DHS METHODOLOGICAL 

REPORTS 22

Assessing the Impact of Imperfect 

Immunoassays on HIV Prevalence

Estimates from Surveys Conducted by 

The DHS Program

SEPTEMBER 2017

This publication was produced for review by the United States Agency for International Development. It was prepared by 

Mathieu Maheu-Giroux, Lawrence Joseph, Patrick Belisle, Samantha Lancione, and Jeffrey W. Eaton.

DHS Methodological Report No. 22

Assessing the Impact of Imperfect Immunoassays on HIV 

Prevalence Estimates from Surveys Conducted 

by The DHS Program 

Mathieu Maheu-Giroux 

Lawrence Joseph 

Patrick Belisle 

Samantha Lancione 

Jeffrey W. Eaton 

ICF 

Rockville, Maryland, USA 

September 2017 

*Corresponding author: Mathieu Maheu-Giroux, McGill University, 1020 Avenue des Pins Ouest, 

Montréal, Québec, Canada; phone : (+1) 514-398-5110; email : mathieu.maheu-giroux@mcgill.ca 
Acknowledgment: We are grateful for Joy Fishel, Shireen Assaf, and Dean Garrett for their helpful suggestions and 

comments on an earlier version of this report. 

Editor: Diane Stoy 

Document Production: Joan Wardell 

This study was conducted with support provided by the United States Agency for International Development (USAID) 

through The DHS Program (#AID-OAA-C-13-00095). The views expressed are those of the authors and do not 

necessarily reflect the views of USAID or the United States Government. 

The DHS Program assists countries worldwide in the collection and use of data to monitor and evaluate population, 

health, and nutrition programs. For additional information about The DHS Program contact: DHS Program, ICF, 530 

Gaither Road, Suite 500, Rockville, MD 20850, USA. Phone: +1 301-407-6500; fax: +1 301-407-6501; email: 

reports@dhsprogram.com; Internet: www.dhsprogram.com. 

Recommended citation: 

Maheu-Giroux, Mathieu, Lawrence Joseph, Patrick Belisle, Samantha Lancione, and Jeffrey W Eaton. 2017. Assessing 

the Impact of Imperfect Immunoassays on HIV Prevalence Estimates from Surveys Conducted by The DHS Program.

DHS Methodological Reports No. 22. Rockville, Maryland, USA: ICF. 
iii

Contents 

TABLES ............................................................................................................................................................... v

FIGURES ............................................................................................................................................................. v

PREFACE .........................................................................................................................................................vii

ABSTRACT ........................................................................................................................................................ix

EXECUTIVE SUMMARY ...............................................................................................................................xi

LIST OF ABBREVIATIONS ......................................................................................................................... xiii

1. INTRODUCTION................................................................................................................................. 1

2. METHODS ............................................................................................................................................ 3

2.1. HIV testing for population-based surveys estimates ................................................................. 3

2.2. Surveys conducted by The DHS Program and DHS testing algorithms ................................... 3

2.3. DHS testing standards .............................................................................................................10

2.4. Description of the assays used in the DHS testing algorithms ................................................10

2.5. Potential sources of misclassification ......................................................................................15

2.6. Model specifications ................................................................................................................15

3. RESULTS ............................................................................................................................................25

4. DISCUSSION ......................................................................................................................................41

5. CONCLUSIONS ................................................................................................................................. 43

REFERENCES .................................................................................................................................................45

APPENDIX ........................................................................................................................................................49

TEXT S1: JUSTIFICATION OF PRIOR DISTRIBUTIONS FOR THE BAYESIAN LATENT 

CLASS MODEL’S PARAMETERS ................................................................................................. 51

A) Priors for the continuous assays (EIA) .............................................................................................51

B) Priors for dichotomous assays (Western Blot or line immunoassay) ...............................................55

TEXT S2: DETAILS ON BAYESIAN LATENT CLASS CONTINUOUS MODEL 

SPECIFICATION ...............................................................................................................................57

v

Tables 

Table 1. Unweighted HIV prevalence estimates presented in the DHS reports ...................................... 4

Table 2. DHS testing algorithms and HIV assays used ........................................................................... 8

Table 3. Properties of HIV enzyme immunoassays ............................................................................... 12

Table 4. Properties of supplemental assays ........................................................................................... 14

Table 5. Priors for the true positive and true negative distributions of log-transformed signal-tocutoff ratios for the nine enzyme immunoassays ..................................................................... 23

Table 6. Priors for the sensitivity and specificity of the dichotomous confirmatory assays .................. 23

Table S1. Target detection of the nine EIAs used in The DHS Program surveys (2010-2014) ............... 49

Table S2. Target detection of supplementary assays ............................................................................... 50

Table S3. Data structure ........................................................................................................................... 57

Figures 

Figure 1. General DHS testing strategy - Type 1 ..................................................................................... 6

Figure 2. General DHS testing strategy - Type 2 ..................................................................................... 6

Figure 3. General DHS testing strategy - Type 3 ..................................................................................... 7

Figure 4. General DHS testing strategy - Type 4 ..................................................................................... 7

Figure 5. Flowchart describing the derivation of equations for the dichotomous Bayesian latent 

class model .............................................................................................................................. 16

Figure 6. Graphical representation of continuous model specification .................................................. 20

Figure 7A. Distribution of log transformed signal-to-cutoff ratio from samples tested on both 

enzyme immunoassays with results from the third assay ........................................................ 26

Figure 7B. Distribution of log transformed signal-to-cutoff ratio from samples tested on both 

enzyme immunoassays with results from the third assay ........................................................ 27

Figure 7C. Distribution of log transformed signal-to-cutoff ratio from samples tested on both 

enzyme immunoassays with results from the third assay ........................................................ 28

Figure 7D. Distribution of log transformed signal-to-cutoff ratio from samples tested on both 

enzyme immunoassays with results from the third assay ........................................................ 29

Figure 8A. Unadjusted and adjusted HIV prevalence estimates from Bayesian latent class models 

(high prevalence countries) ..................................................................................................... 32

Figure 8B. Unadjusted and adjusted HIV prevalence estimates from Bayesian latent class models 

(low prevalence countries) ....................................................................................................... 32

Figure 9. Comparison of the enzyme immunoassay-based and rapid test algorithms in the Uganda 

AIDS Indicator Survey (2011) ................................................................................................ 36

Figure 10. HIV prevalence from the Uganda AIDS Indicator Survey (2011) according to different 

testing strategies and adjustment procedures, stratified by age and sex .................................. 37

Figure 11. Comparison of the enzyme immunoassay-based algorithm with results from 

confirmatory re-testing in the Zambia Demographic and Health Survey (2013-14) ............... 38

Figure 12. HIV prevalence from the Zambia Demographic and Health Survey (2013-14) according 

to different testing strategies and adjustment procedures, stratified by age and sex ............... 39

vii 

Preface 

The Demographic and Health Surveys (DHS) Program is one of the principal sources of international data 

on fertility, family planning, maternal and child health, nutrition, mortality, environmental health, 

HIV/AIDS, malaria, and provision of health services. 

One of the objectives of The DHS Program is to continually assess and improve the methodology and 

procedures used to carry out national-level surveys as well as to offer additional tools for analysis. 

Improvements in methods used will enhance the accuracy and depth of information collected by The DHS 

Program and relied on by policymakers and program managers in low- and middle-income countries. 

While data quality is a main topic of the DHS Methodological Reports series, the reports also examine 

issues of sampling, questionnaire comparability, survey procedures, and methodological approaches. The 

topics explored in this series are selected by The DHS Program in consultation with the U.S. Agency for 

International Development. 

It is hoped that the DHS Methodological Reports will be useful to researchers, policymakers, and survey 

specialists, particularly those engaged in work in low- and middle-income countries, and will be used to 

enhance the quality and analysis of survey data. 

Sunita Kishor 

Director, The DHS Program 

ix

Abstract 

The DHS Program has supported numerous large-scale HIV seroprevalence surveys, some of which used 

a testing strategy based on enzyme-immunoassays (EIA). There have been recent concerns that this 

algorithm could have led to overestimation of HIV prevalence. This report investigates the impact of 

potential misclassification of samples on HIV prevalence estimates for 23 surveys conducted from 2010-

2014. In addition to visual inspection of laboratory results, we examined how accounting for potential 

misclassification of HIV status through Bayesian latent class models affected the prevalence estimates. Two 

types of Bayesian models were specified: a model that only uses the individual dichotomous test results 

and a continuous model that uses the quantitative information of the EIA (i.e., the signal-to-cutoff values). 

Overall, we found that adjusted prevalence estimates matched the surveys’ original results, with 

overlapping uncertainty intervals. This suggested that misclassification of HIV status should not affect the 

prevalence estimates in most surveys. However, our analyses suggested that two surveys may be 

problematic. The prevalence could have been overestimated in the Uganda AIDS Indicator Survey 2011 

and the Zambia Demographic and Health Survey 2013-14, although the magnitude of overestimation 

remains difficult to ascertain. Interpreting results from the Uganda survey is difficult because of the lack of 

internal quality control and potential violation of the multivariate normality assumption of the continuous 

Bayesian latent class model. In conclusion, despite the limitations of our latent class models, our analyses 

suggest that prevalence estimates from most of the surveys reviewed are not affected by sample 

misclassification. 

KEY WORDS: HIV, enzyme immunoassays, surveillance, seroprevalence survey, Bayesian latent class 

models. 

xi 

Executive Summary 

There have been concerns about HIV laboratory testing results from surveys conducted by The DHS 

Program prior to 2015. The enzyme-immunoassay (EIA) based testing strategies used in these surveys 

could have led, in some instances, to an overestimation of HIV prevalence. These concerns led The DHS 

Program to conduct a review of the performance of these EIAs in 20 surveys conducted between 2010 and 

2014. 

This report extends the preceding analyses of laboratory data by assessing the impact of potential 

serological misclassification of the HIV prevalence estimates from 23 surveys (20 of these were previously 

reviewed by The DHS Program). Along with visual inspection of laboratory results, we accounted for the 

uncertainty associated with potential misclassification of EIA results and confirmatory assays by using two 

different Bayesian latent class models. The first model used dichotomous test results, while the second used 

the continuous information on the distribution of signal-to-cutoff values of the EIA. 

Overall, the prevalence estimates from the latent class models roughly matched the survey results, with 

overlapping uncertainty intervals. This suggested that the impact of misclassification of HIV status is 

relatively minor in most surveys conducted by The DHS Program during 2010-2014. However, the results 

from the EIA-based testing algorithms used in the Uganda AIDS Indicator Survey 2011 and Zambia 

Demographic and Health Survey 2013-14 are potentially biased. The precise magnitude of this bias remains 

difficult to ascertain, especially for Uganda. In the Uganda survey, the lack of internal quality control and 

probable violation of the multivariate normality assumption of the continuous Bayesian latent class model 

limits our confidence in results from this adjustment. In this survey, the true unobserved HIV prevalence is 

probably closer to results from the rapid diagnostic test algorithm, which was conducted during the survey 

visit to the household, rather than the EIA-based algorithm, as suggested by our examination of HIV trends 

by age and sex. In the case of Zambia, the EIA-based algorithm produced a high number of weakly reactive 

samples, especially among men, which were later found to be negative in the confirmatory retesting of 

some samples. In all cases, the adjusted HIV prevalence estimates from the two types of Bayesian latent 

class models should be interpreted with caution. The dichotomous latent class model is strongly dependent 

on prior information on test error rates and the continuous latent class model assumes that the logtransformed signal-to-cutoff values are normally distributed. This latter assumption may have been violated 

in some surveys such as Sierra Leone and Uganda. 

Despite the imperfections of methods used across all surveys, including our latent class models, there is 

strong agreement for most countries between interval estimates (high and/or complete overlap) from the 

different models. Although this is reassuring, further work is needed to improve the Bayesian latent class 

models in order to increase confidence in the estimates. Finally, imperfect laboratory testing is only one of 

several factors that could affect HIV prevalence estimates such as random sampling error, and selection 

and non-response bias. 

xiii 

List of abbreviations 

AIS: AIDS indicator surveys 

CDC: The US Centers for Disease Control and Prevention 

CI: Confidence interval 

CrI: Credible interval 

CT: Confirmatory testing 

DBS: Dried blood spot 

DHS: Demographic and Health Survey 

DRC: Democratic Republic of Congo 

EIA: Enzyme immunoassay 

HIV: Human immunodeficiency virus 

IQC: Internal quality control 

NAT: Nucleic acid test 

OD: Optical density 

RDT: Rapid diagnostic test

S/CO: Signal-to-cutoff 

SD: Standard deviation 

Se: Sensitivity 

Sp: Specificity 

UNAIDS: The Joint United Nations Program on HIV/AIDS 

WHO: World Health Organization 

1

1. Introduction 

Accurate measurements of HIV prevalence are the cornerstone of HIV prevention activities 

(UNAIDS/WHO 2005). Nationally representative HIV seroprevalence surveys enable control programs to 

devise appropriate programmatic responses, monitor trends, and measure the impact of interventions 

(UNAIDS/WHO 2005). Since 2001, The DHS Program has conducted 71 HIV seroprevalence surveys in 

39 countries. These surveys have become an important data source for individual researchers, national 

control programs, and the Joint United Nations Program on HIV/AIDS (UNAIDS). 

HIV testing in these large surveys is logistically challenging with blood samples analyzed in a central 

laboratory located in the host country. The countries used different serological assays, but the HIV testing 

strategy employed usually consisted of two enzyme-immunoassays (EIA) and a third tie-breaker assay, 

which was usually a blot assay. Although the laboratory procedures for HIV serology testing in these 

population-based surveys followed the 2005 recommendations from UNAIDS and the World Health 

Organization (WHO), recent concerns about overestimation of HIV prevalence prompted a revision of the 

recommended testing algorithm (UNAIDS/WHO 2015; Fishel and Garrett 2016). 

In response to these concerns, The DHS Program recently reviewed the quality of EIA-based HIV 

serosurvey data from 20 Demographic and Health Surveys (DHS) and AIDS Indicator Surveys (AIS) 

conducted between 2010 and 2014 (Fishel and Garrett 2016). This review examined agreement between 

the two EIA and the distribution of their signal-to-cutoff (S/CO) values. The findings suggested that the 

proportion of discrepant EIA results was higher than the desired benchmark in 7 of the 20 surveys. In 

addition, the proportion of weakly reactive samples on the first EIA, which may be more likely to be false 

positives, was higher than 20% in 9 of the 20 surveys. These results suggest that the HIV status could have 

been misclassified for some samples, although the magnitude of this problem likely varies with the specific 

survey. 

Although future surveys conducted by The DHS Program will employ the newly recommended testing 

strategy (UNAIDS/WHO 2015; WHO 2015a), understanding the impact of potential misclassification on 

past surveys’ prevalence estimates is important both for epidemic monitoring and assessing the 

effectiveness of current and future HIV interventions. The re-testing of specimens collected from more than 

20 serosurveys is not logistically possible and is also hindered by potentially suboptimal storage conditions. 

In such cases, using statistical models to incorporate the uncertainty associated with the imperfect 

sensitivity and specificity of the testing algorithm could enable a more detailed appraisal of the laboratory 

data. 

This report will present analyses that explore the impact of the imperfect accuracy of EIA. First, we briefly 

discuss how population-based HIV seroprevalence surveys are conducted by The DHS Program (Sections 

2.1 to 2.3). Second, we provide a description of the different assays and the potential sources of 

misclassification (Sections 2.4 to 2.5). Third, we describe the dichotomous and continuous Bayesian latent 

class model specifications used to adjust HIV prevalence estimates (Section 2.6). Fourth, we present results 

from the Bayesian latent class models and contrast them with those that assume no misclassification 

(Section 3). Finally, we discuss the relevance of these findings for HIV surveillance and highlight some 

limitations of our work (Section 4). 

3

2. Methods 

2.1. HIV testing for population-based surveys estimates 

According to the 2005 UNAIDS/WHO testing recommendations, all samples reactive on a first test should 

be confirmed using a second test (UNAIDS/WHO 2005). If these two tests are discrepant, a third test should 

be used as a tie breaker. The testing strategies employed over that period for surveys conducted by The 

DHS Program was consistent with these recommendations. In comparison, the updated WHO guidelines 

endorsed the use of different testing algorithms in settings with low and high HIV prevalence. For 

populations where the expected HIV prevalence is low (<5%), all samples that test positive on the first two 

EIA should be confirmed with a third assay. The assays should be chosen so that the first EIA has the 

highest sensitivity and the second EIA the highest specificity (UNAIDS/WHO 2005; Fishel and Garrett 

2016; Urassa et al. 1999). 

The high prevalence setting (>5%) algorithm now recommends mandatory repeat testing if the sample 

produces discrepant results on the first two assays. If the results are still discrepant, the sample is tested on 

a third assay. The guidelines for interpreting the results of the third assay have also changed since the 2005 

testing strategy for both low and high prevalence settings. If the third assay is reactive, it is not 

recommended to use this result as the final HIV status because it selects for false positive results 

(UNAIDS/WHO 2015; WHO 2015a). Because such false positives could lead to the overestimation of HIV 

prevalence in population-based serosurveys (Hakim et al. 2016; Parekh and McDougal 2005), the individual 

is categorized as inconclusive (WHO 2015a).

