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A multi-level model for estimating region-age-time-type specific male circumcision coverage from household survey and health system data in South Africa

Voluntary medical male circumcision (VMMC) reduces the risk of male HIV acquisition by 60%. Programmes to provide male circumcision (MC) to prevent HIV infection have been introduced in sub-Saharan African countries with high HIV burden. While large-scale provision of MMC is recent, traditional MC has long been conducted as part of male coming-of-age practices. How and at what age traditional MC occurs varies by ethnic groups within countries. Accurate estimates of MC coverage by age and type of circumcision (traditional or medical) over time at sub-national levels are essential for planning and delivering VMMCs to meet targets and evaluating their impacts on HIV incidence. In this paper, we developed a Bayesian competing risks time-to-event model to produce region-age-time-type specific probabilities and coverage of MC with probabilistic uncertainty. The model jointly synthesises data from household surveys and health system data on the number of VMMCs conducted. We demonstrated the model using data from five household surveys and VMMC programme data to produce estimates of MC coverage for 52 districts in South Africa between 2008 and 2019. Nationally in 2008, 24.1% (CI: 23.4-24.8%) of men aged 15-49 were traditionally circumcised and 19.4% (CI: 18.9-20.0%) were medically circumcised. Between 2008 and 2019, five million VMMCs were conducted, and MC coverage among men aged 15-49 increased to 64.0% (CI: 63.2-64.9%) and medical MC coverage to 42% (CI: 41.3-43.0%). MC coverage varied widely across districts, ranging from 13.4-86.3%. The average age of traditional MC ranged between 13 to 19 years, depending on local cultural practices.


