clinical events is estimated:

Viral suppression (plasma HIV-1 RNA <50 copies/mL)
Regimen switch due to virologic failure
Regimen switch not due to virologic failure (e.g.: toxicity)
Resistance development
Hospitalization

This section provides a concise description of the modeling steps. Further details can be found in the original publication [34].

Weibull distributions are considered for the estimation of event times for each of the clinical events. Upon the occurrence of any event (except hospitalization), time to occurrence of all events is updated using a conditional distribution approach. Virologic failure is defined as a confirmed plasma HIV-1 RNA level >50 copies/mL after initial viral suppression or unreached viral suppression 6 months after therapy initiation.

With respect to time to viral suppression, the plasma HIV-1 log₁₀ RNA level is assumed to decline linearly from the current value until reaching the value 0.5 (corresponding approximately to 3 plasma HIV-1 RNA copies/mL) at the estimated time, and is kept constant until virologic failure. Plasma HIV-1 log₁₀ RNA rebound levels for virologic failure are sampled from a uniform distribution, with parameters calibrated on observational data [34]. Meanwhile, the evolution of CD4⁺ T cell counts is governed automatically by the basic HIV-D model. Patients may switch regimens for reasons other than virologic failure an unlimited number of times within each treatment line. When a regimen switch due to virologic failure occurs, patients move to a subsequent treatment line. Upon regimen switch due to virologic failure on third-line treatment, patients loop back to this treatment line as many times as necessary until resistance reaches the highest class, regardless of the number of virologic failures. Once the highest resistance class is reached upon line switch, individuals start non-suppressive therapy.

Resistance levels are grouped into four classes, according to the inverted Genotypic Sensitivity Score [34, 50] and it is assumed that patients can move only to an adjacent, higher resistance class because resistance is archived in cellular DNA. Upon reaching the time to (new) resistance development, resistance levels are sampled uniformly from within each class. Adherence evolves over time based on a generalized linear model. Regimen characteristics are updated on occurrence of line and regimen switches.

Non-Suppressive Therapy.

Upon reaching non-suppressive therapy, the plasma HIV-1 log₁₀ RNA level is set to a value sampled from a normal distribution with parameters calibrated on observational data [31]c. After this, modeling of CD4⁺ T cell counts and plasma HIV-1 RNA levels is returned back to the HIV-D model. As a result of the increasing total viral burden, plasma HIV-1 RNA levels keep increasing whereas CD4⁺ T cell counts start dropping to AIDS-defining levels, in turn increasing mortality risk.

Costs.

The model considers monthly ART and non-ART costs, both based on generalized linear models, which are updated upon regimen switch and changes in resistance level. Monthly non-ART costs include in addition, among others, physician appointments, exams and laboratory tests [34].

Mortality and Quality of Life

Before, it was argued how, during the acute stage of the infection CD4⁺ T cell counts initially drop and then increase rapidly, however never returning to pre-infection levels. If untreated, the subsequent clinical latency stage of the infection is characterized by a slow depletion of CD4⁺ T cells until reaching AIDS-defining levels, typically about 8–10 years after seroconversion. If treated, CD4⁺ T cell counts grow slowly, but again usually do not reach pre-infection levels.

Studies show that mortality is CD4⁺ T cell count dependent and, even after ART initiation, remains higher in HIV-1 infected individuals than in the general population [51]. For HIV-1 infected individuals with CD4⁺ T cell counts below 200 cells/mm³, a 30-fold increase in (age and gender standardized) mortality rates has been estimated, whereas for patients with CD4⁺ T cell counts above 500 cells/mm³, this is reduced to a 2.5-fold increase [51].

At model initiation, the life expectancy of each simulated individual is sampled from mortality tables of the general population. Instantaneous HIV-1 infection related excess mortality as compared to the general population is implemented using CD4⁺ T cell count-dependent standardized mortality ratios (SMR, Table 5) [51]. The model is completely flexible with respect to SMR, easily adaptable as more data on the true impact of life expectancy is acquired. In order to keep the total population-size constant, each time an individual dies, a new, uninfected individual is generated, aged 13-years old (considered the minimum age for onset of sexual availability) [32].

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Table 5. Standardized mortality ratios for excess mortality due to HIV-1 infection.

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Given the variable nature of CD4⁺ T cell counts (disease progression and ART dependent) in the model, it is easily understood that CD4⁺ T cell counts are one of the main drivers of mortality in EPICE-HIV.

Similarly, CD4⁺ T cell-dependent quality of life (QoL) utilities are considered for cost-effectiveness modeling in terms of quality adjusted life years (QALY). Two sets of utilities are considered: one for plasma HIV-1 RNA suppressed individuals, and another for unsuppressed individuals (Table 6) [49].

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Table 6. Quality of life utilities for cost-effectiveness modeling.

https://doi.org/10.1371/journal.pone.0149007.t006

External Model Validation

Due to the complexity and comprehensiveness of the EPICE-HIV model as a whole, components that have been previously validated or described in the literature are not presented nor discussed. Though constituting a limitation to the current paper, validation within EPICE-HIV of these model components will be addressed in future work. The secondary treatment regimen part of the within-host model and the transmission module have previously been discussed in detail within comparable contexts [32, 34]. As such, the present analysis focuses on the HIV-D model and the implementation of the primary treatment regimen in the within-host model.

To strengthen the external validity of the HIV-D model, a simulation study was performed to allow comparisons to the data from the RPV/FTC/TDF arm of the STaR study [33]. The STaR study was a phase 3b, randomized, multicenter, international, open-label, 96-week clinical trial comparing the safety and efficacy of two single-tablet regimens, RPV/FTC/TDF and EFV/FTC/TDF, in 786 ART-naive, HIV-1 infected patients. Full validation against STaR study results, also including once-daily treatment with coformulated EFV/FTC/TDF will be discussed in an upcoming paper. In future work, the validation of the model against data from observational studies will also be considered.

The simulation consisted of 100,000 hypothetical infected individuals, initiating first-line ART with once-daily, coformulated RPV/FTC/TDF, using the same set of conditions in terms of baseline characteristics, clinical management and efficacy criteria of the STaR study [5]. We tested the hypothesis if the HIV-D model component of EPICE-HIV would be able to accurately produce 96-week percentages of virologically suppressed patients (as determined by the FDA Snapshot algorithm), qualitatively and quantitatively comparable to the percentages observed in the STaR study [33], and what effect alternative adherence distributions have on the results.

Results and Discussion