The US Centers for Disease Control and Prevention (CDC) have also updated their recommendations for 

HIV testing in a clinical setting. The HIV-1 Western blots and HIV-1 indirect immunofluorescence assays 

are no longer included in the testing algorithm. Instead, indeterminate results produced from the EIA are 

tested with an HIV-1 nucleic acid test (NAT), which detects HIV RNA and not HIV antibodies 

(CDC/APHL 2014). Evidence now suggests that relying on Western blots or immunofluorescence assays 

for confirmation of positive samples on EIA can produce indeterminate results for early HIV infections 

(CDC/APHL 2014). The HIV NAT results reduce the number of indeterminate results because they 

distinguish between false positive EIA results and acute HIV infections. However, HIV NAT is not 

generally used for population-based HIV surveillance estimates (UNAIDS/WHO 2015).

2.2. Surveys conducted by The DHS Program and DHS testing algorithms 

Detailed laboratory results from 23 surveys were provided by The DHS Program. All surveys except two 

(Dominican Republic and Haiti) were conducted in sub-Saharan Africa and one country (Rwanda) had two 

surveys conducted during that period. The sample size and HIV prevalence estimate for each survey are 

presented in Table 1. 

To conduct the proposed analyses, we obtained the laboratory data files from each survey. The individual 

assay results of all samples from each survey were individually merged with CSPro to their DHS/AIS HIV 

recode file (Fishel and Garrett 2016). The laboratory files included individual results from all assays that 

were conducted during the surveys: the lab ID, plate ID, plate cutoff value, optical density (OD), and S/CO 

value for each sample, as well as basic demographical information for each participant. 
4

Table 1. Unweighted HIV prevalence estimates

The unweighted HIV prevalence among men and women (age ≥15 years, upper age limit varies by survey), the 

unweighted total number of HIV positive participants, and the unweighted total number of participants who were tested for 

HIV, by survey

Unweighted HIV prevalence among women and men age ≥15 years 

(upper age limit varies by survey❖)

Survey

Point 

estimate*

95% confidence 

interval

Total number of 

HIV positive 

(unweighted)

Total number tested 

(unweighted)

Sub Saharan Africa

Burundi DHS 2010 1.9 (1.6-2.2%) 164 8588

Cameroon DHS 2011 4.6 (4.2-4.9%) 649 14,202

Chad DHS 2014-15 1.5 (1.3-1.8%) 166 10,726

Côte d’Ivoire DHS 2011-12 3.7 (3.3-4.1%) 336 9008

DRC DHS 2013-14 1.0 (0.9-1.2%) 177 17,638

Gabon DHS 2012 4.4 (4.0-4.8%) 483 10,992

Gambia DHS 2013 1.8 (1.5-2.1%) 136 7769

Ghana DHS 2014 1.9 (1.6-2.2%) 164 8848

Guinea DHS 2012 2.0 (1.7-2.3%) 164 8380

Malawi DHS 2010 10.2 (9.7-10.7%) 1420 13,910

Mali DHS 2012-13 1.1 (0.9-1.3%) 97 8861

Namibia DHS 2013 13.9 (13.2-14.7%) 1233 8858

Niger DHS 2012 0.5 (0.4-0.7%) 44 8628

Rwanda DHS 2010 3.2 (2.9-3.5%) 420 13,248

Rwanda DHS 2014-15 3.2 (2.9-3.5%) 415 12,940

Senegal DHS 2010-11 0.9 (0.8-1.1%) 93 9917

Sierra Leone DHS 2013 1.5 (1.3-1.7%) 222 14,600

Tanzania AIS/MIS 2011-12 4.6 (4.3-4.9%) 815 17,745

Togo DHS 2013-14 2.2 (1.9-2.5%) 199 9172

Uganda AIS 2011 7.0 (6.7-7.3%) 1495 21,367

Zambia DHS 2013-2014 13.4 (13.1-13.8%) 3901 29,006

Latin America/Caribbean

Dominican Republic DHS 2013 1.0 (0.9-1.2%) 193 18,614

Haiti DHS 2012 2.3 (2.1-2.5%) 419 18,531

Note: The prevalence estimates in this table are unweighted survey results, and thus do not match the official survey 

prevalence estimates published in the DHS survey reports.

*The indeterminate results were not used in the HIV prevalence calculation except for Côte d’Ivoire and Guinea, where they 

were treated as negative. These results were included in the total number of individuals who were tested.

❖In most surveys, the ages for women ranged from 15-49 and men from 15-59. However, there are a few surveys that did 

not follow these age categories: Malawi (men age 15-54), Namibia (women and men age 15-64), Tanzania (women and men 

age 15-49), and Uganda (women and men age 15-59). All women and men in each country are included in the calculation 

of the HIV prevalence and in the following analysis, despite the varying age ranges.
5

The HIV assays and specific testing strategies used in these surveys vary by survey, and are selected in 

collaboration with the host country. The general testing strategy includes a combination of two EIA and a 

third tie-breaker assay for samples that are discrepant on the first two EIA – which is usually a Western 

Blot or a line immunoassay. It is also customary to randomly retest a certain proportion (5-10%) of samples 

that are negative on the first EIA as part of internal quality control (IQC). The DHS Program reviews 

laboratory procedures if greater than 1% of the IQC-selected samples test positive on the second EIA. 

Testing also differs among surveys according to the HIV assays used and if repeat parallel testing was 

conducted when the two EIA results were discrepant. The description of the different assays and the 

characteristics of the testing algorithms are shown for each survey in Table 2. These surveys can be 

classified into four general categories. In the first general testing strategy (Type 1), all samples are tested 

with the first assay, and those found to be reactive are tested with a second assay. Both assays are EIA. 

Discrepant results on the first two assays are resolved with a third and definitive assay, which is either a 

Western Blot or line immunoassay. Finally, a certain proportion of samples that were initially non-reactive 

on the first assay are re-tested with the second assay as part of IQC (Figure 1). The second testing strategy 

(Type 2) is similar to the first, except that samples with discrepant results on the first two EIA are re-tested 

in parallel. Samples that are discrepant again are tested on a third, definitive assay (Figure 2). With the third 

testing strategy (Type 3), no third assay is involved, but the initially discrepant samples are tested again in 

parallel (Figure 3). With the fourth testing strategy (Type 4), there was no IQC and no repeat testing in 

parallel for initially discrepant results, and a third EIA served as the third, definitive assay instead of the 

usual Western Blot or line immunoassay (Figure 4). 
6

Figure 1. General DHS testing strategy - Type 1. This testing strategy was used in the following surveys: 

Burundi (DHS 2010)*, Cameroon (DHS 2011), Gabon (DHS 2012), Gambia (DHS 2013), Haiti (DHS 2012), 

Mali (DHS 2012-13), Namibia (DHS 2013*), Niger (DHS 2012)*, Rwanda (DHS 2010, 2014-15), Senegal 

(DHS 2010-11)*, and Sierra Leone (DHS 2013)*. (*A line immunoassay was used as the third assay instead 

of a Western Blot.)

Figure 2. General DHS testing strategy - Type 2. This testing strategy was used in the following surveys: 

Chad (DHS 2014-15), Democratic Republic of the Congo (DHS 2013-14), Dominican Republic (DHS 2013), 

Ghana (DHS 2014)*, Malawi (DHS 2010), Tanzania (AIS/MIS 2011-12), Togo (DHS 2013-14)* and Zambia 

(DHS 2013-14). (*A line immunoassay was used as the third assay instead of a Western Blot.)
7

Figure 3. General DHS testing strategy - Type 3. This testing strategy was used in the following surveys: 

Côte d’Ivoire (DHS 2011-12) and Guinea (DHS 2012).

Figure 4. General DHS testing strategy - Type 4. This testing strategy was used in the following survey: 

Uganda (AIS 2011). (*One indeterminate result. Assay 3 was not performed on the sample.)
8

Table 2. DHS testing algorithms and HIV assays used

The name, manufacturer, and generation of the assays used in the HIV testing algorithms and specimen matrix, by survey

Survey EIA 1

EIA 1 

generation* EIA 2

EIA 2 

generation*

Parallel 

re-testing Ass

Sub-Saharan Africa

Burundi DHS 2010 Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II

(Siemens)

4 No Inno-Lia 

(Innoge

Cameroon DHS 

2011

Murex HIV Ag/Ab (DiaSorin) 4 Genscreen ULTRA HIV 

Ag/Ab (Bio-Rad)

4 No New Lav 

Ra

Chad DHS 2014-15 Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II 

(Siemens)

4 Yes HIV 2.

(DiaS

Côte d’Ivoire DHS

2011-12

Enzygnost Integral II

(Siemens)

4 Vironostika HIV Ag/Ab

(Biomérieux)

4 Yes No third 

DRC DHS 2013-14 Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II

(Siemens)

4 Yes HIV 2.

(DiaS

Gabon DHS 2012 Genscreen Plus HIV Ag/Ab 

5PL (Bio-Rad)

4 Enzygnost Integral II

(Siemens)

4 No HIV 2.

(DiaS

Gambia DHS 2013 Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II

(Siemens)

4 No HIV 2.

(DiaS

Ghana DHS 2014 Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II 

(Siemens)

4 Yes Inno-Lia 

(Innoge

Guinea DHS 2012 Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II 

(Siemens)

4 Yes No third 

Malawi DHS 2010 Vironostika HIV Uni-Form II 

Plus O (Biomérieux)

3 Enzygnost Anti-HIV 1/2 Plus 

(Siemens)

3 Yes Western 

(Abbot

Mali DHS 2012-13 Vironostika HIV Uni-Form II 

Plus O (Biomérieux)

3 Enzygnost Integral II

(Siemens)

4 No HIV 2.

(DiaS

Namibia DHS 2013 Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II

(Siemens)

4 No Inno-Lia 

(Innoge

Niger DHS 2012 Vironostika HIV Uni-Form II 

Plus O (Biomérieux)

3 Enzygnost Anti-HIV 1/2 Plus 

(Siemens)

3 No Inno-Lia 

(Innoge

Rwanda DHS 2010 Vironostika HIV Ag/Ab

(Biomérieux)

4 Murex HIV Ag/Ab (DiaSorin) 4 No HIV 2.

(DiaS

Rwanda DHS 2014-

15

Vironostika HIV Ag/Ab

(Biomérieux)

4 Murex HIV Ag/Ab 

combination (DiaSorin)

4 No HIV 2.

(DiaS

Senegal DHS 2010-

11

Vironostika HIV Uni-Form II 

Plus O (Biomérieux)

3 Enzygnost Anti-HIV 1/2 Plus 

(Siemens)

3 No Inno-Lia 

(Innoge

Sierra Leone DHS

2013

Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II

(Siemens)

4 No Inno-Lia 

(Innoge

Tanzania AIS/MIS

2011-12

Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II

(Siemens)

4 Yes HIV 2.

(DiaS

Togo DHS 2013-14 Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II

(Siemens)

4 Yes Inno-Lia 

(Innoge
9

Uganda AIS 2011 Murex HIV 1.2.0 (Abbott 

Labs)

3 Vironostika HIV Uni-Form II 

Plus O (Biomérieux)

3 No Ani Labs

HIV

Zambia DHS 2013-

2014

Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II

(Siemens)

4 Yes Western 

(Abbot

Latin America/ Caribbean

Dominican Republic

DHS 2013

Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II

(Siemens)

4 Yes HIV 2.

(DiaS

Haiti DHS 2012 Vironostika HIV Ag/Ab

(Biomérieux)

4 Enzygnost Integral II

(Siemens)

4 No HIV 2.

(DiaS

DBS= Dried blood spot; EIA=Enzyme immunoassay.

Some microplate readers have an upper detection limit and all optical densities (OD) above this limit are hence censored (usually 3 or 4)

in the Democratic Republic of the Congo, Ghana, Guinea, Namibia, Rwanda 2014-15, Dominican Republic, and Haiti all had an upper 

Other surveys include Malawi (OD values censored at 3 and 4), Rwanda 2010 (OD values censored at 4) and Zambia (there are 9 O

that are larger than 3). 

*4

th generation assays can detect the p24 antigen that is characteristically expressed shortly following HIV infections. These 4th ge

shorter test window period of detection than 3

rd generation assay.

❖Côte d’Ivoire (DHS 2011-12) and Guinea (DHS 2012) did not have a third assay. If the specimen had discrepant results on assay 1 

negative when calculating HIV prevalence.

✩ Specimen matrix was plasma instead of DBS. If respondents refused venipuncture, they could provide a DBS specimen from a 

specimens were therefore a mix of plasma and DBS. Fewer than 2% of specimens were DBS.
10

2.3. DHS testing standards 

In all surveys conducted with the assistance of The DHS Program, the laboratory analyses are conducted 

in the host country. The laboratory facility is selected by a DHS biomarker specialist and local agencies to 

ensure that the chosen laboratory can conduct high-quality testing and can handle a large volume of 

specimens. A laboratory training manual was developed by The DHS Program to assist host countries in 

conducting their population-based seroprevalence surveys. In all countries, The DHS Program invests 

heavily in training the laboratory technicians and by providing supplies and equipment for the laboratory 

in order to enhance the countries’ capacity for quality testing. 

Except for the 2011 AIS in Uganda, the type of sample collected from each individual was a dried blood 

spot (DBS), in which a small amount of blood is collected from a finger prick on filter paper. Hakim et al. 

recently suggested that false positivity could be magnified with DBS (Hakim et al. 2016). In Uganda, field 

staff collected plasma samples by venipuncture. However, participants could refuse and provide a DBS 

specimen instead. Field personnel were also trained on DBS collection. Further information on specimen 

collection can be found in The DHS Program standard biomarker training manual (MEASURE DHS 2012). 

2.4. Description of the assays used in the DHS testing algorithms 

The 23 DHS surveys used nine EIA and three supplementary assays (one line immunoassay and two 

Western Blots), as described below. 

Enzyme immunoassays 

The EIA for HIV are used for the qualitative detection of HIV antigens or antibodies against HIV in 

biological samples. The most common types of EIA use the indirect and sandwich methods. EIA for HIV 

detection utilize the sandwich technique for the detection of HIV antigens and/or antibodies elicited from 

an HIV infection. The EIA used by The DHS Program are sandwich assays, in which the antigen of interest, 

or capture antibody, is coated on the bottom of the wells of a microtiter plate and the sample is then added 

to the well where the antigens and/or antibodies bind. A conjugate containing polyclonal antibodies against 

the bound antibody and/or antigen detects the presence of HIV-specific antibodies or antigens bound to the 

wells of the microtiter plate (Truant 2016). 

Testing with EIA begins with the transportation of filter papers to the laboratories, where blood is then 

eluted from the individual DBS sample and the eluate is prepared for analysis (Grüner, Stambouli, and Ross 

2015). The eluate from each DBS sample that represents a different individual is then added to a 

corresponding well in the microtiter plate to allow the antibodies and/or antigens in the sample to bind to 

the bottom of the wells of microtiter plate. Any unbound antibodies and/or antigens are removed by 

washing, and the secondary antibody, which is attached to the detection enzyme, is added to the plate. In 

most of the following assays, horseradish peroxidase (HRP) is used as the enzyme label. After the excess 

antibody is removed, the reaction between HIV proteins in the sample and the plate is observed by using 

the chromogen tetramethylbenzidine dihydrochloride (TMB) which reacts with the enzyme to produce a 

blue to yellow color. The color produced by the enzymatic reaction between the enzyme and TMB is 

measured at 450 nm with a reference wavelength of 630 nm using a microplate reader. Some microplate 

readers have an upper detection limit, and all optical densities (OD) values above this limit are censored. 

The color intensity is approximately proportional to the concentration of HIV antigen and/or HIV antibodies 

in the test sample. For the assay run to be valid, the control sera that are tested on the microtiter plate along 

with the samples must comply with the specifications provided by the manufacturer. That is, the OD of the 

positive and negative controls must meet certain criteria to ensure that the test is working correctly. The 

mean OD of the control samples can then be used to calculate the assay’s cutoff value, as per the

manufacturer’s guidelines (Table 3). This cutoff value is then used to qualitatively define a sample as nonreactive (negative) or reactive (positive). 
11

Positive EIA samples can also be categorized by their reactivity depending on their S/CO values. A highly 

reactive specimen usually has a S/CO value greater than 5, while a S/CO value between 3 and 5 can be 

considered moderately reactive and a S/CO value of 1 to 3 can be considered weakly reactive (Nkengasong 

et al. 1999). Although all three categories are considered positive, specimens with a S/CO value less than 

5.0 were found to be more likely to be false positives in the literature (Fanmi et al. 2013; Nkengasong et al. 

1999; Urassa et al. 1999). Despite the relationship between the strength of this EIA reaction and the true 

HIV status of a sample, the S/CO value cannot differentiate between true and false positive results. False 

positive samples with high S/CO values have been documented in the literature as well as true positive 

samples that have reacted weakly on an EIA (Chacon, Mateos, and Holguin 2017; Fanmi et al. 2013; Hakim 

et al. 2016; Zhang et al. 2013). 

All nine EIA used in the 23 surveys are listed in Table 3 with their respective characteristics. All third and 

fourth generation assays can detect antibodies against HIV-1, HIV-2 and HIV-1 subtype O antigens in 

human serum or plasma. Only fourth generation assays can detect the p24 HIV antigen (Table S1). The 

ability to detect the p24 antigen allows the fourth generation assay to identify more recent HIV infections 

because this antigen can be detected earlier in the seroconversion process. 