Introduction
Preventing HIV continues to be a major public health priority, particularly in southern and eastern Africa. Despite considerable progress combating the epidemic, the numbers of new HIV infections remain well above national and international targets [36]. Voluntary medical male circumcision (VMMC), defined as the complete surgical removal of the foreskin, has emerged as an effective intervention to reduce the risk of HIV acquisition among men. It is estimated to reduce the risk of female-to-male transition of HIV by 60% [12,3,1,11,13]. There is some evidence that VMMC may also reduce the risk of HIV acquisition among men who have sex with men [22] and may decrease the risk of other sexually transmitted infections, such as syphilis, herpes simplex virus type 2, and human papillomavirus [34].
VMMC is appealing as an HIV prevention intervention because it is a one-time, efficient, safe, and costeffective method. The World Health Organization (WHO) and the Joint United Nations Programme on HIV/AIDS (UNAIDS) have identified fifteen African countries with high HIV prevalence and low male circumcision (MC) prevalence as priority countries to scale-up VMMC for HIV prevention [35,8,42].
In 2010, ambitious targets were set to achieve 80% circumcision coverage in men aged 15-49 years by 2015, and while countries are still working towards meeting this, new complementary targets of 90% circumcision coverage in adolescent boys and young men aged 10-29 years by 2021 were set in 2016 [41]. In South Africa, the South African National Strategic Plan for HIV, TB, and STIs 2017-2022 set a target to provide 2.5 million VMMC over the five years as part of a comprehensive combination HIV prevention package [33].
While large-scale provision of medical male circumcision (MMC) for HIV prevention is relatively recent, male circumcision (MC) has traditionally been practiced in many African countries as part of traditional male initiation ceremonies (TMIC). Circumcisions during TMIC are typically conducted among adolescent boys and young men, but its provision, typical age at circumcision, and what it entails differ considerably across and within countries influenced by community-established values, religious, ethnic and cultural identities. In South Africa, there is substantial heterogeneity in traditional circumcision practices across ethnic groups, ranging from rarely conducted to nearly universal [21,6].
Traditional male circumcision (TMC) conducted during TMIC is often performed using non-medical methods in non-clinical settings by a traditional practitioner typically with no formal medical training [9,39,38,39]. Whether TMC involves complete removal of the foreskin varies by practicing groups.
In some cases, TMC may involve partial circumcision or a simple incision in the prepuce and is not thought to confer the same HIV prevention benefits as medical circumcision [40,26,2]. Due to this, VMMC programmes are increasingly working with traditional leaders for MMCs to be conducted as part of TMICs by medical service providers (hereafter referred to as MMC-T for medical male circumcisions conducted in traditional settings). Replacing TMC with MMC-T ensures men circumcised through TMIC have the same protection against HIV infection, as well as safe and sanitary surgical procedures. [40].
In light of this heterogeneity, planning and delivering VMMC services to meet programmatic targets requires detailed information about the coverage of circumcision by age group and type of circumcision (traditional or medical) at subnational level. Data about the MC coverage is available from two sources: (i) household surveys collecting self-reported circumcision status, and (ii) health system programme data on the number of VMMC conducted for HIV prevention. National household surveys, conducted roughly every five years, collect data on current HIV status and other risk factors including the self-reported circumcision status, age at circumcision, and type of circumcision from nationally-representative samples. Household survey estimates of MC coverage are relatively precise at the national level, but have large sampling variation at sub-national levels and granular age groups due to small sample sizes. The numbers of VMMC conducted by HIV prevention services are reported to the National Department of Health (NDoH) by VMMC programme implementers, but this does not reflect men circumcised traditionally or medical circumcisions conducted before the start of the national VMMC programme in 2010.
Previous approaches to estimate district-level circumcision coverage have considered both data sources, but often not together. Cork et al. analysed household survey data using a Bayesian geo-statistical model producing annual estimates of total MC coverage in men aged 15-49 years in sub-Saharan Africa at multiple spatial resolutions between 2000 and 2017 [7]. The Decision Makers' Program Planning Toolkit, Version 2 (DMPPT2) is a model to support planning VMMC scale-up in sub-Saharan Africa to allow countries to enter reported number of VMMCs as well as generate VMMC targets, coverage estimates, and impact projections. DMPPT2 combines estimates of MC coverage prior to MC scale-up (estimated using household surveys) with the reported numbers of VMMCs from various programmes to estimate MC coverage and unmet need at a subnational level over time. This approach is limited as it does not incorporate data from more recent household surveys and does not provide the statistical uncertainty associated with the MC coverage estimates [17,16].
We developed a model that synthesises both survey and VMMC programme data to estimate the probabilities and coverage of MMC and TMC by space, age, and time with probabilistic uncertainty.
Set within a Bayesian hierarchical framework, the model comprises of two components; (i) a time-toevent analysis in which survey data is used to determine space-age-time-type specific probabilities and coverage of MC and (ii) a Poisson modelling for the number of VMMC conducted for HIV prevention to further inform probability of MMC. The remainder of the paper is organised as follows: Section 2 describes the statistical modelling framework used to estimate space-age-time-type specific probabilities and coverage of MC. In Section 3, the model is implemented to estimate annual probabilities and coverage of circumcision using data from South Africa. Finally, Section 4 provides a concluding summary and a discussion of potential areas for future research.

