Structural Design and Data Requirements for Simulation Modelling in HIV/AIDS: A Narrative Review

Abstract

Born out of a necessity for fiscal sustainability, simulation modeling is playing an increasingly prominent role in setting priorities for combination implementation strategies for HIV treatment and prevention globally. The design of a model and the data inputted into it are central factors in ensuring credible inferences. We executed a narrative review of a set of dynamic HIV transmission models to comprehensively synthesize and compare the structural design and the quality of evidence used to support each model. We included 19 models representing both generalized and concentrated epidemics, classified as compartmental, agent-based, individual-based microsimulation or hybrid in our review. We focused on four structural components (population construction; model entry, exit and HIV care engagement; HIV disease progression; and the force of HIV infection), and two analytical components (model calibration/validation; and health economic evaluation, including uncertainty analysis). While the models we reviewed focused on a variety of individual interventions and their combinations, their structural designs were relatively homogenous across three of the four focal components, with key structural elements influenced by model type and epidemiological context. In contrast, model entry, exit and HIV care engagement tended to differ most across models, with some health system interactions-particularly HIV testing-not modeled explicitly in many contexts. The quality of data used in the models and the transparency with which the data was presented differed substantially across model components. Representative and high-quality data on health service delivery were most commonly not accessed or were unavailable. The structure of an HIV model should ideally fit its epidemiological context and be able to capture all efficacious treatment and prevention services relevant to a robust combination implementation strategy. Developing standardized guidelines on evidence syntheses for health economic evaluation would improve transparency and help prioritize data collection to reduce decision uncertainty.

Fig. 1. Colour codes of the quality of evidence.

In each of the following model component figures (Fig. 2-7), coloured cells indicate the inclusion of a structural characteristic in each respective model (as opposed to a blank cell indicating that the model did not incorporate the structural characteristics), grey cells indicate that no data was required for an included structural characteristic and cells with bold outlines indicate that the data required for an included structural characteristics was calibrated.

Fig. 2. Flow diagram of the process for model identification

Seed articles: [20, 21, 29]. * e.g. models focusing exclusively on men who have sex with men (MSM), people who inject drugs (PWID), etc.; ^ models failed to provide sufficient detail (in the manuscript or supporting appendix) to capture the majority of the information required for this review were excluded

Fig. 3. Population construction

The colour schemes presented reflected the evidence used to inform the initial population size of the according compartment or the initial distributions. Uppercase letter: AEs: adverse events, including ART failure, resistance and toxicity; ART: combination antiretroviral therapy; C: continuous measure of CD4 count or viral load; Ds: dichotomous measure of viral load (suppressed or unsuppressed); FSW: female sex workers; Hetero: heterosexuals; MMC: medical male circumcision; MSM: men who have sex with men; OI: opportunistic infections; PWID: people who inject drugs; STI: other sexually transmitted infections; Symbol: # chronic or asymptomatic; * multiple definitions used; ** among female sex workers only; *** among heterosexuals only; ^ equivalent to the three HIV stages; ^^ identical compartment; ^^^ identical compartment; Lowercase letter: a. Fertility; b. Household roles; c. PrEP; d. Sexual activity class; e. Race; f. All the attributes were drawn independently from their empirical distributions; g. Entry rate adjusted to ensure constant proportions within each sexual risk group; h. Entry rate adjusted to equivalence in the number of males and females. i. (1) Age 15-49 sexually active; (2) Age ≥50 sexually inactive; (3) Allowing transitions between risk levels; j. Allowing transitions between non-PWID and PWID; k. (1) Retired FSW or clients were the same as low-risk individuals; (2) Fixed prevalence of HCV-2; (3) A proportion of people were sexually inactive; l. Female PWID were not modeled directly; m. Homogeneity between the susceptible and the undiagnosed.

Fig. 4. Model entry, exit and HIV care engagement

Uppercase letter: A: population change was characterized by the estimated rate of aging-in and -out into or out of the defined study population age range; G: population change was characterized to match observed population growth or fertility rate; N/C: not clear; PB: population-based; SB: symptom-based; Symbol: # risk g/l: risk groups or risk levels; * age-, sex-specific migration rate (in & out); ** among 50+ only; *** calibrated; ^ the reciprocal of the duration between infection and testing; ^^ meeting failure definition (VL, CD4, OI); ^^^ jointly considered with ART drop-out; Lowercase letter: a. Infection state, age; b. Infection state (PB), opportunistic infection state (SB); c. Opportunistic infection state, age, time-increasing; d. Time-increasing; e. Race; f. Linear time-increasing; g. Once certain number of years since infection has passed; h. As a Hill function increase, with greater rate for CD4>200; i. Estimated number of ART initiations over the annual number of new AIDS cases; j. As the reciprocal of the duration between eligibility and treatment; k. By the assumed coverage; l. Regimen; m. (1) Adherence profile, (2) Drug supply; n. (1) Repeat testing occur ≥1 years for HIV-individuals; (2) Longer wait time and lower initiation rate for higher CD4 strata; o. (1) Linear increase in testing rate with stage number; (2) ART Dropout was permanent; p. (1) Retesting no sooner than every 3 years; (2) Treatment stops 3 month after loss to follow-up; (3) ART monitoring occurs every 3-6 months; (4) Toxicity: rate varied by time since ART, can trigger 2nd-line ART; q. (1) Same efficacy for 1st and 2nd line ART; (2) Toxicity: rate varied by regimen, can cause mortality increase; r. (1) Testing rates drawn from lognormal distribution; (2) Toxicity: rate varied by regimen, can trigger 2nd-line ART; (3) Resistance: can be developed (by adherence and # of active drugs) or acquired (by % of resistance presence in the concurrent PLHIV), can reduce number of active drugs; s. (1) Assuming an ART coverage ceiling as 90%; (2) Equal scale-up rate across all locations; t. ART provided to CD4≥350 was considered as TasP and<350 was considered as treatment; u. Reinitiation rate varied by CD4, and then back to the normal track as on ART; v. (1) ART discontinued PLHIV same as untreated; (2) 2nd-line ART same as 1st-line except in cost; w. Resistance: homogeneous rate; x. (1) ART failed cases same as untreated; (2) No ART initiation for CD4>350; y. Testing sensitivity and specificity also considered; z. (1) Same failure rate for 1st and 2nd-line ART; (2) PLHIV who failed 2nd-line ART were the same as the untreated; aa. Resource allocation as the sole impetus of testing, and the testing coverage was proxied by the resources allocated.