Sensitivity and specificity of enzyme immunoassays 

There is a range of sensitivities and specificities reported in the literature for each EIA. In general, EIA are 

highly sensitive, although test accuracy can vary with laboratory conditions (Constantine 2006; Peeling et 

al. 2010). The nine assays used in the 23 surveys have reported sensitivity and specificity estimates higher 

than 99.8% and 98.3%, respectively (Table 3). These estimates are usually reported by the assay’s 

manufacturer, independent organizations such as WHO, or from scientific studies. In general, sensitivity 

and specificity estimates are derived under optimal laboratory conditions by trained lab technicians, and we 

can expect that lower test properties may result from less stringent laboratory conditions and/or less 

experienced users (see Section 2.5). 
12

Table 3. Properties of HIV enzyme immunoassays

All enzyme immunoassays (EIA) used in the 23 surveys conducted by The DHS Program with their respective characteristics. The generation, s

and number/type of controls are specific to the assay itself, whereas the range of signal-to-cutoff value and the delta values are in relation to the 

test.

Assay name 

(manufacturer) Sensitivity (95% CI) Specificity (95% CI)

Cutoff 

calculation

Confirmed HIV (+) 

S/CO mean (range) Delt

Enzygnost Anti-HIV 1/2 Plus 

(Siemens/Dade Behring)*

100% (99.6-100%) (WHO 1999; 

Beelaert et al. 2002)

99.75% (98.60-100%) 

(Weber et al. 2002)

100% (99.44-100%) 

(Nkengasong et al. 1999)

99.7% (99.1-100%) (WHO 1999; 

Beelaert et al. 2002)

99.94% (99.80-99.99%) 

(Weber et al. 2002)

99.75% (98.64-99.99%) 

(Nkengasong et al. 1999)

NC+0.4 

(WHO 1999)

7.5 (2.3-18.5) 

(Urassa et al. 1999)

8.0 (2.3-8.6) 

(Aboud et al. 2006)

δ

+

: 

(WHO 1999

δ

+

: 

(Nkenga

δ

+

: 5.0; δ

-

: 

Enzygnost Integral II 

(Siemens/Dade Behring)

100% (97.7-100%) (WHO 2004) 100% (98.8-100%) (WHO 2004) PC*0.23 

(WHO 2004)

13.7 (5.3-31.0) 

(Urio et al. 2015)

Genscreen Plus HIV Ag/Ab 

(Bio-Rad)

100% (97.7-100%) (WHO 2004)

100% (98.8–100%) 

(Piwowar-Manning et al. 2015)

98.3% (96.1–99.4%) (WHO 2004)

96.7% (94.0–98.4%) 

(Piwowar-Manning et al. 2015)

NC+0.2 

(BioRadLaboratori

es 2011)

N/A 

Genscreen ULTRA HIV Ag/Ab 

(Bio-Rad)

100% (99.2-100%) (WHO 2013)

100% (98.3-100%) (Francis 2013)

99.24% (98.2-99.8%) (WHO 2013)

99.90% (99.75-99.96%) (Francis 

2013)

NC+0.2 

(WHO 2013)

N/A δ

+

: 

(F

HIV EIA (Ani Labsystems)* 100% (99.6-100%) (WHO 1998; 

Beelaert et al. 2002)

99.4% (98.6-100%) (WHO 1998; 

Beelaert et al. 2002)

0.3(PC-BC) 

+ BC 

(WHO 1998)

N/A δ

+

: 

(WHO 1998

Murex HIV 1.2.O (Abbott Labs/ 

DiaSorin)*

100% (99.97-100%) (Abbott 

Laboratories 2007)

100% (99.44-100%) 

(Nkengasong et al. 1999)

99.91% (99.82-99.96%) (Abbott 

Laboratories 2007)

100% (99.10-100%) 

(Nkengasong et al. 1999)

NC+0.2 

(Abbott 

Laboratories 

2007)

N/A δ

+

: 

(Nkenga

δ

+

: 4.5; δ

-

: 

Murex HIV Ag/Ab (DiaSorin) 100% (99.2-100%) (WHO 2015c)

100% (98.83-100%) 

(Lemee et al. 2014)

99.7% (98.9-100%) (WHO 2015c)

98.9% (97.5-99.6%) (Lemee et al. 

2014)

NC+0.15 

(WHO 2015c)

12.2 (5.2-16.0) 

(Urio et al. 2015)

13.3 (5.3-18.6) 

(Aboud et al. 2006)

Vironostika HIV Ag/Ab 

(Biomérieux/ Organon Teknika)

100% (97.7-100%) (WHO 2004) 99.0% (97.1-99.8%) (WHO 2004) NC+0.10 

(WHO 2004)

15.5 (12.1-19.0) 

(Urio et al. 2015)

15.8 (10.8-20.7) 

(Aboud et al. 2006)

Vironostika HIV Uni-Form 2 

Plus O (Biomérieux/ Organon 

Teknika)*

100% (99.6-100%) (WHO 1999; 

Beelaert et al. 2002)

100% (99.44-100%) 

(Nkengasong et al. 1999)

100% (99.7-100%) 

(WHO 1999; Beelaert et al. 2002)

99.50% (98.24-99.94%) 

(Nkengasong et al. 1999)

NC+0.10 

(WHO 1999)

14.8 (6.5-21.2) 

(Aboud et al. 2006)

δ

+

: 

(WHO 1999

δ

+

: 

(Nkenga

δ

+

: 5.3; δ

-

: 

NC: Mean optical density of negative controls; PC: Mean optical density of positive controls; BC: Mean optical density of blank controls.

N: Negative control; P: Positive control; WPC: Weak positive control; B: Blank control; IC: Internal control.

*Indicates that this is a third generation assay, and does not detect the p24 antigen.
13

Confirmatory assays 

Two different types of supplemental assays were used to resolve discrepant results: Western Blot and line 

immunoassays. A Western Blot is a qualitative test that detects HIV proteins on a membrane after their 

subsequent transfer from a gel. The manufacturer provides guidelines on band appearance patterns that 

indicate when the sample is HIV positive or negative (or indeterminate) and sometimes can distinguish the 

HIV subtypes. The HIV specific proteins are first separated by their molecular weight using gel 

electrophoresis. The molecules are then transferred (blotted) onto a membrane and detected by antibodies. 

In contrast with Western Blots, a line immunoassay procedure involves coating the HIV specific proteins 

as discrete lines on a nylon strip, which avoids electrophoresis. The test sample is added to the membrane 

and then washed away. The alkaline phosphatase-labeled anti-human IgG antibodies are incubated on the 

membrane and then bind to the HIV antigen/antibody complex that was previously formed. A combination 

of enzymes, 5-bromo-4-chloro-3-indolyl-phosphate and nitro blue tetrazolium (BCIP/NBT) produces a 

dark brown color. The reaction is stopped by removing the developing solution from the strips. The 

appearance of specific colored bands demonstrates the presence of HIV antibodies in the test sample. 

Inno-Lia HIV I/II Score Line, New Lav Blot and HIV 2.2 Blot/Western Blot 2.2 detect the presence of 

antibodies against HIV-1, HIV-2, and HIV-1 subgroup O antigens in a human sera or plasma sample (Table 

4). New Lav Blot has separate nitrocellulose strips for HIV-1 and HIV-2 proteins, although the HIV Blot 

2.2 nitrocellulose strips contain all the HIV-1 proteins and a specific HIV-2 peptide (Table S2). 

Sensitivity and specificity of confirmatory assays 

Confirmatory assays are used because the lower specificity of the EIA can result in false positives. To fill 

this role, the assays must have very high specificity. Estimates of specificity reported in the literature are 

100% for the three types of confirmatory assays used in the surveys, if the indeterminate results are excluded 

from the numerator and denominator of the specificity estimates (Table 4). Here again, the actual specificity 

of the tests can vary depending on laboratory conditions (Constantine 2006; Peeling et al. 2010). 
14

Table 4. Properties of supplemental assays

Supplemental assays used in the 23 surveys conducted by The DHS Program with their respective characteristics: assay type, sensitivit

results from these assays are qualitative.

Assay name (manufacturer) Assay type Sensitivity (95% CI) Specific

Inno-Lia HIV I/II Score Line (Innogenetics) Line immunoassay 100% (98.6-100%) (WHO 2015b) 100% (98.0-10

New Lav Blot (Bio-Rad/Sanofi Diagnostics 

Pasteur)

Western Blot 100% (98.1-100.0%) (WHO 2015b) 100% (96.8-100

HIV 2.2 Blot/Western Blot 2.2 

(DiaSorin/MP Diagnostics/Abbott Labs)

Western Blot HIV-1: 99.52% (97.36-99.99%) 

(MP Diagnostics 2003)

HIV-2: 95.33% (89.43-98.47%) 

(MP Diagnostics 2003)

HIV-1: 100%*

HIV-2: 100%❖

HIV-1/2: 93.50

(MP Diag

HIV-1

*

If the indeterminate results are considered, then sensitivity (99.52%) remains the same where # of true positives is 208/209. If in

disregarded then sensitivity becomes 208/208 (100%).

❖If the indeterminate results are considered, then sensitivity (95.33%) remains the same where # of true positives is 102/107. If in

disregarded then sensitivity becomes 102/102 (100%).

✩If the indeterminate results are considered, then specificity (93.5%) remains the same where # of true positives is 187/200. If indeterminat

then specificity becomes 187/187 (100%).
15

2.5. Potential sources of misclassification 

Misclassification of HIV status can result from different factors such as limitations of the assay, operatorrelated factors, facility-related factors, suboptimal testing algorithms, and inadequate training (Johnson et 

al. 2015). Some of these errors may not be corrected in certain laboratories because of the lack of quality 

management systems or external quality assessments. Half of the studies that reported poor management 

and supervision in a WHO review of HIV testing services also reported poor management of supplies 

(Johnson et al. 2015). It is also possible that an assay is not suitable for detecting a circulating HIV variant 

in a particular region. In addition, cross-reactivity has been documented for antibodies from intercurrent 

infections, HIV subtypes, or even environmental exposure to the assay components (Johnson et al. 2015). 

Operator-related factors could include data reporting problems, incorrectly performing the assay, and 

misinterpreting the results. A common challenge is the interpretation of faint lines and weak reactive 

specimens on the qualitative confirmatory test (Western Blot and line immunoassay), which has been well 

documented and addressed in the literature (Gray et al. 2007; Sacks et al. 2012). Although the equipment 

is tested prior to testing blood specimens, clerical and user errors are still possible (Fishel and Garrett 2016). 

Poor record keeping and labeling, incorrect use of supplies such as incorrect buffer volumes, and 

technicians who do not follow appropriate reading times could lead to misdiagnosis (Johnson et al. 2015). 

The traffic of samples in a facility may also lead to misclassification—a high volume of specimens can 

overload the staff and a lower volume may lead to poor staff proficiency (Johnson et al. 2015). Finally, 

though the use of DBS with EIA is common, most EIA manufacturers have not validated their tests on this 

specimen type, and the use of DBS with these assays may magnify false positivity (Hakim et al. 2016). 

2.6. Model specifications 

In the absence of a gold-standard to assess HIV prevalence for large-scale household-based surveys, 

and the impossibility of retrospectively re-testing samples, a Bayesian latent class analysis can be used to 

adjust HIV prevalence estimates for potential misclassification (Joseph, Gyorkos, and Coupal 1995). By 

explicitly modeling the misclassification process and using external information on the accuracy of the 

different assays and the potential correlation between assays, it is possible to explore the extent to which 

HIV prevalence could have been over or under-estimated. 

Two different types of models can be used to adjust HIV prevalence estimates, depending on whether 

all the information of the continuous assay results are used, or whether these results are first dichotomized 

by using the assays’ manufacturer cutoffs. In this report, we explore both model types. The first class of 

Bayesian latent class model we considered uses only dichotomous test results. A more comprehensive way 

to model the tests results is to include the continuous score information from the OD of each assay. This 

second class of models uses the continuous information from the OD and the dichotomous information 

from the third assay (from which no continuous information is available) to provide adjusted prevalence 

estimates. In this section, we first describe the dichotomous class of model, and then the specification of 

the continuous latent class model. 

Dichotomous assay model 

Four different dichotomous assay models were derived, depending on the general testing strategy they used. 

We briefly present how the equations for the dichotomous assay model were derived. In the Type 1 testing 

strategy, there are two EIA used, with discrepant results resolved by using a third tie-breaker assay (no 

repeat testing) (Figure 5). For example, the equation for the probability of a sample being negative on the 

first EIA, and not selected for IQC, is equal to the product of the complement of the proportion tested for 

IQC and sum of the probabilities of being a false negative (π[1-Se1]) and a true negative ([1-π]Sp1), where 

the probabilities of being a false negative and true negative depends on the true unobserved prevalence (π) 

and the first EIA’s properties in terms of sensitivity (Se1) and specificity (Sp1). If a sample that was 

negative on the first EIA was selected to be part of IQC and was found to be negative on the second EIA, 
16

the equation would be equal to the product of the proportion of samples tested for IQC and the sum of 

probabilities of false negatives on both EIA (π[1-Se1][1-Se2]) and true negatives ([1-π]Sp1Sp2). The same 

logic is applied to all possible combinations of assays to derive the equations for the expected probability 

distribution (Figure 5). 

The section below presents the equations for all four testing strategies. 

Figure 5. Flowchart describing the derivation of equations for the dichotomous Bayesian latent 

class model. 

Type 1 testing strategy: two EIA, no repeat testing, with a third assay 

The equations below describe the expected probabilities of positive and negative samples for each possible 

combination of assays in the Type 1 testing algorithm.

X~M(μ, N)

EIA1

− ∶ μ1 = (1 − IQC)(π(1 − Se1

) + (1 − π)Sp1)

EIA1

− & EIA2− ∶ μ2 = IQC(π(1 − Se1)(1 − Se2

) + (1 − π)Sp1Sp2)

EIA1

− & EIA2

+ & ASS3

−: μ3 = IQC(π(1 − Se1)Se2(1 − Se3

) + (1 − π)Sp1(1 − Sp2)Sp3)

EIA1

+ & EIA2

− & ASS3−: μ4 = π(Se1)(1 − Se2

)(1 − Se3) + (1 − π)(1 − Sp1)Sp2Sp3

EIA1

+ & EIA2+: μ5 = π(Se1Se2

) + (1 − π)(1 − Sp1)(1 − Sp2)

EIA1

+ & EIA2

− & ASS3

+: μ6 = πSe1(1 − Se2)Se3 + (1 − π)(1 − Sp1

)Sp2(1 − Sp3)

EIA1

− & EIA2

+ & ASS3+: μ7 = IQC(π(1 − Se1)Se2Se3 + (1 − π)Sp1

(1 − Sp2)(1 − Sp3))

where X is a vector that contains the counts of samples for each possible combination of assays (Figure 5), 

as per the surveys’ testing algorithm. These counts follow a multinomial distribution of size N and μ is a 

vector that contains the probabilities of observing these X counts; IQC is the proportion of samples negative 

on the first EIA (EIA1) that are re-tested as part of the internal quality control with the second EIA (EIA2); 

π is the true unobserved HIV prevalence; Se1, Se2, and Se3 are the sensitivities of the first EIA, second EIA, 

EIA 1

μ1= [π (1-Se1) + (1- π)Sp1] (1- IQC)

EIA 2

μ5= π(Se1)(Se2) + (1- π)(1- Sp1)(1-Sp2)

μ6= π(Se1)(1-Se2)(Se3) + (1- π)(1-Sp1)(Sp2)(1-Sp3)

μ4= π(Se1)(1-Se2)(1-Se3) + (1- π)(1-Sp1)(Sp2)(Sp3)

EIA 2

Assay 3

μ2= [π(1-Se1)(1-Se2) + (1- π)(Sp1)(Sp2)] IQC

Assay 3

μ7=[π(1-Se1)(Se2)(Se3) + (1- π)(Sp1)(1-Sp2)(1-Sp3)] IQC

μ3= [π(1-Se1)(Se2)(1-Se3) + (1- π)(Sp1)(1-Sp2)(Sp3)] IQC

- Positive

- Negative

(-) (+)

(-) (+)

(-) (+)

(+) (-)

(-) (+)
17

and third assays, respectively. Similarly, Sp1, Sp2, and Sp3 are the specificities of the first EIA, second EIA, 

and the third assay, respectively. 

For simplicity, we have assumed that the three assays are conditionally independent. In other words, we did 

not model the potential correlation between the three tests. A recent study evaluated the effect of conditional 

dependence on Bayesian latent class adjusted estimates of prevalence using dichotomous tests and found 

that the bias due to ignoring conditional dependence is generally small (Wang, Dendukuri, and Joseph 

2017). In addition, we ran both correlated and non-correlated models for the continuous data (see below), 

and found the results to be similar. 

Type 2 testing strategy: two EIA, repeat testing, with a third assay 

The model for the Type 1 algorithm can be extended easily to account for repeat testing. Preliminary 

analyses (not shown) using an extended model accounting for repeat testing did not produce adjusted 

estimates that were very different from those estimated by the model above. Because of the assumption that 

the assays are conditionally independent, a model not including the repeated tests is more likely to produce 

good estimates, since we ignored potential conditional dependence. Hence, when using the Bayesian latent 

class model for dichotomous tests for the Type 2 testing strategy, we use the model above (Type 1) where 

the repeated parallel test results replace the initial test of the same type. 