Statistical Methods
Using a Bayesian hierarchical model with small area estimation methods, we modelled probabilities of circumcision stratified by region, age, and time for two types of circumcision: (1) circumcisions that occurred in traditional male initiation ceremonies or for other religious or cultural reasons (TMIC) and (2) circumcisions for non-traditional reasons and/or HIV prevention that take place in a clinical setting using medical methods (MMC-nT). Reflecting recent efforts to encourage adoption of medical methods in TMICs, TMICs were sub-categorised into: (1) traditional circumcisions conducted using non-medical methods (TMC) and (2) circumcisions conducted as part of TMIC but using medical methods (MMC-T), determined by a district-and year-specific probability that TMIC circumcisions were performed as MMC-Ts.
Probabilities of circumcision were estimated using a competing risk discrete time-to-event model [23], with estimates of circumcision coverage by type within each cohort calculated using the cumulative incidence. These were combined with data on male population size to calculate the predicted number of circumcisions conducted per year. Likelihood functions were specified for the two data sources to inform parameter calibration: (1) the probability of individual-level observations of circumcision age, type, and year reported by men in national household surveys in a time-to-event framework, and (2) the reported number of medical male circumcisions conducted in each district for HIV prevention among males 10 years and older using a Poisson count model.
Throughout the methods and applications sections, we refer to the following types of circumcision ( Figure 1): • MMC-nT: Medical male circumcisions conducted outside of traditional male initiation ceremonies, representing the large majority of MMC conducted.
• TMC: Traditional male circumcisions, assumed to be conducted outside a medical setting for traditional male initiation purposes.
• MMC-T: Medical male circumcisions conducted as part of traditional male initiation ceremonies, typically in place of circumcisions that previously would have been conducted as TMC.
Useful aggregates of these circumcision types are referred to as: • MMC: All medical male circumcisions (MMC-nT + MMC-T), assumed to be consistent with circumcisions reported through VMMC programme data reporting.
• TMIC: All male circumcisions conducted as part of traditional male initiation practices (TMC + MMC-T).
Survey data  We defined λ TMIC iat as the probability that an individual in region i received TMIC at age a and time step t, given they were uncircumcised by age a − 1 and time t − 1, This was modelled using piece-wise logit-linear function: whereα is the intercept,ψ i is a regional random effect,φ a is an age random effect, andγ ia is an age-space interaction term to allow different age patterns of TMIC across regions. We assumed that the probability of TMIC was constant over time (i.e. λ TMIC iat ≡ λ TMIC ia ) as TMIC practices have been relatively stable over time.
Similarly, we defined λ MMC-nT iat as the probability an individual in region i received MMC-nT at age a and time t, λ MMC-T iat , given they were uncircumcised by age a − 1 and time t − 1, To ensure the overall probability of circumcision λ TMIC such that The probabilityλ MMC-nT iat was separated into two processes: (i) paediatric circumcision (for those aged 0-9) and (ii) adolescent and adult circumcision (for those aged 10 and over). VMMC programmes only provide MMCs for HIV prevention to those aged 10 and over, while infant and paediatric medical circumcision tends to occur through cultural or religious practices unrelated to scale-up of VMMC for HIV prevention. Therefore, we modelledλ MMC-nT iat using a piece-wise logit-linear function: whereᾱ and α are intercepts,ψ i and ψ i and are regional random effects,φ a and φ a are age random effects,γ ia and γ ia are age-space interaction terms to allow for different age patterns of MMC-nTs between regions, for paediatric circumcision and adolescent and adult circumcision respectively. The For individuals circumcised in TMIC, we defined a probability, p iat that circumcision was conducted as a MMC-T versus TMC, specified for region i, age a, and time t. The probability an individual in region i received MMC-T at age a and time t, λ MMC-T iat was thus and the probability an individual in region i received TMIC was Prior to VMMC programmes, all circumcisions conducted in TMIC were TMC, in which case p iat = 0. The proportion of TMICs conducted as MMC-Ts may not be identifiable from the survey data, particularly for years since the most recent survey. Thus p iat > 0 should only be introduced in regions where there is knowledge that MMC-Ts were implemented in TMIC settings.
Taken together, the probability of circumcision of any type, at age a and time t given they were uncircumcised by age a − 1 and time t − 1 was The probability an individual in region i remained uncircumcised at age a and time t, given they were uncircumcised by age a − 1 and time t − 1, was

Cumulative incidence of circumcision
The probability S iat of remaining uncircumcised up to age a and time t, typically referred to as the survivor function, was expressed as The cumulative incidence function (CIF) defines the marginal probability (or proportion/coverage of) individuals who were circumcised by type k ∈ K = { MMC, MMC-nT, MMC-T, TMC, TMIC or MMC} by age a and time t, accounting for the competing risk of other circumcision type. This was calculated as the sum of incidence of circumcision by type k at each age up to a: where I k iat is the incidence of circumcision type k in region i, age a and time t. For types k ∈ {TMIC, TMC, MMC-T}, this was defined by the probability of remaining uncircumcised by any type up to age a at time t times the probability of circumcision by type k in year t at age a The overall incidence and CIF by any circumcision type can be obtained by summing across all circumcision types. The CIF is also often referred to as the 'sub-distribution function', due to the fact that the cumulative probability of a particular event k by time t will remain below one [23].

