A Simultaneous Equation Approach to Estimating HIV Prevalence With Nonignorable Missing Responses

Marra, Giampiero; Radice, Rosalba; Bärnighausen, Till; Wood, Simon N.; McGovern, Mark E.

doi:10.1080/01621459.2016.1224713

Cited by 49 publications

(53 citation statements)

References 64 publications

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“…We also report some typical measures of interest. For more details on the models dealing with (i) and (ii), the reader is to referred to [44] and [35].…”

Section: The Modelsmentioning

confidence: 99%

“…The additive predictor for the copula parameter only depends on the Markov random eld term and allows the association parameter to vary by region. See [35] for a detailed discussion of this model speci cation.…”

Section: Hiv Prevalencementioning

confidence: 99%

“…Intervals derived using (6) have good frequentist properties since they account for both sampling variability and smoothing bias; see [35] and references therein for details. Intervals for non-linear functions of the model's coe cients (e.g., τ, joint and conditional predicted probabilities) can be conveniently obtained by simulation from the posterior distribution of δ using the following steps:…”

Section: Further Considerationsmentioning

confidence: 99%

“…To this end, we recommend using the Akaike information criterion (AIC) and/or the Bayesian information criterion (BIC), and hypothesis testing. The AIC and BIC are given by − (δ) + edf and − (δ) + log(n)edf , where the log-likelihood is evaluated at the penalized parameter estimates and edf represents the e ective degrees of freedom (see [35] for the exact de nition). Approximate p-values for testing smooth components for equality to zero are obtained using the results by Wood [56] and Wood [57].…”

Section: Further Considerationsmentioning

confidence: 99%

“…In practice, estimation of δ and λ is achieved by using a stable and e cient trust region algorithm (based on rst and second order analytical derivative information) with integrated automatic multiple smoothing parameter selection [35,44].…”

Section: Parameter Estimationmentioning

confidence: 99%

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A joint regression modeling framework for analyzing bivariate binary data in R

Marra

Radice

2017

Dependence Modeling

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Abstract:We discuss some of the features of the R add-on package GJRM which implements a exible joint modeling framework for tting a number of multivariate response regression models under various sampling schemes. In particular, we focus on the case in which the user wishes to t bivariate binary regression models in the presence of several forms of selection bias. The framework allows for Gaussian and non-Gaussian dependencies through the use of copulae, and for the association and mean parameters to depend on exible functions of covariates. We describe some of the methodological details underpinning the bivariate binary models implemented in the package and illustrate them by tting interpretable models of di erent complexity on three data-sets.

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“…We also report some typical measures of interest. For more details on the models dealing with (i) and (ii), the reader is to referred to [44] and [35].…”

Section: The Modelsmentioning

confidence: 99%

Section: Hiv Prevalencementioning

confidence: 99%

Section: Further Considerationsmentioning

confidence: 99%

Section: Further Considerationsmentioning

confidence: 99%

Section: Parameter Estimationmentioning

confidence: 99%

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A joint regression modeling framework for analyzing bivariate binary data in R

Marra

Radice

2017

Dependence Modeling

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Correcting for selection bias in HIV prevalence estimates: an application of sample selection models using data from population‐based HIV surveys in seven sub‐Saharan African countries

et al. 2022

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Introduction Population‐based biomarker surveys are the gold standard for estimating HIV prevalence but are susceptible to substantial non‐participation (up to 30%). Analytical missing data methods, including inverse‐probability weighting (IPW) and multiple imputation (MI), are biased when data are missing‐not‐at‐random, for example when people living with HIV more frequently decline participation. Heckman‐type selection models can, under certain assumptions, recover unbiased prevalence estimates in such scenarios. Methods We pooled data from 142,706 participants aged 15–49 years from nationally representative cross‐sectional Population‐based HIV Impact Assessments in seven countries in sub‐Saharan Africa, conducted between 2015 and 2018 in Tanzania, Uganda, Malawi, Zambia, Zimbabwe, Lesotho and Eswatini. We compared sex‐stratified HIV prevalence estimates from unadjusted, IPW, MI and selection models, controlling for household and individual‐level predictors of non‐participation, and assessed the sensitivity of selection models to the copula function specifying the correlation between study participation and HIV status. Results In total, 84.1% of participants provided a blood sample to determine HIV serostatus (range: 76% in Malawi to 95% in Uganda). HIV prevalence estimates from selection models diverged from IPW and MI models by up to 5% in Lesotho, without substantial precision loss. In Tanzania, the IPW model yielded lower HIV prevalence estimates among males than the best‐fitting copula selection model (3.8% vs. 7.9%). Conclusions We demonstrate how HIV prevalence estimates from selection models can differ from those obtained under missing‐at‐random assumptions. Further benefits include exploration of plausible relationships between participation and outcome. While selection models require additional assumptions and careful specification, they are an important tool for triangulating prevalence estimates in surveys with substantial missing data due to non‐participation.

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HIV estimation using population‐based surveys with non‐response: A partial identification approach

Adegboye,

Fujii,

Leung

et al. 2024

Statistics in Medicine

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HIV estimation using data from the demographic and health surveys (DHS) is limited by the presence of non‐response and test refusals. Conventional adjustments such as imputation require the data to be missing at random. Methods that use instrumental variables allow the possibility that prevalence is different between the respondents and non‐respondents, but their performance depends critically on the validity of the instrument. Using Manski's partial identification approach, we form instrumental variable bounds for HIV prevalence from a pool of candidate instruments. Our method does not require all candidate instruments to be valid. We use a simulation study to evaluate and compare our method against its competitors. We illustrate the proposed method using DHS data from Zambia, Malawi and Kenya. Our simulations show that imputation leads to seriously biased results even under mild violations of non‐random missingness. Using worst case identification bounds that do not make assumptions about the non‐response mechanism is robust but not informative. By taking the union of instrumental variable bounds balances informativeness of the bounds and robustness to inclusion of some invalid instruments. Non‐response and refusals are ubiquitous in population based HIV data such as those collected under the DHS. Partial identification bounds provide a robust solution to HIV prevalence estimation without strong assumptions. Union bounds are significantly more informative than the worst case bounds without sacrificing credibility.

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A Simultaneous Equation Approach to Estimating HIV Prevalence With Nonignorable Missing Responses

Cited by 49 publications

References 64 publications

A joint regression modeling framework for analyzing bivariate binary data in R

A joint regression modeling framework for analyzing bivariate binary data in R

Correcting for selection bias in HIV prevalence estimates: an application of sample selection models using data from population‐based HIV surveys in seven sub‐Saharan African countries

HIV estimation using population‐based surveys with non‐response: A partial identification approach

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