Type 3 testing strategy: two EIA, repeat testing, no third assay 

X~M(μ, N)

EIA1

− ∶ μ1 = (1 − IQC)(π(1 − Se1

) + (1 − π)Sp1

)

EIA1

− & EIA2− ∶ μ2 = IQC(π(1 − Se1)(1 − Se2

) + (1 − π)Sp1Sp2

)

EIA1

− & EIA2

+ ∶ μ3 = IQC(π(1 − Se1

)Se2 + (1 − π)Sp1(1 − Sp2))

EIA1

+ & EIA2+: μ4 = π(Se1Se2

) + (1 − π)(1 − Sp1

)(1 − Sp2

)

EIA1

+ & EIA2

− ∶ μ5 = πSe1(1 − Se2) + (1 − π)(1 − Sp1

)Sp2

Here again, the sample counts are modeled using a multinomial distribution. Tests that are still discrepant 

after repeat testing are considered indeterminate, and results from repeat testing are considered final. 

Type 4 testing strategy: three EIA, no repeat testing, no internal quality control 

X~M(μ, N)

EIA1

− ∶ μ1 = π(1 − Se1

) + (1 − π)Sp1

EIA1

+ & EIA2

− & EIA3− ∶ μ2 = πSe1(1 − Se2)(1 − Se3) + (1 − π)(1 − Sp1

)Sp2Sp3

EIA1

+ & EIA2+: μ4 = π(Se1Se2

) + (1 − π)(1 − Sp1

)(1 − Sp2)

EIA1

+ & EIA2

− & EIA3

+ ∶ μ5 = πSe1(1 − Se2)Se3 + (1 − π)(1 − Sp1

)Sp2

(1 − Sp3)

This final model, used only in Uganda, has the particularity that there was no internal quality control. 

Prior distributions 

We used a Bayesian framework to estimate HIV prevalence from the above models, which account for 

imperfect sensitivities and specificities of all tests regardless of the cutoff used for the serological 

classification. Bayesian models require the elicitation of prior distributions, which represent what is known 

about the unknown parameter values from expert opinion or past data. All our dichotomous models are 

non-identifiable because there are more parameters to estimate than degrees of freedom in the data. We 

chose to provide informative priors for the sensitivities and specificities of each of the three tests in order 

for the model to be essentially identifiable. This means that reasonable estimates can be produced for all 

parameters when combining the information in the data with the prior information. These priors were 
18

chosen to account for the potential suboptimal laboratory conditions in which the samples could have been 

analyzed, and do not necessarily match those suggested by the manufacturers, which may reflect optimal 

lab conditions and highly experienced technicians. We chose a non-informative uniform prior for the true 

unknown HIV prevalence (equivalent to a Beta(1,1) density) and used informative beta distributions that 

match the 95% confidence intervals for sensitivity (95% confidence interval (95% CI: 98.0-99.9%)) and 

specificity (95% CI: 85.0-99.0%) of the EIA. For the third assay (Western Blot or line immunoassay), we 

assume that specificity would be slightly higher (95% CI: 99.0-99.9%). In this way, the combination of 

prior information on the tests with the testing data itself enables us to have identifiable models where the 

prior for the true unobserved HIV prevalence parameter has a very low information prior placed on it (i.e., 

uninformative).

Posterior distributions 

According to Bayes’ Theorem, we combined the likelihood function with the prior information to derive 

posterior densities, from which all inferences follow. Because the posterior distributions of the parameters 

of interest do not have closed form expressions, random samples from the posterior density are obtained 

using Markov Chain Monte Carlo (MCMC) simulations implemented with JAGS software (Hornik, Leisch, 

and Zeileis 2003; Plummer 2013). Three chains of 15,000 iterations were run after a burn-in of 7,000 

iterations. These samples are then summarized to form inferences about all unknown parameters, including 

the prevalence. Parameters estimates are summarized with the median and 95% credible intervals (95% 

CrI; corresponding to the 2.5th and 97.5th percentiles) of their posterior distribution. 

Continuous assay model 

The main advantage to modeling continuous test results (the log[S/CO]) rather than dichotomizing at a 

cutoff value, as in the above analyses, is that continuous variables generally carry more information per 

observation as compared to discrete variables. Thus, sharper inferences on the estimated probabilities of 

each subject being truly positive or truly negative can lead to better prevalence estimates. To see why 

continuous values may carry more information, compare a weakly reactive sample, which should have a 

smaller chance of being a true positive to a sample that is strongly reactive, which should have a greater 

probability of being a true positive. Under dichotomous modeling, this detailed information is lost, which 

can lead to poorer estimates. Modeling continuous test results is more complex compared to using 

dichotomous test results. To facilitate understanding of the models, we introduce the following notation. 

Samples tested with one, two, three, and four (repeat testing in parallel) EIA are labeled S1, S2, S3, and S4, 

respectively. All discrepant samples on the first two EIA are tested with a third dichotomous assay (Western 

Blot or line immunoassay), except for the Uganda AIS 2011 survey, which used a third continuous EIA 

assay as a tie-breaker. 

The OD from the continuous assays were modeled by first calculating their S/CO value. That is, the 

continuous OD were divided by their plate-specific cutoff value. Samples with a S/CO value greater than 

or equal to 1 were considered as reactive in the dichotomous analyses in the preceding section. By contrast, 

the continuous model specification does not explicitly use any threshold to categorize samples as nonreactive or reactive. Instead, the continuous model specification considers that each population of true 

positives and true negatives has their own densities of test results and that these two distributions overlap. 

Assuming that the distribution of positives lies to the right (higher values) of the distribution of negatives, 

very high S/CO values are more likely to have arisen from the positive density, while subjects with very 

low values are likely to be true negatives. However, subjects with intermediate values—values that lie in 

between the two density peaks—are of uncertain origin. For those values of uncertain origins, their 

probability of being positive will depend on their relative proximity to the positive and negative density 

peaks. These probabilities will be proportional to the heights of the density curves at the observed test value.

These two densities can be modeled parametrically or non-parametrically. Nevertheless, because of the 
19

large number of tests for each subject (up to four) and the potential for correlation between tests, we ruled 

out non-parametric models because no one has developed a model that accommodates four tests with 

correlations from a non-parametric viewpoint. In fact, it is also true that to date no one has developed a 

model that accommodates four tests with correlations from a parametric viewpoint, although this is a 

somewhat easier problem. For this report, we developed a novel model that accomplishes that. As is usual 

for these problems, we assumed normality of the densities conditional on true infection status. Since the 

S/CO values are not normally distributed, we log-transformed them (Feng et al. 2014; Qiu et al. 2008). 

Hence, we assumed that in sets S2, S3, and S4, the vectors of test results Xi follow multivariate normal 

distributions of length 2, 3, or 4, respectively. While we realize that potential cross-contamination of 

samples, especially negative samples contaminated by positive residue, may lead to data that violate the 

normality assumption, we believe that our models will nevertheless produce reasonable estimates for most 

countries. Close inspection of all parameter estimates across analyses from the data from all countries led 

to a small number of unreasonable estimates that we believe were caused by imposing normality on 

contaminated samples. We attempted to resolve these problems by the judicious use of further prior 

information, for example, by restricting the range of means and/or standard deviations to plausible values 

when potential violations of multivariate normality (or surveys with censored OD values) led to highly 

implausible estimates. 

The intuition behind our continuous latent class model is depicted in the figure below (Figure 6). Samples 

A, B, and C are tested with only one assay and each sample contribute information on the prevalence 

depending on their likelihood of arising from the distribution of true negatives (blue) or the distribution of 

true positives (red). As such, it does not directly use a single threshold value to differentiate positive from 

negative samples. In the example below, which depicts an ideal situation with near-perfect tests based on 

the distance between the positive and negative results, sample A would contribute a high probability of 

being part of the true negative distribution and a corresponding low probability of arising from the 

distribution of true positives. Sample B, which is almost exactly between the two distributions, and whose 

S/CO value would result in a positive classification with the dichotomous model despite its low reactivity, 

has a roughly equal chance of being a true negative or a true positive. It would therefore contribute the 

equivalent of “half a subject” to the prevalence (if the prior on the unobserved prevalence is uninformative). 

Finally, sample C is highly reactive and has a high probability of being a true positive and low probability 

of being a true negative. Thus, each subject’s test score is classified not as a definitive positive or a negative 

result, but as a probability of being positive. The sum of these positive probabilities across all subjects 

determines the overall prevalence estimate. 
20

Figure 6. Graphical representation of continuous model specification. Graphical display of the 

continuous model specification where the signal-to-cutoff ratio on the logarithmic scale is displayed on the 

x-axis and the density of the normal distributions of the true negative (blue) with mean μ0 and standard 

deviation σ0 and of the true positive (red) with mean μ1 and standard deviation σ1. Points A, B, and C are 

hypothetical results that would lead to low, equivocal, and high probabilities of being positive, respectively, 

according to the ratios of the heights of the two densities at each point.

Likelihood for continuous assay results 

Each sample is either truly positive or truly negative, which is modeled with the “True Status” latent 

variable Ti, a vector of length N, corresponding to the total number of samples in each respective survey. 

The contribution of Ti to the likelihood depends on the true unobserved prevalence π, as follows:

LTi = πTi(1 − π)1−Ti

The contribution of test scores (i.e., the log[S/CO]) from the i

th subject Xi

to the likelihood is either Li1|s= 

L1(xi|θs), Li2|s = L2(xi|θs), Li3|s=L3 (xi|θs) or Li4|s= L4(xi|θs), depending on the set k={1,2,3,4} to which sample 

i belongs and its latent true status Ti=s, where θsis the set of parameters associated with corresponding set 

and true status s. The likelihoods of these four different sets are presented below: 

Li1|s = 

1

σ1

exp {− (Xi − μ1

)

2

2σ1

2

}

Li2|s = 

1

|Σ2s|

exp {− 1

2|Σ2s|

(Xi − μ)

⊤Λ2s(Xi − μ)} where Σ2 = ( σ1

2 ρσ1σ2

ρσ1σ2 σ2

2

)

Li3|s = 

1

|Σ3s|

exp {− 1

2|Σ3s|

(Xi − μ)

⊤Λ3s(Xi − μ)} where Σ3 = (

σ1

2 ρ12σ1σ2 ρ13σ1σ3

ρ12σ1σ2 σ2

2 ρ23σ2σ3

ρ13σ1σ3 ρ23σ2σ3 σ3

2

)

Li4|s =

1

|Σ4s|

exp {−

1

2|Σ4s|

(Xi − μ)

⊤Λ4s(Xi − μ)} where Σ4 =

(

 

 

σ1

2 ρ11σ12

ρ11σ1

2 σ12

 

ρ12σ1σ2 ρ12σ1σ2

ρ12σ1σ2 ρ12σ1σ2

ρ12σ1σ2 ρ12σ1σ2

ρ12σ1σ2 ρ12σ1σ2

 

σ2

2 ρ22σ22

ρ22σ2

2 σ22

)

 

 

where μ is a vector of distribution means, whose value depends on the set k to which it belongs, and σ is the 
21

standard deviation of that distribution; ks is the cofactor matrix corresponding to the covariance matrix 

ks, k={2, 3, 4}. These covariance matrices take into account potential conditional dependence between the 

different assays (the correlation parameter ρ). Since the models that account for conditional dependence 

gave similar results to the model that assumed independence, we chose to present HIV prevalence estimates 

from the latter model only, for simplicity. For these models, the covariance parameters on the off-diagonal 

entries of ks are simply replaced by zeros. The contribution of scores Xi to the likelihood, provided sample 

i pertain to set k, can be written as: 

LXi = Lik|0

1−TiLik|1′Ti

i ∈ Sk

Likelihood for confirmatory assay results 

Each sample for which an additional confirmatory dichotomous assay was performed (Western Blot or line 

immune-assays) contributes an additional term to the likelihood. Given prior information on this 

confirmatory assay’s sensitivity SeW and specificity SpW, the contribution of this test (with binary results wi, 

taking values of 0 if non-reactive and 1 if reactive) to the likelihood is given by: 

LWi = [SeW

wi

(1 − SeW)

1−wi]

Ti

[(1 − Spw)

wiSpW

1−wi

]

(1−Ti)

Prior distributions 

As in the previous section, our Bayesian models require prior densities for each parameter. The prior 

distribution for the unobserved true HIV prevalence follows a uniform or, equivalently, a Beta distribution 

with: 

π ~ Beta(1, 1)

The mean of the log(S/CO) for assay t among true positive samples (s=1) and true negative samples (s=0) 

are given normal prior distributions μts with standard deviation σts and where the mean of the normal 

distribution is νts. As justified below, a minimum (δts) and/or a maximum (ψts) standard deviation was 

sometime used: 

μts~N(νts, σts)

νts~N(ηts, ξts)

f(σts) = 1, and δts > σts ≤ ψts

The different prior correlation terms (either between two tests or between the two measurements of a same 

test) are assumed to be uniform: 

ρ~U(−1,1)

Finally, the sensitivity and specificity parameters of the confirmatory (dichotomous) assays are given 

truncated Beta distributions: 

SeW~Beta(1,1) ∗ I(LowerSe, 1)

SpW~Beta(1,1) ∗ I(LowerSp, 1)

where LowerSe and LowerSp represent prior lower limits, whose values varied between surveys and were 

typically 0.96 or 0.98. Preliminary analyses using non-truncated informative Beta priors on those 

parameters resulted in HIV prevalence estimates that were often much higher than the observed 
22

(unadjusted) prevalence. Given the reported high sensitivity of EIA (UNAIDS/WHO 2015), it seemed 

unlikely that there would be such a high number of false negatives. For example, the posterior distribution 

for the sensitivity of the third confirmatory assays (Western Blot or line immunoassay) was as low as 79% 

(using a uniform prior), which was much lower than any reported estimates in the literature (Table 4). To 

better reflect the characteristics of the different assays, more informative prior distributions were elicited 

(Table 5). Specifically, truncated beta distributions were used where the lower limits of the distributions 

(indicator I) bounded the posterior distributions to high minimum values that are in line with their reported 

sensitivity and specificity. 

We also provided a minimum value for the standard deviation (δts) for the distribution of the true negative 

samples. This value ensured that the distribution of true negative would be wide enough to capture both 

samples that were non-reactive and those that were reactive and near the cutoff. For surveys that had 

censored OD values, we also found it necessary to place a further constraint on the maximum mean of the 

true negative density so that the S/CO ratio would not be higher than 44.7, the maximum S/CO value 

observed in the non-censored surveys. Without an upper limit, imputing values for these censored OD data 

points produced, in some countries, a mean that was artificially raised to unreasonable levels. For similar 

reasons, a maximum standard deviation (ψts) for the distribution of true positives was also elicited for 

surveys with censored OD values. The values used for all priors are presented in Tables 5 and 6 and a full 

justification is provided in Text S1. 

Posterior distributions 

The special nature of the likelihood functions and priors limited the ability to fit our models in standard 

MCMC programs such as WinBUGS (Lunn et al. 2000), Nimble (Nimble 2017), or Stan (Carpenter et al. 

2016). For example, Nimble does not allow random indices, and censoring can be problematic for programs 

such as WinBUGS. We therefore created our own MCMC routines in R to sample from the posterior 

distributions of the parameters of interest. This was achieved by generating random values for each 

parameter based on their respective full conditional posterior distribution. The full conditional distributions 

are presented in Text S2. For each analysis, we ran 1,000 burn-in iterations followed by 5,000 iterations for 

inference. 
23

Table 5. Priors for the true positive and true negative distributions of log-transformed 

signal-to-cutoff ratios for the nine enzyme immunoassays

Assays Prior distributions*

Enzygnost Integral II (Siemens) μt1 ~ N(νt1, σt1)

νt1 ~ N(log(13.7), 0.43), and f(σt1)=1, and σt1 > 0

μt0 ~ N(νt0, σt0)

νt0 ~ N(log(0.31), 0.11), and f(σt0)=1, and σt0 > 0.71

Enzygnost Anti-HIV 1⁄2 Plus (Siemens) μt1 ~ N(νt1, σt1)

νt1 ~ N(log(7.7), 0.19), and, f(σt1) = 1, and σt1 > 0

μt0 ~ N(νt0, σt0)

νt0 ~ N(log(0.23), 0.43), and f(σt0)=1, and σt0 > 0.89

Genscreen Plus HIV Ag/Ab (Bio-Rad), 

Genscreen ULTRA HIV Ag/Ab (Bio-Rad), HIV 

EIA (Ani Labsystems), and Murex HIV 1.2.0 

(Abbott Labs)

μt1 ~ N(νt1, σt1)

νt1 ~ N(log(15), 0.47), and f(σt1) = 1, and σt1 > 0

μt0 ~ N(νt0, σt0)

νt0 ~ N(log(0.30), 0.35), and f(σt0)=1, and σt0 > 0.73

Murex HIV Ag/Ab Combination (DiaSorin) μt1 ~ N(νt1, σt1)

νt1 ~ N(log(12.7), 0.40), and f(σt1) = 1, and σt1 > 0

μt0 ~ N(νt0, σt0)

νt0 ~ N(log(0.30), 0.35), and f(σt0) = 1 and σt0 > 0.73

Vironostika HIV Ag/Ab (Biomérieux) μt1 ~ N(νt1, σt1)

νt1 ~ N(log(21.5), 0.63), and f(σt1) = 1, and σt1 > 0

μt0 ~ N(νt0, σt0)

νt0 ~ N(log(0.33), 0.26), and f(σt0) = 1 and σt0 > 0.67

Vironostika HIV Uni-Form II Plus O (Biomérieux) μt1 ~ N(νt1, σt1)

νt1 ~ N(log(19.4), 0.58), and f(σt1)=1 and σt1 > 0

μt0 ~ N(νt0, σt0)

νt0 ~ N(log(0.33), 0.26), and f(σt0)=1 and σt0 > 0.67

*For surveys with censored optical density (OD) values, further constraints were placed on the maximum 

value that can take the mean and standard of the distribution of true positive samples. If OD values were 

censored, the mean of true positive (νt1) could not be higher than log (44.7) – the maximum observed S/CO 

value - and the standard deviation (σt1) larger than 1.63 (on the log(S/CO) scale), the latter based on having 

less than 1% of the true positive distribution below the cutoff (i.e., a S/CO below 1).