Priors
In space, we assigned the random effectsψ i ,ψ i , ψ i ,γ ia , γ ia and ζ it , intrinsic conditional autoregressive (ICAR) priors [4]. An ICAR model encodes spatial dependence between neighbours, defined as areas that share a common boundary, and allows information to be borrowed across regions, which may be useful in areas where data is sparse or non-existent. For a generic parameter β i , an ICAR model assumes that the expected value of β i is a weighted average its neighbours, where j ∼ i refers to the neighbours of region i, n i is the number of neighbours and τ β is the marginal precision. The joint distribution may be equivalently expressed as β ∼ N (0, τ −1 β Q −1 I ) where Q I is the precision matrix encoding the adjacency structure of the neighbourhoods. The precision matrix Q I is rank deficient and consequently the prior is improper [25].
In time, we assigned the random effects θ t , δ at and ζ it an autoregressive process of order 1 (AR1) priors, where |ρ φ | < 1 is an autocorrelation parameters controlling the correlation of the effect of the current age on the previous age and τ β is the precision. The joint distribution may be equivalently expressed where Q T is the precision matrix and encodes the first order dependency in time controlled by the autocorrelation parameter ρ β .
In age, we modelled the random effectsφ a ,φ a , φ a ,γ ia ,γ ia , γ ia and δ at using penalised B-spline functions of the form, where f aj are B-spline basis functions with knots every five years, N J is the number of splines used and ω a are the spline weight parameters to be estimated. The weights ω a are penalised using an AR1 process (as above) and the joint distribution is given by where Q A is the precision matrix as defined by the smoothed function. Then defining β = W β · ω where W β is a design matrix evaluating the basis functions f aj at each age of interest, the joint distribution of Moreover, the age-space, age-time, and space-time interaction terms (γ ia ,γ ia , γ ia , δ at and ζ it ) are modelled as Type IV interactions as defined by Knorr-Held and Leonard [15], where the precision matrices constructed using Kronecker products Here, Q I , Q A and Q T are precision matrices discussed above.
Gaussian priors were assigned to each of the intercepts, α,α,ᾱ ∼ N (0, 5 2 ). Exponential priors were placed on standard deviations, σ (·) = τ −1 (·) ∼ Exp(1). Gaussian priors were set for all correlation parameters on the logit scale, such that corresponding to 95% CI prior weight that the autocorrelation parameters are between 0.48 and 0.99 on the real scale. The proportion of TMICs performed as MMC-Ts, p iat , were assigned independent Gaussian distributions on the logit scale, if there is evidence or knowledge of the VMMC programmes to suggest MMC-Ts are taking place with some mean, µ iat , and standard deviation, σ iat . Otherwise, the proportions of TMICs performed as MMC-Ts are fixed at zero (p iat =0).

Likelihood
The full likelihood function consists of the product of the likelihoods for two independent data sources: (1) household survey data on individual male's age at circumcision and circumcision type, and (2) VMMC programme data about the number of circumcisions conducted for HIV prevention in each region.