Fig. 5. HIV disease progression

Uppercase letter: D: characterized by the duration between two stages or strata (i.e. as the reciprocal); Ds: characterized by dichotomous measure, suppressed or unsuppressed; F: characterized by functions (linear, non-linear), see underlying assumptions; N/C: not clear; Symbol: # including CD4 recovery, VL decrease and VL suppression; ## HIV-related mortality considered for final stage (e.g. AIDS, CD4<200) only; * calibrated; ** equivalent; *** different progression rate by CD4 strata; ^ may return to a higher CD4 stratum after dropout; ^^ Weibull distribution; Lowercase letter: a. Age; b. Homogeneous; c. OI, toxicity; d. OI; e. Gender, time since infection; f. Diagnosis; g. (1) CD4 declines according to a quadratic function with prognosis; (2) Total survival time for PLHIV was stochastically sampled from an age-dependent Weibull distribution (with fixed duration for acute and AIDS stages); (3) Assuming all new infected cases started with the same initial CD4 counts as 594 cells/mm³; h. Linear decrease of CD4 in different stages; i. CD4 modeled continuously based on VL, and ART; j. (1) CD4 decrease determined by VL; (2) Progression and clinical events were observed periodically at clinical visits or when OIs occur; k. (1) VL changes sampled from normal distribution. CD4 changes by declining rate, adjusted by VL and age; (2) Initial VL randomly sampled from log normal distribution. Initial CD4: 756 cells/mm³; (3) ART effects on progression varied by number of active drugs and adherence level; l. (1) Linear decrease of CD4; (2) Survival after infection followed a Weibull distribution (with fixed duration for acute and AIDS stages); (3) CD4 decreased by 25% immediately after infection; m. (1) PLHIV may enter any CD4 strata after acute stage; (2) CD4 during ART represented the stage to which when treatment being interrupted; n. The duration for each stage was exponentially distributed; o. (1) Post-ART AIDS (treated but unsuppressed) stage is a dead-end: no regimen changes allowed; (2) Treated and suppressed stage is a dead-end: no failure allowed; p. % of VL suppression as the multiplication of conditional % of linked to care, % retained to care, % linked to treatment and % achieving suppression; q. HSV-2 co-infection assumed to have stable prevalence and increase HIV infectivity.

Fig. 6. The force of HIV infection

Uppercase letter: A: age-dependent; G: gender-dependent; pref.: preference; PT: partnership type-dependent; R: risk group or risk level-dependent; Symbol: # colours indicate the assessment of evidence used to inform the baseline infectivity of different transmission routes; ## number of partners (sexual or injection-sharing), also referred to as the rate of partner change in some models; * all transmission routes were jointly modeled in one force of infection; ** the effect of ART on reducing transmission was modeled indirectly through viral load; ^ proportional mixing; Lowercase letter: a. Mother to child (MTC); b. Coital type: only the evidence evaluation for its effect on was infectivity shown; the behavioural parameter was based on best quality evidence with lowest external validity; c. Years since infection; d. Based on a Spectrum projections (exogenous to the model), influenced by the distribution of CD4 strata due to their distinct infectivity; e. Probability of needle sharing; f. Reversely estimated by the observed incidence; g. (1) Partnership types: transitory, informal, and marital, with different duration (Weibull distribution); (2) Assuming exponential distribution of the interval between coital acts; (3) Allowing coital dilution for multiple partnerships; h. (1) Partnership mostly within the community; (2) Maximum 2 partners (1 long-term) at a time; (3) Allowing external short-term partnership; (4) Males tended to be older than females in pairs; i. (1) Partnership type: marital, casual, commercial; (2) The rate of sex partner change is determined by a supply and demand mechanism (from previous studies) depending on age, sex and marital status; j. (1) Partnership type: spousal and non-spousal; (2) The risk of having HIV-positive partner was age- and gender-specific; k. Partnership type: long-term, short-term; l. (1) No interactions between locations; (2) No transmission considered for population aged 50+; m. Partnership type: primary and secondary; n. (1) Sexual contact rate reduction followed a logistic function ensuring symmetry around the midpoint of behaviour change period; (2) # of sexual contacts geometrically adjusted to balance the male and female contacts; o. No sexual activity in final AIDS stage; p. (1) Reduced sexual activity in the wound healing period after MMC; (2) 5% of the partnerships formed with outside partners; q. (1) Partnership type: marital, casual, commercial; (2) Disease advanced PLHIV had reduced sexual behaviours; r. Frequency of needle sharing decayed over time according to observed trends; s. Partnership type: occasional commercial, regular commercial, and main; t. Partnership type: commercial, casual, and regular; u. Fixed force of infection.

Fig. 7. Health economic evaluation

Symbol: # also including modified societal; ## e.g. capital cost, program operational cost, research cost; * e.g. productivity loss. Lowercase letter: a. Approximated by life-years gained.