Table 6. Priors for the sensitivity and specificity of the dichotomous 

confirmatory assays

Assays Prior distributions

Inno-Lia HIV I/II Score Line Immunoassay (Innogenetics) Sew ~ Beta(1,1)*I(0.986, 1)

Spw ~ Beta(1,1)*I(0.980, 1)

New Lav Blot (Bio-Rad) Sew ~ Beta(1,1)*I(0.981, 1)

Spw ~ Beta(1,1)*I(0.968, 1)

HIV 2.2 Blot (DiaSorin) / Western Blot 2.2 (Abbott Labs) Sew ~ Beta(1,1)*I(0.982, 1)

Spw ~ Beta(1,1)*I(0.980, 1)

25

3. Results 

To better understand agreement between the different assays, plots of the log-transformed S/CO values of 

the two EIA and confirmatory assay results were first produced (Figures 7A, 7B, 7C, and 7D). If the testing 

algorithm involved repeat testing, the final EIA values were plotted. These plots are divided into four 

quadrants. The bottom left quadrant includes all samples that were negative on the first EIA, that were 

selected for testing with a second EIA, and that were found to be non-reactive as part of the IQC procedure. 

The upper left quadrant has the samples that were initially non-reactive on the first EIA that were found 

reactive on the second EIA as part of the IQC procedure. The upper right quadrant includes all samples 

reactive on both EIA. Finally, the bottom right quadrant includes all samples that were reactive on the first 

EIA and non-reactive on the second EIA. All discrepant results (upper left and bottom right quadrants) were 

tested with a third confirmatory assay with the final results plotted with different colors (blue squares for 

negatives and red circles for positive samples). The medians of the posterior means, along with the 50% 

and 95% coverage intervals of the distributions (based on their median standard deviations) of the true 

negative and true positive distributions are also plotted on the margins of these graphs (Figures 7A, 7B, 7C, 

and 7D). 

For many surveys, we see a clear clustering of almost all samples in the bottom left and top right quadrants. 

This indicates that samples were either non-reactive or strongly reactive on both EIA. For surveys with 

such clear clustering of positive and negative samples, we do not expect our misclassification adjustments 

to have much impact on HIV prevalence estimates. This group includes the following surveys: Côte d’Ivoire 

DHS 2011-12, Chad DHS 2014-15, DRC DHS 2013-14, Dominican Republic DHS 2013, Ghana DHS 

2014, Guinea DHS 2012, Malawi DHS 2010, Mali DHS 2012-13, Rwanda DHS 2010, Rwanda DHS 2014-

15, Tanzania AIS/MIS 2011-12, and Togo DHS 2013-14. An additional two surveys had relatively clear 

clustering of strongly reactive samples, although the agreement was slightly lower than for the preceding 

surveys: Gambia DHS 2013 and Senegal DHS 2010-11.

Surveys for which agreement was suboptimal and/or there was no clear clustering of strongly non-reactive 

or reactive samples include: Burundi DHS 2010, Cameroon DHS 2011, Gabon DHS 2012, Haiti DHS 2012, 

Namibia DHS 2013, Niger DHS 2012, Sierra Leone DHS 2013, Uganda AIS 2011, and Zambia DHS 2013-

14. Of those, HIV testing results from the Uganda AIS 2011 and the Zambia DHS 2013-14 appear the most 

problematic. In Uganda, the 2011 AIS did not include any IQC and the third confirmatory assay was another 

EIA instead of the more specific Western Blot or line immunoassay. Further, a high number of samples 

have discordant results and there is no clear clustering of reactive samples. In Zambia, the 2013-14 DHS 

had higher agreement between the two EIA, although the high number of weakly reactive samples could 

suggest that a certain proportion of these are false positive. 
26

Figure 7A. Distribution of log transformed signal-to-cutoff ratio from samples tested on both enzyme immunoassays with 

Final HIV status is represented as the shape and color of each plot point. Samples tested on Western Blot or line immunoassays in the applicab

d’Ivoire DHS 2011-12 did not have a third assay. A1/A2=Agreement between EIA 1 and EIA 2 before and after repeat testing respectively; A=Ag

testing; IQC=Proportion of negative samples on EIA1 selected for internal quality control. Negative and positive posterior distributions, from the 

indicated on the top (EIA1) and right side (EIA2) of the graph (grey areas), where the point corresponds to the mean of the distribution, and the thi

95% of the highest posterior density of the distributions. 
27

Figure 7B. Distribution of log transformed signal-to-cutoff ratio from samples tested on both enzyme immunoassays with 

Final HIV status is represented as the shape and color of each plot point. Samples tested on Western Blot or line immunoassays in the applicable 

DHS 2012 did not have a third assay. A1/A2=Agreement between EIA 1 and EIA 2 before and after repeat testing respectively; A=Agreemen

IQC=Proportion of negative samples on EIA1 selected for internal quality control. Negative and positive posterior distributions, from the continuo

on the top (EIA1) and right side (EIA2) of the graph (grey areas), where the point corresponds to the mean of the distribution, and the thick and t

the highest posterior density of the distributions. 
28

Figure 7C. Distribution of log transformed signal-to-cutoff ratio from samples tested on both enzyme immunoassays with 

Final HIV status is represented as the shape and color of each plot point. Samples tested on Western Blot or line immunoassays in the app

A1/A2=Agreement between EIA 1 and EIA 2 before and after repeat testing respectively; A=Agreement for surveys without repeat testing; IQC

EIA1 selected for internal quality control. Negative and positive posterior distributions, from the continuous latent class model, are indicated on th

the graph (grey areas), where the point corresponds to the mean of the distribution, and the thick and thin lines represent 50% and 95% of 

distributions. 
29

Figure 7D. Distribution of log transformed signal-to-cutoff ratio from samples tested on both enzyme immunoassays with 

Final HIV status is represented as the shape and color of each plot point. Samples tested on Western Blot or line immunoassays in the app

Dominican Republic DHS 2013 did not perform any Western blots for discrepant results after repeat testing. Uganda DHS 2011 did not have inte

third EIA instead of a Western blot. A1/A2=Agreement between EIA 1 and EIA 2 before and after repeat testing respectively; A=Agreement 

IQC=Proportion of negative samples on EIA1 selected for internal quality control. Negative and positive posterior distributions, from the continuo

on the top (EIA1) and right side (EIA2) of the graph (grey areas), where the point corresponds to the mean of the distribution, and the thick and t

the highest posterior density of the distributions.

Latin America
30

Prevalence estimates from the latent class models 

Surveys with optimal assay concordance 

For the category of surveys with optimal agreement between assays and clear clustering of non-reactive 

and strongly reactive samples, our Bayesian latent class adjustments – either using the dichotomous or the 

continuous model – did not have much effect on the prevalence estimates and all uncertainty intervals were 

overlapping (Figures 8A and 8B). For example, Côte d’Ivoire had an observed HIV prevalence of 3.7% 

(95% CI: 3.3-4.1%), an adjusted prevalence from the dichotomous model of 3.8% (95% CrI: 3.4-4.2%), 

and an adjusted prevalence from the continuous model of 3.7% (95% CrI: 3.3-4.1%) (Table 7). 

In Tanzania, agreement between the two EIA was 99.7% after repeat testing (92.1% before repeat testing). 

There were a few weakly reactive samples on both EIA, however. The unadjusted and dichotomous model 

adjustments resulted in the same prevalence of 4.6%. This was expected because the dichotomous model 

does not qualitatively differentiate between weakly reactive and strongly reactive samples. The continuous 

model, however, gave a higher likelihood of being truly negative to those few weakly reactive samples, and 

resulted in a slightly lower HIV prevalence of 4.5%. Because the great majority of samples were strongly 

reactive on both EIA, however, the adjustment with the continuous model had little effect on the HIV 

prevalence estimate and all uncertainty intervals overlapped. 

Surveys with sub-optimal assay concordance 

For the surveys where agreement between the assays was suboptimal and/or there was no clear clustering 

of non-reactive and reactive samples, the effects of the model adjustments on the HIV prevalence estimates 

are case-specific. 

In Burundi, the HIV prevalence estimate from the dichotomous model was similar to the unadjusted 

prevalence (1.9%). The continuous model, however, suggested that prevalence could be 0.1% point higher 

than the unadjusted estimate at 2.0% - but with a wide overlapping uncertainty interval. This small 

difference could result from the high number of samples that were positive on the first EIA and negative 

on the second EIA that were ultimately reactive according to the confirmatory line immunoassay. 

In Niger, where all prevalence estimates overlap, the dichotomous model provides a slightly lower 

prevalence estimate (0.4%; 95% CrI: 0.3-0.5%) than the unadjusted estimates (0.5%; 95% CI: 0.4-0.7%). 

This resulted mainly from the combination of a low HIV prevalence and the relatively low estimated median 

posterior specificity for the first EIA in this country (99.3%; 95% CrI: 97.9-99.9%). The latter could have 

generated a high number of false positives. On the other hand, the results from the continuous model suggest 

that HIV prevalence could be 0.6% (95% CrI: 0.4-0.6%). In this case, prevalence is slightly higher because 

a high proportion of samples that were resolved with the line immunoassay are non-reactive or weakly 

reactive on the second EIA. As such, the continuous model gives a relatively high likelihood of being a true 

positive to samples that are close to the cutoff. For both dichotomous and continuous models, the low 

number of reactive samples makes it difficult to clearly estimate the distribution of true positives. In this 

context, our modeling assumptions will have more impact on HIV prevalence estimates. 

In Cameroon and Gabon, both the dichotomous model and adjusted estimates, along with their 

confidence/credible intervals, were the same with an HIV prevalence of 4.6% (95% CrI: 4.2-4.9%) in 

Cameroon and 4.4% in Gabon (95% CrI: 4.0-4.8%). The estimates from the continuous model were slightly 

lower for both countries, however. In Cameroon and Gabon, the adjusted HIV prevalence estimates from 

the continuous model were 4.4% (95% CrI: 4.0-4.7%) and 4.2% (95% CrI: 3.8-4.6%), respectively. In both 

cases, the relatively high number of samples that were weakly reactive were given a higher likelihood of 

being true negatives than true positives. 
31

In Haiti, the result from the dichotomous latent class model was the same as the unadjusted prevalence 

(2.3%; 95% CI: 2.1-2.5%), whereas the prevalence estimate from the continuous latent class model was 

slightly lower at 2.2% (95% CrI: 2.0-2.5%). Although this survey had censored OD values, the posterior 

variance of the true positive was rather small, which explained the slightly lower prevalence estimate. Our 

prevalence estimates for the Namibia DHS survey, which also had censored OD values, were relatively 

consistent between models: the unadjusted prevalence was 13.9% (95% CI: 13.2-14.7%), the prevalence 

from the dichotomous latent class model was 14.1% (95% CrI: 13.4-14.9%), while the prevalence from the 

continuous latent class model was 14.0% (95% CrI: 13.3-14.7%), with all uncertainty intervals overlapping. 

In Sierra Leone, prevalence from the continuous latent class model suggested an estimate close to three 

times higher than the unadjusted and dichotomous latent class model. This is the consequence of the low 

posterior median of the distribution of true positives on the first EIA, which is very close to the cutoff. This 

low median resulted from the high proportion of samples initially negative on the first EIA that became 

positive on the second EIA. This result should be interpreted with caution because such a low median for 

the distribution of true positive on the first EIA could be considered unrealistic. More informative priors 

for the parameters governing the distribution of true positive could have resulted in lower prevalence. 
32

Figure 8A. Unadjusted and adjusted HIV prevalence estimates from Bayesian latent class models 

(high prevalence countries). 

Unadjusted HIV prevalence estimates in countries where prevalence is above 3% along with the Bayesian latent class 

adjusted HIV prevalence estimates for the dichotomous and continuous models. Error bars correspond to the 95% 

confidence/credible intervals. (Note that estimates do not consider surveys weights and survey design.) 

Figure 8B. Unadjusted and adjusted HIV prevalence estimates from Bayesian latent class models 

(low prevalence countries).

Unadjusted HIV prevalence estimates in countries where prevalence is below 3% along with the Bayesian latent class 

adjusted prevalence estimates for the dichotomous and continuous models. Error bars correspond to the 95% 

confidence/credible intervals. (Note that estimates do not consider surveys weights and survey design.) 
33

Table 7. Unadjusted versus adjusted HIV prevalence estimates (unweighted)

The unadjusted and adjusted HIV prevalence estimates among men and women for the 23 surveys (age ≥15 years, upper 

age limit varies by survey). Adjusted prevalence estimates are provided for both the dichotomous and continuous latent 

class models.

Unweighted HIV prevalence among men and women age ≥15 years 

(upper age limit varies by survey)

Survey

Unadjusted 

(95% CI)

Adjusted – Dichotomous 

test 

(95% CrI)

Adjusted- Continuous 

test 

(95% CrI)

Sub Saharan Africa

Burundi DHS 2010 1.9% (1.6-2.2%) 1.9% (1.6-2.2%) 2.0% (1.7-2.3%)

Cameroon DHS 2011 4.6% (4.2-4.9%) 4.6% (4.2-4.9%) 4.4% (4.0-4.7%)

Chad DHS 2014-15 1.5% (1.3-1.8%) 1.6% (1.3-1.8%) 1.5% (1.3-1.8%)

Côte d’Ivoire DHS 2011-12 3.7% (3.3-4.1%) 3.8% (3.4-4.2%) 3.7% (3.3-4.1%)

DRC DHS 2013-14* 1.0% (0.9-1.2%) 1.0% (0.9-1.2%) 1.0% (0.9-1.2%)

Gabon DHS 2012 4.4% (4.0-4.8%) 4.4% (4.0-4.8%) 4.2% (3.8-4.6%)

Gambia DHS 2013 1.8% (1.5-2.1%) 1.8% (1.5-2.1%) 1.7% (1.4-2.0%)

Ghana DHS 2014* 1.9% (1.6-2.2%) 1.9% (1.6-2.2%) 1.8% (1.6-2.2%)

Guinea DHS 2012* 2.0% (1.7-2.3%) 2.0% (1.7-2.3%) 1.9% (1.6-2.2%)

Malawi DHS 2010* 10.2% (9.7-10.7%) 10.3% (9.7-10.8%) 10.3% (9.8-10.8%)

Mali DHS 2012-13 1.1% (0.9-1.3%) 1.1% (0.9-1.3%) 1.1% (0.9-1.3%)

Namibia DHS 2013* 13.9% (13.2-14.7%) 14.1% (13.4-14.9%) 14.0% (13.3-14.7%)

Niger DHS 2012 0.5% (0.4-0.7%) 0.4% (0.3-0.5%) 0.6% (0.4-0.8%)

Rwanda DHS 2010* 3.2% (2.9-3.5%) 3.2% (2.9-3.5%) 3.1% (2.8-3.4%)

Rwanda DHS 2014-15* 3.2% (2.9-3.5%) 3.2% (2.9-3.5%) 3.2% (2.9-3.5%)

Senegal DHS 2010-11 0.9% (0.8-1.1%) 1.0% (0.8-1.2%) 0.9% (0.8-1.1%)

Sierra Leone DHS 2013 1.5% (1.3-1.7%) 1.5% (1.3-1.7%) 4.6% (4.0-5.1%)❖

Tanzania AIS/MIS 2011-12 4.6% (4.3-4.9%) 4.6% (4.3-4.9%) 4.5% (4.2-4.8%)

Togo DHS 2013-14 2.2% (1.9-2.5%) 2.2% (1.9-2.5%) 2.1% (1.8-2.4%)

Uganda AIS 2011 7.0% (6.7-7.3%) 6.8% (6.4-7.3%)

5.7% (4.7-6.5%)✩

7.1% (6.8-7.5%)

Zambia DHS 2013-2014* 13.4% (13.1-13.8%) 13.5% (13.1-13.9%) 12.2% (11.8-12.6%)

Latin America/Caribbean

Dominican Republic DHS 2013* 1.0% (0.9-1.2%) 1.0% (0.9-1.2%) 1.0% (0.9-1.2%)

Haiti DHS 2012* 2.3% (2.1-2.5%) 2.3% (2.1-2.5%) 2.2% (2.0-2.5%)

*Surveys with censored optical density values

✩Using different priors, accounting for the potentially lower sensitivities and specificities of the three enzyme immunoassays 

used in the Uganda AIS 2013

❖Interpret this value with caution as the high number of samples tested as part of internal quality control that were found 

positive on the second enzyme immunoassay influences the distribution of true positive. Refer to the relevant results section

for further details.
34

Surveys with no clear clustering of reactive EIA: Uganda and Zambia 

The Uganda AIS 2011 survey only had 51.8% of initially reactive samples were reactive on the second EIA 

and did not include IQC. Furthermore, the third tie-breaker assay was also an EIA, which could have had a 

higher false positivity rate than if the third assay had been a Western Blot or line immunoassay. 