Survey data
Survey data consisted of individual observations of self-reported age at circumcision, date of birth, and circumcision was calculated as the year of birth plus the age at circumcision. It was assumed that no circumcisions occurred after age 59, so for uncircumcised individuals, censoring occurred either in the survey year or when they were 59. Individuals who self-reported they were circumcised but have a missing age at circumcision were included in the analysis through left censoring.
The partial likelihood contribution for each individual is this defined by the following groups: • TMIC observed: Individuals in region i reporting they were circumcised through TMI ceremonies aged a at time t. The likelihood of this outcome was the probability an individual in region i reported a TMIC at age a and time t, • MMC-nT observed: Individuals in region i reporting they were medically circumcised aged a at time t. The likelihood of this outcome was the incidence of MMC-nT in region i, at age a and time t, • Right censored: Individuals in region i who were uncircumcised by age a at time t. The likelihood of this outcome was the probability of remaining uncircumcised in region i, at age a and time t,S iat • Left censored: Individuals in region i reporting a circumcision at an unknown age and time between birth at time t−a and age a at time t. The likelihood of this outomce was the probability of being circumcised in region i before age a at time t, (1 − S iat ) Taken together, the partial likelihood for the survey data may be expressed as Survey data are often collected through a complex two-stage cluster sampling design with unequal sampling probabilities. As a result, performing model inference using a standard likelihood may lead to biased estimates. To account for these survey designs, the probabilities of circumcision were estimated using a weighted pseudo-likelihood in which we replaced the observed counts N l iat with weighted counts N l iat , calculated using survey weights. Each individual j in survey s residing in region i had sampling weight ω sji which were normalised using the Kish effective sample size, Here,ω si is the arithmetic mean of all survey weights from the individuals sampled in survey s and region i and M s is the total sample size in survey s and M eff s is the Kish effective sample size which accounts for heterogeneity in sampling weights and is calculated using Using the normalised sampling weights,ω sji , we calculate the weighted counts,Ñ where l is either TMIC, MMC-nT, RC or LC.

VMMC programme data
where k is MMC-T or MMC-nT. The mean µ k iat is determined by multiplying the male population size in region i, at age a and time t, P iat , the probability of remaining uncircumcised in region i, up to age a and time t, S iat , and the probability of being having a MMC-T or MMC-nT at age a and time t given they were uncircumcised by age a − 1 and time t where k is MMC-T or MMC-nT. It then follows that the total number of MMCs conducted in region i at time t and age group G = [a 1 , a 2 ], Y iGt are modelled using

Inference
Models were implemented and fitted in R [24] using Template Model Builder (TMB) [18]. TMB is a software package that enables users to flexibly fit latent process/variable models to data. It uses automatic differentiation and Laplace approximations to estimate posterior distributions for model parameters. Models were optimised using the quasi-newton L-BFGS-B optimisation method [5].
Predictions of the district-age-time probabilities of circumcision and other quantities of interest were estimated using Monte Carlo sampling, drawn from the joint posterior distribution, conditional on the optimised hyper-parameters [10]. Marginal predictive distributions of any quantity of interest, for example, circumcision coverage aggregated to any geographical unit and/or age groups can then be made by summarising the joint samples generated.

Application to male circumcision coverage in South Africa
In this section, we applied the methods described in Section 2 to estimate annual probabilities of becoming circumcised and the corresponding circumcision coverage in South Africa between 2008 and 2019, by type, by single-year age group, and at a district-level (admin-2).

Data and outputs
We included nationally-representative household survey data on self-reported circumcision status from
The model presented here utilises both survey and programme data to produce timely estimates of MC coverage, particularly where survey data is limited or no longer available. Estimates of MC coverage were similar in most provinces when produced from models with and without the programme data, except in KwaZulu-Natal where MC coverage was substantially higher by 2019 when including programme data (58.6%; 95% CI: 57.1% to 60.3%) than excluding programme data (46.0%; 95% CI: 41.8% to 52.2%) (Figure 8). Overall, national MC coverage was 64.0% (95% CI: 63.2% to 64.9% in 2019 when including programme data, 1.6% higher than without program data included in the model