Using the dichotomous model, we obtain an HIV prevalence estimate of 6.8% (95% CrI: 6.4-7.3%) in 

Uganda, slightly lower than the unadjusted estimate of 7.0% (95% CI: 6.7-7.3%) but with overlapping 

uncertainty intervals. Similarly, the continuous model estimated HIV prevalence at 7.1% (95% CrI: 6.8-

7.5%). It is possible to validate these estimates by comparing them to prevalence estimates obtained with 

an algorithm of three rapid diagnostic tests (RDT) that were performed during field visits for that survey 

(Ministry of Health/Uganda and ICF International 2012). According to the RDT algorithm, the unweighted 

HIV prevalence in the Uganda AIS 2011 was 6.0% (95% CI: 5.7-6.3%). Using the Type 1 dichotomous 

latent class model presented in the methods section, we adjusted results from the RDT algorithm with 

estimates of sensitivity and specificity reported in the literature (not shown). The adjusted HIV prevalence 

estimates with the RDT algorithm were estimated at 5.7% (95% CrI: 5.4-6.1%). Comparing both EIA-based 

and RDT algorithms, we notice that the concordance of samples positive on the first EIA with the results 

from the RDT algorithm is rather poor (Figure 9). If the RDT algorithm is believed to be more accurate, 

this could suggest that the prevalence estimate that rely on the EIA-based algorithm could be overestimated 

in the Uganda AIS 2011. 

It is possible to adjust, using the dichotomous model, the EIA-based algorithm to reproduce the 5.7% 

prevalence from the adjusted RDT algorithm. To do this, we need to provide priors with lower sensitivity 

and specificity for all three EIA. Specifically, if we assume that the 95% confidence intervals for the prior 

sensitivity is 90.0-99.0% (instead of 98.0-99.9%) and prior specificity is 85.0-95.0% (instead of 85.0-

99.0%) for the three EIA, we obtain an adjusted prevalence estimate of 5.7% (95% CrI: 4.7-6.5%). This 

highlights the impact of our prior distributions for sensitivity and specificity on the adjusted prevalence 

estimates. This is especially true for the Uganda survey because of the absence of IQC. This means that the 

prior for the sensitivity of the first EIA will influence the prevalence estimates since there is no re-testing 

of potentially false negative samples. The lack of IQC also limited inferences from the continuous Bayesian 

latent class model and the true positive distribution of the second EIA was wide. The resulting posterior 

distribution of true positives on the third EIA was also very wide, with a median very close to the cutoff. 

This, in turn, increased prevalence estimates. Along with Sierra Leone, more informative priors on the 

distribution of true positives for Uganda could affect HIV prevalence estimates from this model. 

To obtain a better sense of how HIV prevalence estimates from the EIA-based algorithm (unadjusted), 

RDT-based algorithm (unadjusted), and continuous Bayesian latent class adjustments compare in Uganda, 

we examine the sex-specific age trends (Figure 10). For both men and women, the RDT-based algorithm 

consistently yielded lower prevalence estimates across all age groups. The RDT-based algorithm yielded 

prevalence estimates that drop precipitously with age, with large drops between age 50-54 and 55-59 of 2.9 

percentage points for men and by 4.1 percentage points for women, as compared to the unadjusted EIAbased algorithm. Differences between the EIA-based algorithm and the Bayesian adjustments were small 

for most age groups. The largest differences are observed for men in the 45-49 and 50-54 age groups, where 

the Bayesian adjustments were closer to the RDT-based algorithm. The relatively high HIV prevalence 

among young men with the EIA-based algorithm suggests that prevalence from the RDT-based algorithm 

is probably closer to the true HIV prevalence. 

In contrast, the Zambia DHS 2013-14 survey included IQC and the concordance between assays was higher 

than in Uganda. In Zambia, however, HIV prevalence estimates could be affected by the very high 

proportion of weakly reactive samples on both EIA. Because the dichotomous model does not make any 

qualitative difference between weakly and strongly reactive specimens in its adjustment, the resulting 
35

adjusted HIV prevalence estimates are not very different from the unadjusted ones. However, the adjusted 

prevalence estimate for the continuous model is lower at 12.2% (95% CrI: 11.8-12.6%), with a partly 

overlapping uncertainty interval. Here again, it is also possible to cross-validate these estimates with those 

of an independent confirmatory testing of some samples in Zambia. Recently, samples for the Zambia DHS 

2013-14 survey that were classified as positives in the original testing algorithm - and which had one or 

two negatives RDT, or no RDT results at all - were independently re-tested with a line immunoassay (InnoLia HIV I/II). The samples that were positive on the original EIA-based algorithm and had positive results 

from the two RDT conducted in the household were considered positives without further testing with the 

line immunoassay. With this new algorithm, HIV prevalence decreased to 11.3% (95% CI: 10.5-11.9%) 

(unpublished data), which is lower than our adjusted estimates from the continuous model. There were, 

however, 632 samples with inconclusive test results on the confirmatory testing algorithm, meaning they 

were positive on the two EIA and negative or indeterminate on the line immunoassay. For the purpose of 

HIV prevalence estimation, these are considered negatives, although a proportion of them could be true 

positives. 

A visual comparison of the confirmatory testing and the EIA-based results suggests that most weakly 

reactive samples on both EIA could be false positives (Figure 11). In fact, 97% (194/201) of samples that 

were weakly reactive on the first EIA – defined as having a S/CO value between 1 and 3 - and positive on 

the second EIA were found to be inconclusive according to the confirmatory testing algorithm including 

the line immunoassay. For samples that were positive on the first EIA and weakly reactive on the second 

EIA, 81% (311/385) were inconclusive in confirmatory testing. Notably, some samples that were highly 

reactive on both EIA were inconclusive in confirmatory testing. Overall, these observations suggest that 

unadjusted HIV prevalence estimates from the EIA-based algorithm could overestimate prevalence. 

A further examination of the differences in estimates of HIV prevalence by age and sex in Zambia suggests 

that overestimation of prevalence in the EIA-based algorithm could be higher among men than for women 

(Figure 12). For women, the age trend in prevalence from the three types of prevalence estimates is 

relatively consistent. We note, however, that adjusted HIV prevalence estimates from the continuous 

Bayesian latent class model are generally slightly closer to the confirmatory testing results for younger 

females. For men, important differences are observed between the EIA-based algorithm and the 

confirmatory testing. The prevalence estimates from the adjusted continuous Bayesian latent class model 

are also much closer to those from the confirmatory testing than the EIA-based algorithm, especially for 

younger males (age 15-24). This could have resulted from a higher proportion (15%) of weakly reactive 

samples on both the first and second EIA of the EIA-based algorithm among young men. In contrast, only 

5% of young women were weakly reactive on both the first and second EIA of the algorithm. 
36

Figure 9. Comparison of the enzyme immunoassay-based and rapid test algorithms in the Uganda 

AIDS Indicator Survey (2011). 

The HIV test results from the enzyme-immunoassay-based (EIA) and rapid diagnostic test-based (RDT) algorithm for 

sample in the 2011 Uganda AIS. Each possible final classification on both algorithms has its own symbol and color, 

where concordance between the two can be seen by the overlaying colors of the plot points. 
37

Figure 10. HIV prevalence from the Uganda AIDS Indicator Survey (2011) according to different 

testing strategies and adjustment procedures, stratified by age and sex. 

Three different testing models are represented in the above graphs: EIA-based testing (unadjusted), rapid diagnostic 

test (unadjusted) and adjusted estimates from the continuous Bayesian latent class model. Data are stratified by sex 

and age. 
38

Figure 11. Comparison of the enzyme immunoassay-based algorithm with results from 

confirmatory re-testing in the Zambia Demographic and Health Survey (2013-14). 

Graph displaying the HIV status classification for both the enzyme immunoassay-based (EIA) algorithm and 

confirmatory testing (CT) algorithm (using Inno-Lia HIV I/II). Specimens with positive results on the EIA and the RDT 

tests were considered confirmed positive and negative results on the EIA were considered confirmed negative with no 

further confirmatory testing with Inno-Lia. Samples were tested on the confirmatory testing algorithm if they were 

classified as HIV positive in the original laboratory testing algorithm (all samples in the upper right quadrant) and had 

one or two negative RDT, or no RDT results at all. For a sample to be considered positive on confirmatory testing, all 

3 assays must be positive (green stars). If the first and second EIA were positive but the third assay was negative, the 

sample was classified as inconclusive (orange triangles). If the first and second EIA had discordant results, the final 

HIV status could be either inconclusive (if the confirmatory assay was positive, orange stars), negative (if the 

confirmatory assay was negative, purple diamonds) or indeterminate (if the confirmatory assay was indeterminate, but 

no samples were found to be indeterminate). Eight samples were excluded from the confirmatory testing algorithm due 

to insufficient blood from the original survey DBS collection (not shown on graph). 
39

Figure 12. HIV prevalence from the Zambia Demographic and Health Survey (2013-14) according to 

different testing strategies and adjustment procedures, stratified by age and sex. 

Three different testing models are represented in the above graphs: EIA-based testing (unadjusted), confirmatory 

testing (CT) (unadjusted), and the adjusted estimates from the continuous Bayesian latent class model. Data are 

stratified by sex and age. 

41

4. Discussion 

Using the Bayesian latent class models, we attempted to re-estimate results from the HIV seroprevalence 

surveys conducted by The DHS Program during 2010-2014. These adjustments account for the potential 

misclassification of HIV status that resulted from using a single cutoff value to qualitatively describe results 

as positive or negative. These analyses, along with visual inspection of the clustering of reactive and nonreactive samples, suggest that the misclassification of HIV status from the use of imperfect assays should 

not have a major influence on HIV prevalence estimates for most surveys. The observed differences 

between the adjusted and unadjusted results were often small and should be considered along with other 

potential biases such as random errors and/or selective non-response. Our analyses suggest, however, that 

EIA-based laboratory results from two surveys appear problematic: Uganda AIS 2011 and Zambia DHS 

2013-14. 

In the case of Uganda, we can triangulate our adjusted estimates with those from a RDT-based algorithm 

that was performed concomitantly with field data collection. Results from this RDT algorithm suggest that 

HIV prevalence could be 1% point lower (6.0% vs. 7.0%) than the EIA-based algorithm. Considering that 

errors in administering and interpreting results from RDT are probably less likely to occur than for the EIAbased algorithm (but not impossible), and that this latter algorithm resulted in low agreement between the 

first and second EIA, results from the EIA-based algorithm probably overestimate HIV prevalence. Because 

Uganda did not include IQC, our Bayesian latent class adjustments could be less precise than for other 

surveys and are more likely to be affected by our elicited prior distributions. 

In Zambia, the high proportion of weakly reactive samples and the poor agreement between EIA raised 

concerns about potential overestimation of HIV prevalence. As expected, the dichotomous latent class 

model that does not consider the strength of the reaction did not produce a prevalence estimate that differed 

notably from the original unadjusted estimates. In this case, the continuous latent class model is more 

appropriate and yielded an HIV prevalence estimate of 12.2%, which was in between the unweighted 

estimates from the EIA-based algorithm (13.4%) and the confirmatory testing algorithm (11.3%). In this 

survey, the proportion of weakly reactive samples was highest among young males (age 15-24) and the 

EIA-based results could overestimate prevalence, especially within this group. 

Limitations 

Results from the dichotomous model are strongly influenced by the informative priors used for sensitivity 

and specificity. These priors reflect the high reported sensitivity and specificity of EIA, Western Blot, and 

line immunoassay when performed under good laboratory conditions. As exhibited by our comparisons 

between the EIA-based and rapid test algorithms in Uganda, the sensitivity and specificity of EIA can be 

much lower in practice. It is thus possible that the priors used for the dichotomous latent class models do 

not reflect the actual sensitivity and specificity of the EIA, as they were performed. If more realistic priors 

were used, the estimated prevalence might be quite different. Further work can study real-world conditions 

for the use of these assays to derive the best possible priors for the properties of the tests, which in turn 

should lead to more accurate estimates of the prevalence from these models. 

The main assumption underlying the continuous latent class model is that the log(S/CO) values of the 

different EIA are normally distributed. In practice, however, this assumption could have been violated. For 

example, suboptimal laboratory practices (incorrect microplate washing, pipetting techniques, etc.) and 

performance of the assays (not validated for use on DBS) could have led to the misclassification of true 

negative samples as weakly reactive (i.e., false positive results). This would result in a skewed, non-normal 

distribution. We attempted to take this into account by imposing a minimum SD for the distribution of true 

negatives. This minimum SD would render the tails of the distribution “thicker”. It is nevertheless possible 
42

that the true distribution of the log(S/CO) values within positive and negative populations is not normal. 

This is probably true for the Sierra Leone and Uganda surveys, where non-reactive and reactive samples do 

not seem to cluster and follow a multivariate normal distribution. In such cases, the results from this 

continuous Bayesian latent class model could be improved by using non-parametric models, but these have 

not yet been developed. 

A further limitation needs to be acknowledged for surveys with censored OD values. For these surveys, the 

continuous latent class model imputes non-censored log(S/CO) values for each censored observation, and 

the resulting mean then depends on the allowed upper limit for the test values on the log scale. We attempted 

to mitigate this issue by imposing a reasonable maximum value for the mean and SD based on past 

information from these tests. The resulting posterior distribution of the true positives is affected by these 

priors which, although reasonable, influence HIV prevalence estimates. 
43

5. Conclusions

Our examination of the impact of misclassification of HIV status on prevalence estimates has implications 

for population-based HIV surveillance. Importantly, it appears that for most surveys, the impact of 

misclassification due to testing errors is relatively minor compared to other potential sources of bias and 

uncertainty. We also found that the agreement between the first and second EIA is a relatively good 

indicator of the quality of laboratory testing, although it is not sufficient to rule out misclassification bias 

in HIV prevalence estimates. In addition, we suggest visual assessment of the clustering of non-reactive 

and reactive samples as a secondary measure of diagnostic accuracy. 

The original EIA-based results in most surveys are considered reasonably accurate if we assume good assay 

properties. Our analyses suggest that this is most likely the case for surveys with good agreement between 

EIA and clear clustering of non-reactive and strongly reactive samples. In contrast, the EIA-based results 

from the Uganda AIS 2011 and the Zambia DHS 2013-14 surveys could be problematic. In Uganda, the 

lack of IQC and probable violation of the multivariate normality assumptions limits our confidence in 

results from the continuous Bayesian latent class model. For this survey, the true unobserved HIV 

prevalence is probably closer to results from the RDT-based rather than the EIA-based algorithm, as 

suggested by our examination of HIV trends by age and sex. In the case of Zambia, the EIA-based algorithm 

produced a high number of weakly reactive samples that were found later to be negatives on the 

confirmatory re-testing of samples. In this case, we recommend that future studies use the prevalence results 

from the confirmatory testing with the line immunoassay, although this algorithm could underestimate 

prevalence if the inconclusive test results from the line immunoassays that are strongly reactive on both 

EIA are indeed true positives. 

In conclusion, our HIV prevalence estimates, adjusted for the imperfect sensitivity and specificity of the 

testing procedures using Bayesian latent class modeling, should be interpreted with caution because their 

underlying assumptions, including prior information crucial to some estimates, are difficult to verify in 

practice. Further knowledge about the test properties under real-world conditions will help to improve HIV 

prevalence estimates. 

45

References 

Abbott Laboratories. 2007. Murex HIV 1.2.O [Package insert]. United Kingdom: Abbott 

Laboratories. 

Aboud, S., W. Urassa, E. Lyamuya, F. Mhalu, and G. Biberfeld. 2006. "Evaluation of HIV Antibody and 

Antigen/Antibody Combination ELISAS for Use in an Alternative Confirmatory HIV Testing 

Strategy in Dar Es Salaam, Tanzania." J Virol Methods 135(2):192-6.

Beelaert, G., G. Vercauteren, K. Fransen, M. Mangelschots, M. De Rooy, S. Garcia-Ribas, and G. van der 

Groen. 2002. "Comparative Evaluation of Eight Commercial Enzyme Linked Immunosorbent 

Assays and 14 Simple Assays for Detection of Antibodies to HIV." J Virol Methods 105(2):197-

206.

Bio-Rad Laboratories. 2011. GS HIV Combo Ag/Ab EIA [Package insert]. Redmond, Washington, 

USA: Bio-Rad Laboratories. 

Carpenter, B., A. Gelman, M. Hoffman, D. Lee, B. Goodrich, M. Betancourt, M.A. Brubaker, J. Guo, P. 

Li, and A. Riddell. 2016. "Stan: A Probabilistic Programming Language." Journal of Statistical 

Software 20:1-37.

Centers for Disease Control and Prevention and Association of Public Health Laboratories (CDC and 

APHL). 2014. Laboratory Testing for the Diagnosis of HIV Infection: Updated 

Recommendations. CDC. Available at http://dx.doi.org/10.15620/cdc.23447.

Chacon, L., M. L. Mateos, and A. Holguin. 2017. "Relevance of Cutoff on a 4th Generation ELISA

Performance in the False Positive Rate During HIV Diagnostic in a Low HIV Prevalence 

Setting." J Clin Virol 92:11-13.

Constantine, N. 2006. HIV Antibody Assays. UCSF Center for HIV Information. Available at 

http://hivinsite.ucsf.edu/InSite?page=kb-02-02-01#.

Fanmi, A. N., C. Ramière, J. C. Tardy, and P. Andre. 2013. "Real-Life Evaluation of a Human 

Immunodeficiency Virus Screening Algorithm Using a Single Combined P24 Antigen-Antibody 

Assay." Eur J Clin Microbiol Infect Dis 32(3):425-30. 

Feng, C., H. Wang, N. Lu, T. Chen, H. He, Y. Lu, and X. M. Tu. 2014. "Log-Transformation and Its 

Implications for Data Analysis." Shanghai Arch Psychiatry 26(2):105-9.

Fishel, J.D., and D. Garrett. 2016. Performance of Enzyme Immunoassays for HIV Serology in Surveys 

Conducted by the Demographic and Health Surveys Program. DHS Comparative Reports No. 39.

Rockville, Maryland: ICF International. 

Francis, B. 2013. Evaluation of the Bio-Rad Genscreen HIV Ag-Ab Ultra. NRL. Available at 

http://nrl.gov.au/search/?value=genscreen&srcimg.x=0&srcimg.y=0. 

Gray, R. H., F. Makumbi, D. Serwadda, T. Lutalo, F. Nalugoda, P. Opendi, G. Kigozi, S. J. Reynolds, 

N.K. Sewankambo, and M. J. Wawer. 2007. "Limitations of Rapid HIV-1 Tests During Screening 
46

for Trials in Uganda: Diagnostic Test Accuracy Study." BMJ : British Medical Journal

335(7612):188-188.

Grüner, N., O. Stambouli, and R. S. Ross. 2015. "Dried Blood Spots - Preparing and Processing for Use 

in Immunoassays and in Molecular Techniques." J Vis Exp (97):52619. 

Hakim, I., H. K. Patel, Y. T. Duong, J. Katoro, W. Gregory, I. Farouk, A. Hakim, and B. Parekh. 2016. 

Evaluation of an EIA-Based Testing Algorithm in Antenatal Survey Using Dried Blood Spot 

Specimens from South Sudan. Poster presented at the Conference on Retroviruses and 

Opportunistic Infections (CROI). 

Hornik, K., F. Leisch, and A. Zeileis. 2003. JAGS: A Program for Analysis of Bayesian Graphical 

Models Using Gibbs Sampling. Paper in Proceedings of the Driving Simulation Conference 

(DSC), 2003. 

Johnson, C., V. Fonner, A. Sands, S. Tsui, N. Ford, V. Wong, C. Overmeyer, and R. Baggaley. 2015. 

"Annex 14: A Report on the Misdiagnosis of HIV Status.” In: Consolidated Guidelines on HIV 

Testing Services: 5Cs: Consent, Confidentiality, Counselling, Correct Results and Connection 

2015. Geneva: WHO. 

Joseph, L., T. W. Gyorkos, and L. Coupal. 1995. "Bayesian Estimation of Disease Prevalence and the 

Parameters of Diagnostic Tests in the Absence of a Gold Standard." Am J Epidemiol 141(3):263-

72.

Lemee, V., M. Leoz, M. Etienne, F. De Oliveira, and J.C. Plantier. 2014. "Performance of the Liaison XL 

Murex HIV Ab/Ag Test on Clinical Samples Representing Current Epidemic HIV Variants." J 

Clin Microbiol 52(9):3277-9.

Lunn, D. J., A. Thomas, N. Best, and D. Spiegelhalter. 2000. "WinBUGS-a Bayesian Modelling 

Framework: Concepts, Structure, and Extensibility." Statistics and Computing 10(4):325-337. 

MEASURE DHS. 2012. MEASURE DHS Biomarker Field Manual. ICF International. Calverton, 

Maryland, U.S.A.: ICF International. 

Ministry of Health/Uganda and ICF International. 2012. Uganda AIDS Indicator Survey (UAIS) 2011. 

Calverton, Maryland, USA: Ministry of Health/Uganda and ICF International. Available at 

http://dhsprogram.com/pubs/pdf/AIS10/AIS10.pdf. 

MP Diagnostics. 2003. HIV Blot 2.2. Western Blot Assay [Package Insert]. Geneva: MP Diagnostics. 

Nimble - An R Package for Programming with BUGS Models Version 0.6-6. 2017. 

Nkengasong, J. N., C. Maurice, S. Koblavi, M. Kalou, D. Yavo, M. Maran, C. Bile, K. N'Guessan, J. 

Kouadio, S. Bony, S. Z. Wiktor, and A. E. Greenberg. 1999. "Evaluation of HIV Serial and 

Parallel Serologic Testing Algorithms in Abidjan, Cote d'Ivoire." AIDS 13(1):109-17.

Parekh, B.S., and J. S. McDougal. 2005. "Application of Laboratory Methods for Estimation of HIV-1 

Incidence." Indian J Med Res 121(4):510-8. 

Peeling, R. W., H. Artsob, J. L. Pelegrino, P. Buchy, M. J. Cardosa, S. Devi, D. A. Enria, J. Farrar, D.J. 

Gubler, M. G. Guzman, S. B. Halstead, E. Hunsperger, S. Kliks, H. S. Margolis, C. M. 
47

Nathanson, V. C. Nguyen, N. Rizzo, S. Vazquez, and S. Yoksan. 2010. "Evaluation of Diagnostic 

Tests: Dengue." Nat Rev Microbiol 8(12 Suppl):S30-8.

Piwowar-Manning, E., J. M. Fogel, P. Richardson, S. Wolf, W. Clarke, M. A. Marzinke, A. Fiamma, D. 

Donnell, M. Kulich, J. K. Mbwambo, L. Richter, G. Gray, M. Sweat, T.J. Coates, and S. H. 

Eshleman. 2015. "Performance of the Fourth-Generation Bio-Rad GS HIV Combo Ag/Ab 

Enzyme Immunoassay for Diagnosis of HIV Infection in Southern Africa." J Clin Virol 62:75-9.

Plummer, M. 2013. "rjags: Bayesian Graphical Models Using MCMC." R package version 3.

Qiu, X., S. Hodges, T. Lukaszewska, S. Hino, H. Arai, J. Yamaguchi, P. Swanson, G. Schochetman, and 

S. G. Devare. 2008. "Evaluation of a New, Fully Automated Immunoassay for Detection of 

HTLV-I and HTLV-II Antibodies." J Med Virol 80(3):484-93. 

Sacks, R., A. Omodele-Lucien, N. Whitbread, D. Muir, and A. Smith. 2012. "Rapid HIV Testing Using 

Determine HIV 1/2 Antibody Tests: Is There a Difference between the Visual Appearance of 

True- and False-Positive Tests?" Int J STD AIDS 23(9):644-6.

Truant, A. L. 2016. Manual of Commercial Methods in Clinical Microbiology, International Edition. 

John Wiley & Sons. 

UNAIDS/WHO Working Group on Global HIV/AIDS and STI Surveillance. 2005. Guidelines for 

Measuring National HIV Prevalence in Population-Based Surveys. Geneva: UNAIDS and WHO. 

UNAIDS/WHO Working Group on Global HIV/AIDS and STI Surveillance. 2015. Monitoring the 

Impact of the HIV Epidemic Using Population-based Surveys. Geneva: UNAIDS and WHO. 

Urassa, W., K. Godoy, J. Killewo, G. Kwesigabo, A. Mbakileki, F. Mhalu, and G. Biberfeld. 1999. "The 

Accuracy of an Alternative Confirmatory Strategy for Detection of Antibodies to HIV-1: 

Experience from a Regional Laboratory in Kagera, Tanzania." J Clin Virol 14(1):25-9.

Urio, L. J., M. A. Mohamed, J. Mghamba, A. Abade, and S. Aboud. 2015. "Evaluation of HIV

Antigen/Antibody Combination ELISAs for Diagnosis of HIV Infection in Dar Es Salaam, 

Tanzania." Pan Afr Med J 20:196. 

Wang, Z., N. Dendukuri, and L. Joseph. 2017. "Understanding the Effects of Conditional Dependence in 

Research Studies Involving Imperfect Diagnostic Tests." Stat Med 36(3):466-480. 

Weber, B., L. Gurtler, R. Thorstensson, U. Michl, A. Muhlbacher, P. Burgisser, R. Villaescusa, A. Eiras, 

C. Gabriel, H. Stekel, S. Tanprasert, S. Oota, M. J. Silvestre, C. Marques, M. Ladeira, H. 

Rabenau, A. Berger, U. Schmitt, and W. Melchior. 2002. "Multicenter Evaluation of a New 

Automated Fourth-Generation Human Immunodeficiency Virus Screening Assay with a Sensitive 

Antigen Detection Module and High Specificity." J Clin Microbiol 40(6):1938-46. 

World Health Organization (WHO). 1998. Operational Characteristics of Commercially Available 

Assays to Determine Antibodies to HIV-1 and/or HIV-2 in Human Sera. Geneva: WHO. 

World Health Organization (WHO). 1999. Operational Characteristics of Commercially Available 

Assays to Determine Antibodies to HIV-1 and/or HIV-2 in Human Sera. Geneva: WHO. 
48

World Health Organization (WHO). 2004. HIV Assays: Operational Characteristics (Phase 1). Geneva: 

WHO. 

World Health Organization (WHO). 2013. WHO Prequalification of Diagnostics Programme. Product: 

Genscreen Ultra HIV Ag-Ab. Geneva: WHO. 

World Health Organization (WHO). 2015a. Consolidated Guidelines on HIV Testing Services. Geneva: 

WHO. 

World Health Organization (WHO). 2015b. HIV Assays. Laboratory Performance and Other Operational 

Characteristics. Rapid Diagnostic Tests (Combined Detection of HIV-1/2 Antibodies and 

Discriminatory Detection of HIV-1 and HIV-2 Antibodies). Geneva: WHO. 

World Health Organization (WHO). 2015c. WHO Prequalification of in Vitro Diagnostics Programme. 

Product: Murex HIV Ag/Ab Combination. Geneva: WHO. 

World Health Organization (WHO). 2016. WHO Prequalification of in Vitro Diagnostics Programme - 

Public Report for MP Diagnostics HIV Blot 2.2. Geneva: WHO. 

Zeh, C., B. Oyaro, H. Vandenhoudt, P. Amornkul, A. Kasembeli, P. Bondo, D. Mwaengo, T. K. Thomas, 

C. Hart, K. F. Laserson, P. Ondoa, and J.N. Nkengasong. 2011. "Performance of Six Commercial 

Enzyme Immunoassays and Two Alternative HIV-Testing Algorithms for the Diagnosis of HIV-1 

Infection in Kisumu, Western Kenya." J Virol Methods 176(1-2):24-31.

Zhang, R., Y. Sun, L. Wang, K. Zhang, J. Xie, and J. Li. 2013. "Blood Screening for Human 

Immunodeficiency Virus: A New Algorithm to Reduce the False-Positive Results." Transfus Med

23(4):260-4.
49

Appendix 

Table S1. Target detection of the nine EIAs used in The DHS Program surveys (2010-2014)

The name, manufacturer, generation and format of the HIV screening enzyme immunoassays (EIA) used in the DHS 

reports. The solid phase antibodies and antigens coat the bottom of the microplate wells. The conjugate contains 

the substrate which allows for the detection of HIV antibodies or antigens in human sera or plasma. 

Solid Phase Conjugate

Assay Name 

(manufacturer) Generation

EIA 

format

Antibody 

detection

Antigen 

detection

Antibody 

detection

Antigen 

detection

Enzygnost Integral 

II (Siemens)

4 Sandwich R+S mixture: 

HIV-1 gp41, 

HIV-1 (subtype 

O) gp41, HIV-2 

gp36

Anti p24 

Mab

Biotin 

conjugated 

solid phase 

peptides

Biotinconjugated 

anti-p24 Mab

Enzygnost AntiHIV 1/2 Plus 

(Siemens)

3 Sandwich HIV-1 gp41 (R)

HIV-1 (subtype 

O) gp41 (R)

HIV-2 gp36 (R)

- (R) + (S) 

mixture of 

solid phase 

peptides

-

Genscreen Plus 

HIV Ag/Ab 5PL 

(Bio-Rad)

4 Sandwich HIV-1 gp160 (R)

HIV-1 (subtype 

O) gp41 (S)

HIV-2 gp36 (S)

Anti p24 

Mab

HIV-1 gp41 

(R)

HIV-1 

(subtype O) 

gp41 (S)

HIV-2 gp36 

(R)

Biotinconjugated 

polyclonal 

anti-p24

Genscreen ULTRA 

HIV Ag/Ab (BioRad)

4 Sandwich HIV-1 gp160 (R)

HIV-1 (subtype 

O) gp41 (S)

HIV-2 gp36 (S)

Anti p24 

Mab

HIV-1 gp41 

(R)

HIV-1 

(subtype O) 

gp41(S)

HIV-2 gp36 

(S)

Biotinconjugated 

polyclonal 

anti-p24

HIV EIA (Ani 

Labsystems)

3 Sandwich HIV-1 gp41 (S)

HIV-1 gp120 (S)

HIV-1 p24 (S)

HIV-2 gp36 (S)

- Same as solid 

phase

-

Murex HIV 1.2.0

(Abbott Labs)

3 Sandwich HIV-1 gp41 (R)

HIV-1 p24 (R)

HIV-1 (subtype 

O) gp41 (S)

HIV-2 gp36 (R)

- Same as solid 

phase

-

Murex HIV Ag/Ab 

(DiaSorin)

4 Sandwich HIV-1 gp41 (R)

HIV-1 

polymerase (R)

HIV-1 (subtype 

O) gp41 (R) HIV2 gp36 (R)

Anti p24 

Mab

Same as solid 

phase

HRP 

conjugated 

anti-p24 Mab

Vironostika HIV 

Ag/Ab 

(Biomérieux)

4 Sandwich HIV-1 gp160 (R)

HIV-1 p24 (R)

HIV-1 (subtype 

O) gp41 (S)

HIV-2 gp36 (S)

Anti-p24 

Mab

Same as solid 

phase

HRP 

conjugated 

anti-p24 Mab

Vironostika HIV 

Uni-Form 2 Plus O 

(Biomérieux)

3 Sandwich HIV-1 gp160 (R)

HIV-1 p24 (R)

HIV-1 (subtype 

O) gp41 (S)

HIV-2 gp36 (S)

- Same as solid 

phase

-

Mab: monoclonal antibody, (R): recombinant peptide, (S): synthetic peptide 
50

Table S2. Target detection of supplementary assays

The name, manufacturer, and type of each supplementary assay used in the DHS reports, with their respective antigen 

detection profile

Antibody detection in human sera or plasma

HIV-1 antigens HIV-2 antigens

Assay 

(manufacturer)

Assay 

type

gp

41

gp

120

gp

160 p17 p18 p24 p31 p39 p51 p55 p66

gp

36

gp

105

gp

125

gp

140 p16 p26 p34 p56 p68

Inno-Lia HIV I/II 

Line Score

(Innogenetics)

Line 

immunoassayX X X X X X X X

New Lav Blot 

(Bio-Rad)*

Western 

Blot X X X X X X X X X X X X X X X X X X

HIV Blot 2.2 

(DiaSorin)

Western Blot 

2.2 

(Abbott Labs)

Western 

Blot X X X X X X X X X X X

*The New Lav Blot assay uses two separate strips to detect both HIV types.
51

Text S1: Justification of prior distributions for the Bayesian latent 

class model’s parameters 

A) Priors for the continuous assays (EIA) 

Enzygnost Integral II (Siemens) 

The mean S/CO ratio of confirmed positive samples collected in Dar es Salaam (Tanzania) using Enzygnost 

Integral II was independently estimated at 13.7 (95% CI: 13.1-14.5) (Urio et al. 2015). Because this study 

was conducted in Tanzania and other countries could have different average values, the standard deviation 

of this parameter was chosen so that this mean has a 99% probability of being higher than a S/CO value of 

5 (threshold for highly reactive specimens). This translates in the following prior for the mean of the 

distribution of true positive (νt1):

νt1 ~ Normal (log(13.7), 0.4333)) 

For the standard deviation of the distribution of true positives (σt1), the following non-informative prior was 

chosen: 

σt1 >0 

For the distribution of true negatives, the mean S/CO value of confirmed HIV negatives was not available 

from the literature. To provide a prior for this assay, we examined the median S/CO values of the surveys 

with the two highest concordances between the first and second EIA: 0.25 in Côte d’Ivoire and 0.38 in 

Chad (for a log-average of 0.31). We estimated the SD of this parameter so that there is a 95% probability 

that the mean lies within the 0.25-0.38 range (the range of values given by the two surveys with highest 

concordance). Accordingly, we will provide the following prior for the mean of the distribution of true 

negatives (νt0):

νt0 ~ Normal(log(0.31), 0.1097) 

For the standard deviation of this distribution (σt0), we chose a minimum SD so that the probability that a 

true negative has a value greater than the cutoff is 5% (conditional on a mean S/CO of 0.31 for true 

negatives). This reflects the fact that most weakly reactive samples are probably due to lab errors and/or 

higher false positivity resulting from the use of DBS. 

σt0 ≥ 0.7120 (note this is the SD for the log-transformed S/CO) 

Enzygnost Anti-HIV 1/2 Plus (Siemens)

Two independent studies were conducted in Tanzania and reported average S/CO values of 7.5 (95 CI%: 

7.3-7.7) and 8.0 (95% CI: 7.8-8.2) for this test (Aboud et al. 2006; Urassa et al. 1999). Averaging this value 

(log-scale), we obtain 7.7. Because these two studies were conducted in Tanzania and other countries could 

have different average values, the standard deviation of this parameter was chosen so that this mean has a 

99% probability of being higher than a S/CO value of 5 (threshold for highly reactive specimens). This 

translates in the following prior for the mean of the distribution of true positive (νt1):

νt1 ~ Normal(log(7.7), 0.1856)) 
52

For the SD of the distribution of true positives (σt1), we chose a non-informative prior, such that: 

σt1 >0

For the distribution of true negatives, the mean S/CO value of confirmed HIV negatives was not available 

from the literature. To provide a prior for this assay, we examined the distributions of S/CO values of the 

survey with the highest concordance between the first and second EIA. This would correspond to Malawi 

which reached 99.0% concordance after repeated testing (including IQC). In this survey, the median S/CO 

values of negative sample were estimated at 0.23. It is difficult to estimate a prior for this estimate’s 

precision and we gave it a weakly informative prior. Specifically, the precision was chosen so that there is 

a 95% probability that the mean lies in the 0.10-0.53 interval. 