Discussion
The ability to produce comprehensive, accurate and timely estimates of MC coverage by age and type of circumcision (traditional or medical) over time at sub-national levels are essential for planning and delivering VMMCs to meet programmatic targets, and evaluating the impact of VMMC campaigns on HIV incidence. In this paper, we developed a model to produce region-age-time-type specific probabilities and the corresponding coverage of MC along with associated measures of uncertainty.
The model extends a competing risks time-to-event model in order to integrate both survey data and VMMC programme data, building on previous approaches from Kripke et al. [16] and Cork et al. [7], which did not model both data sources formally. focussing programmes in specific areas will ensure many more districts will achieve these targets in the near future. The number of MMCs conducted were largely similar in models with and without the inclusion of programme data, however, we found considerable differences in KwaZulu-Natal, which has the largest HIV prevalence and largest uptake in MMC services. It is therefore important to consider both data sources when estimating MC coverage.
The granular results produced can be used to identify areas and key age groups in which either circumcision coverage is low or there are large numbers of uncircumcised men. Furthermore, stratifying by circumcision type allows VMMC programmes to make programmatic decisions about how to intervene in areas where TMCs remain high or where TMC is most prevalent. For HIV prevention purposes, it may be beneficial to offer "recircumcision" if TMCs are commonly only partial circumcision that does not involve complete removal of the foreskin. Furthermore, when assessing the impact of the VMMC programmes on HIV incidence, our estimates stratified by circumcision type enable models to account for different protective effects of full medical circumcision versus traditional circumcision.
There were several circumcision dynamics which are anecdotally known, but about which limited data were available and which required strong modelling assumptions. The first, was surrounding the proportion of traditional circumcisions conducted using medical methods (MMC-T) as ensuring safe and complete circumcisions for young men has been a major initiative for the VMMC programme. We made prior assumptions about the proportion of circumcisions in TMIC settings that were medical in recent years based on expert knowledge of programme managers and evidence of years in which large number of MMCs were reported in districts that have high levels of traditional circumcision.
In 2020, the national health information system began explicitly recording the number of MMC-T, so quantitative data on this will be available for future analyses. The second, was uncertainty was about re-circumcision of men who were previously traditionally circumcised. We assumed that rates of re-circumcision were sufficiently low that it was not important to incorporate into the model.
Future household surveys in South Africa plan to separately capture data on medical and traditional circumcision, which will substantiate or guide revision of this assumption. However, re-circumcision of those who previously underwent only partial circumcision could be important for maximising the HIV prevention impact of VMMC.
The models presented here have several limitations and opportunities for further development. First, surveys typically record self-reported circumcision status, which may be susceptible to misreporting as a result of social desirability bias. Many cultures that promote male circumcision as a rite of passage into manhood and some studies using physical examinations have shown that there is some misreporting in circumcision status [19,20]. Second, the classification of circumcision type is based on self-reported questions from surveys, which may be subject to similar misreporting errors due to confusion between medical and traditional circumcision practices. Third, a complete-case analysis was used, that did not adjust for non-response bias in the self-reported circumcision status. Fourth, the models used did not make use of any covariates that are predictive of circumcision coverage, such as ethnicity, culture, or religion, to improve precision of the estimates. Extending the models in this way could allow for further targeting of VMMC services for specific population groups. Fifth, the model did not account for any uncertainty about the male population sizes by age and district. Small area population estimates are uncertain in many countries where the most recent census was long ago (in South Africa the last census was in 2011). Finally, the model did not explicitly represent migration between districts and its impact on district probabilities of circumcision and the corresponding coverage over time. It is suspected that many young men in South Africa move away from rural homes for work and return for their traditional male initiation ceremony. This is particularly the case with Xhosa men from Eastern Cape who move to Western Cape for work. When compiling the programme dataset used in the case study in this paper, we redistributed MMC-T conducted in the Eastern Cape to Xhosa populations residing in the Western Cape and Gauteng under the assumption that this is the normal place of residence for some men circumcised in the Eastern Cape, but future work should more explicitly model these migration dynamics and how they have changed over age and time. nelson-mandela-hsrc-study-of-hiv-aids-full-report. [