νt0 ~ Normal(log(0.23), 0.4250)) 

For the standard deviation of this distribution (σt0), we chose a minimum SD such that the probability that 

a true negative has a value greater than the cutoff is 5% (conditional on a mean S/CO of 0.23 for true 

negatives). This reflects the fact that most weakly reactive samples are probably due to lab errors and/or 

higher false positivity resulting from the use of DBS. 

σt0 ≥ 0.8935 (note this is the SD for the log-transformed S/CO) 

Genscreen Plus HIV Ag/Ab 5PL (Bio-Rad) 

There is no information available in the literature on the distribution of S/CO values for true positives and 

negatives for this assay. Only one survey used this test (Gabon) and agreement between the two EIA in this 

survey was suboptimal. The prior for the distribution of true positives was assumed to have a mean S/CO 

of 15 and the standard deviation chosen so that the parameter has a 99% probability of being higher than 5 

(threshold for highly reactive specimens). This translates in the following prior for the mean of the 

distribution of true positive (νt1):

νt1 ~ Normal(log(15), 0.4722)) 

For the SD of the distribution of true positives (σt1), we chose a non-informative prior, such that: 

σt1 >0

For the distribution of true negatives, the mean S/CO value of confirmed HIV negatives was not available 

from the literature. The prior for the mean (νt0) of this distribution was thus assumed to be 0.30, with a 95% 

probability of lying in the 0.15-0.60 interval. 

νt0 ~ Normal(log(0.30), 0.3537) 

For the standard deviation of this distribution (σt0), we chose a minimum SD such that the probability that 

a true negative has a value greater than the cutoff is 5% (conditional on a mean S/CO of 0.30 for true 

negatives). 

σt0 ≥ 0.7320 (note this is the SD for the log-transformed S/CO) 
53

Genscreen ULTRA HIV Ag/Ab (Bio-Rad) 

Only one survey (Cameroon) used this EIA and there are no data in the literature on the distribution of 

S/CO for confirmed positives and negatives. Hence, the same general priors used for Greenscreen Plus HIV 

Ag/Ab 5 PL are used. 

HIV EIA (Ani Labsystems) 

Only one survey (Uganda) used this EIA and there are no data in the literature on the distribution of S/CO 

for confirmed positives and negatives. The same general priors used for Greenscreen Plus HIV Ag/Ab 5 

PL and GreenScreen ULTRA HIV Ag/Ab are used. 

Murex HIV 1.2.0 (Abbott Labs) 

Only one survey (Uganda) used this EIA and there are no data in the literature on the distribution of S/CO 

for confirmed positives and negatives. The same general priors used for Greenscreen Plus HIV Ag/Ab 5 

PL, GreenScreen ULTRA HIV Ag/Ab, and HIV EIA are used. 

Murex HIV Ag/Ab combination (Diasorin)

The mean S/CO ratio of confirmed positives samples was estimated at 12.2 and 13.3 in two independent 

studies (Aboud et al. 2006; Urio et al. 2015). The mean for the distribution of true positives was chosen as 

the average (log scale) of these two studies. The standard deviation of this parameter was chosen so that 

this mean has a 99% probability of being higher than a S/CO value of 5 (threshold for highly reactive 

specimens). This translates in the following prior for the mean of the distribution of true positive (νt1):

νt1 ~ Normal(log(12.7), 0.4007)) 

For the SD of the distribution of true positives (σt1), we chose a non-informative prior, such that: 

σt1 >0 

For the distribution of true negatives, the mean S/CO value of confirmed HIV negatives was not available 

from the literature and the only survey that used this assay (Cameroon). In Cameroon, this first EIA did not 

have good concordance with the other assay. (Rwanda 2010 and Rwanda 2014-15 also used this test but as 

the second EIA.) As for previous assays, the prior for the mean of this distribution (νt0) was thus assumed 

to be 0.3 with a 95% probability of lying in the 0.15-0.60 interval. 

νt0 ~ Normal(log(0.30), 0.3537) 

For the standard deviation of this distribution (σt0), we chose a minimum SD such that the probability that 

a true negative has a value greater than the cutoff is 5% (conditional on a mean S/CO of 0.30 for true 

negatives). 

σt0 ≥ 0.7320 (note this is the SD for the log-transformed S/CO) 

Vironostika HIV Ag/Ab (Biomérieux) 

The mean S/CO ratio of confirmed positives samples was estimated at 15.5 and 15.8 in two independent 

studies (Aboud et al. 2006; Urio et al. 2015). Surveys with the highest concordance on the first and second 

EIA that used Vironostika HIV Ag/Ab as the first assay – and whose OD distributions were not censored – 

generally had higher median S/CO: 24.9 (Chad), 25.7 (Togo), and 29.8 (Tanzania). The prior for the mean 

of this value was chosen to correspond to the midpoint between the minimum (15.5) and maximum (29.8) 

of these values (the midpoint on the log scale of 21.5). The standard deviation of this parameter was chosen 
54

so that this mean has a 99% probability of being higher than a S/CO value of 5 (threshold for highly reactive 

specimens). This translates in the following prior for the mean of the distribution of true positive (νt1):

νt1 ~ Normal(log(21.5), 0.6270)) 

For the SD of the distribution of true positives (σt1), we chose a non-informative prior, such that: 

σt1 >0 

For the distribution of true negatives, we use the mean S/CO of the negatives samples of the Chad survey, 

which had the best concordance (99.8% concordant) between the two EIA. This mean was 0.33. Other 

surveys which use the same firs assay and that had good concordance (>98.5%) had similar means (Togo 

0.33, Dominican Republic 0.36, Tanzania 0.35, Rwanda 2010 0.40, Guinea 0.53, Ghana 0.31). It is difficult 

to estimate a prior for this estimate’s precision and we gave it a weakly informative prior with 95% 

probability of lying in the 0.15-0.54 interval. 

νt0 ~ Normal(log(0.33), 0.2555) 

For the standard deviation of this distribution (σt0), we chose a minimum SD such that the probability that 

a true negative has a value greater than the cutoff is 5% (conditional on a mean S/CO of 0.33 for true 

negatives). 

σt0 ≥ 0.6740 (note this is the SD for the log-transformed S/CO) 

Vironostika HIV Uni-Form II Plus O (Biomérieux) 

The mean S/CO ratio of confirmed positives samples was estimated in an independent study at 14.8 in 

Tanzania (Aboud et al. 2006). Among surveys with the best concordance on first and second EIA, and that 

used this test on the first assay, the median S/CO was highest at 25.5 in Mali and 21.7 in Senegal. The prior 

for the mean of this parameter was chosen to correspond to the midpoint between the minimum and 

maximum of these values (the midpoint on the log scale of 19.4). The standard deviation of this parameter 

was chosen so that this mean has a 99% probability of being higher than a S/CO value of 5 (threshold for 

highly reactive specimens). This translates in the following prior for the mean of the distribution of true 

positive (νt1):

νt1 ~ Normal(log(19.4), 0.5828)) 

For the SD of the distribution of true positives (σt1), we chose a non-informative prior, such that: 

σt1 >0 

For the distribution of true negatives, we use the mean S/CO of the negatives samples of the two surveys 

(Mali and Senegal) which had the best concordance (>97%) between the two EIA. The mean S/CO of the 

negative samples was estimated at 0.34 and 0.32 in Mali and Senegal, respectively. Because this median is 

very close to the mean of negative samples tested with the 4th generation version of this test, the same 

parameters were used. The prior for the mean of the true negative (νt0) is: 

νt0 ~ Normal(log(0.33), 0.2555) 

For the standard deviation of this distribution (σt0), we chose a minimum SD such that the probability of 

that a true negative has a S/CO value greater than the cutoff is 5% (conditional on a mean S/CO of 0.33 for 
55

true negatives). This reflects the fact that most weakly reactive samples are probably due to lab errors and/or 

higher false positivity resulting from the use of DBS. 

σt0 ≥ 0.6740 (note this is the SD for the log-transformed S/CO) 

B) Priors for dichotomous assays (Western Blot or line immunoassay) 

Inno-Lia HIV I/II Score line immunoassay (Innogenetics) 

The sensitivity and specificity of this test are estimated to be 100% (95% CI: 98.6%-100%) and 100% (95% 

CI: 98.0-100%), respectively (WHO 2015b). For the posterior distributions of this test’s sensitivity and 

specificity to remain within these ranges, the lower limit of the confidence interval defined the prior’s lower 

bound. Specifically, we have: 

Sew ~ Beta(1,1)*I(0.986, 1) 

Spw ~ Beta(1,1)*I(0.980, 1) 

New Lav Blot (Bio-Rad) 

The sensitivity and specificity of this test are estimated to be 100% (95% CI: 98.1%-100%) and 100% (95% 

CI: 96.8-100%), respectively (WHO 2015b). For the posterior distributions of this test’s sensitivity and 

specificity to remain within these ranges, the lower limit of the confidence interval defined the prior’s lower 

bound. 

Sew ~ Beta(1,1)*I(0.981, 1) 

Spw ~ Beta(1,1)*I(0.968, 1) 

HIV 2.2 Blot (DiaSorin) / Western Blot 2.2 (Abbott Labs) 

The sensitivity and specificity of this test are estimated by the test manufacturer, excluding indeterminate 

samples, to be 100% (95% CI: 98.2%-100%) and 100% (95% CI: 98.0-100%) for HIV-1, respectively 

(WHO 2016). For the posterior distributions of this test’s sensitivity and specificity to remain within these 

ranges, the lower limit of the confidence interval defined the prior’s lower bound. 

Sew ~ Beta(1,1)*I(0.982, 1) 

Spw ~ Beta(1,1)*I(0.980, 1) 

57

Text S2: Details on Bayesian Latent Class Continuous Model 

Specification 

Table S3 below summarizes the different patterns of tests used for classifying the different algorithm for 

the Bayesian latent class analysis based on the distribution of the continuous assay data. All countries, 

except Uganda, use two continuous diagnostic tests. “Type 1” surveys administer one test to all subjects; 

those who tested positive on the first test are then administered a second test (along with those subjects 

selected for IQC). If the two test results disagree, a final dichotomous test is used. 

For “Type 2” and “Type 3” surveys, the first and second EIA are repeated in parallel if their results do not 

match. For “Type 2” surveys, a final dichotomous test is administered to subjects for whom the repeated 

tests still disagree (for “Type 3” survey, there is no third assay). 

Uganda is the only “Type 4” survey. A first assay is performed on all samples, a second EIA is administered 

to subjects who test positive to the first assay, and a third EIA is conducted on specimens with discrepant 

results on the first two EIA. In surveys with a Type 4 testing strategy, there is no confirmatory dichotomous 

assay such a Western Blot or line immunoassay. 

Table S3 Data Structure

Survey type Description Subjects sets Parameters list (data sets)

Type 1 One or two continuous assay 

(only once each) are used

S1, S2 μ2, σ2, ρ

μ1, σ1

S2

S2 & S1

Type 2 and 3 One or two continuous assay & 

parallel testing are used

S1, S2, S4 ρ11, ρ22

μ2, σ2, ρ12

μ1, σ1

S4

S4 & S2 (ρ = ρ12)

S4, S2 & S1

Type 4 Up to three continuous assays 

(only once each) are used

S1, S2, S3 μ3, σ3, ρ13, ρ23

μ2, σ2, ρ12

μ1, σ1

S3

S3 & S2 (ρ = ρ12)

S3, S2 & S1

MCMC algorithm 

We wrote our custom Monte Carlo Markov Chain (MCMC) algorithm to sample the posterior distributions 

of interest. This code was written in R where we generated random values for each parameter based on their 

respective full conditional posterior distributions at each iteration. 

Developing the likelihood terms LXi

The likelihood terms Li1|s - Li4|s are involved in the calculation of LXi which are of the form: 

 Lik|s ∝

1

|Σ|

exp −

1

2

{(Xi − μ)

⊤ Σ−1(Xi − μ)}

=

1

|Σ|

exp −

1

2|Σ|

{(Xi − μ)

⊤Λ(Xi − μ)}

=

1

d

exp −

q

2d
58

Where Λ is the cofactor matrix of Σ, d is its determinant, d = |Σ|and q =(Xi − μ)

⊤Λ(Xi − μ). Note that 

the quadratic term q above is a polynomial of degree 2 in terms of μ1, μ2 and/or μ3. 

It is not important to acknowledge the following at this point, but q is also a polynomial of degree 2 in terms 

of the different correlation terms (ρ's), while it is a polynomial of degree 2 or higher in terms of SD's (σ's).

Full conditional posterior distributions for the means 

The full conditional posterior distribution for the mean of assay t scores in either the positive (s = 1) or 

negative (s = 0) assay distributions (μts) is relatively easy to drive since μts appears only in the quadratic 

parts q of the various likelihood terms. 

We illustrate its calculation through the elicitation of μ2’s full conditional posterior distribution. We drop 

the s index indicating to which distribution the corresponding mean corresponds: both cases (s=0, 1) are 

done exactly along the same lines. 

Depending on the survey type, μ2 is present in L2 (Types 1 and 2), L2 and L3 (Type 4) or L2, L3 and L4 (Type 

3). Again, we illustrate only the calculation of the term in μ2 present in L4 for the sake of conciseness, as the 

contribution of terms L2 and L3 to μ2’s full conditional posterior distributions are derived the same way. 

The contribution of subject i ∈ S4 to μ2s full conditional posterior distribution (provided the true latent 

status of subject i is equal to s, that is, Ti = s) is proportional to: 

L4i ∝ exp {− 1

2

(Xi − μs)

⊤Σ4s

−1(Xi − μs

)} 

Where μ2 is absent of the covariance matrix Σ4s and the mean is: 

μs = (

μ1s

μ1s

μ2s

μ2s

) = μ1s (

1

1

0

0

)

⏟ 

K1

+ μ2s (

0

0

1

1

)

⏟ 

K2

Hence the contribution of subjects in S4 to μ2s full conditional posterior distribution is proportional to: 

∏ L4i

i∈S4: Ti=s

∝ exp {−

1

2

 ∑ (X⏟i − μ 1s K 1

X̃

i

− μ2sK2)

⊤

 Σ4s

−1

i∈S4: Ti=s

(Xi − μ1sK1 − μ2sK2)}

= exp {−

1

2

 ∑ (X̃

i

⊤ − μ2sK2

⊤

)Σ4s

−1(X̃

i − μ2sK2 )

i∈S4: Ti=s }

∝ exp

{

 

 

 

 

−

1

2

(

 

 

μ2s

2 n4sK2⊤Σ4s−1 ⏟ K 2

A4

 − 2μ2s ∑ K2

⊤Σ4s−1X̃

i

i∈S ⏟ 4 : T i=s 

B4 )

 

 

}

 

 

 

 
59

Where n4s is the number of subjects in S4 with status s, s = 0, 1. Similarly, subjects in S2 contribute to the 

full conditional posterior distribution of μ2s and we note (A2, B2) the terms corresponding to (A4, B4) in the 

above expression. Since the prior distribution for to μ2s is Normal (to μ02s, σ02s

2

), we have: 

f(μ2s) ∝ exp {− 1

2σ02s

2

(μ2s − μ02s)

2}

∝ exp {− 1

2

 (μ2s

2

1

σ02s

2 − 2μ2s

μ02s

σ02s

2

)}

It follows that the full posterior conditional distribution is of the form: 

f(μ2s| data, other parms) ∝ exp {− 1

2

(μ2s

2 A − 2μsB)} 

where A = ∑ Aj

j=0,2,4

and B = ∑ Bj

j=0,2,4

That is, μ2s full conditional posterior distribution is also normal. If a constraint was imposed on the 

maximum value for the mean, the posterior distribution is the same as the one below but truncated to the 

limits imposed. 

μ2s| data, other parms ~ N (mean = 

B

A

, variance = 

1

A

)

Full conditional posterior distributions for correlations and SDs 

The elicitation of SD's or correlations’ full conditional posterior distributions is by far the most complex in 

this project. However, their calculations are manageable after we recognize their form. 

Consider for example the full conditional posterior distribution of σ2 in a survey of Type 3, that is, a survey 

with two EIA and parallel retesting of discrepant results. As we can see from Table S3, the parameter σ2 is 

present in the multivariate normal distribution for subjects in either S2 or S4. 

The multivariate normal distribution for subjects in S2 (or S4) is presented and worked out - in terms of θ ∈

{ρ11, ρ12, ρ22, σ1, σ2

}'s full conditional posterior distribution. In Type 3 surveys, the log of the full 

conditional posterior distribution for σ2 is given by: 

l(σ2

|data, other parameters)

= l2

(σ2|data, other parameters) + l4(σ2|data, other parameters)

where l2 and l4 are obtained from the equation above, applied to subjects from S2 and S4 respectively. Its 

first two derivatives are the sum of the derivatives of l2 and l4 (respectively, the first- and second-order), 

also obtained from the equations above. 
60

Full conditional posterior distribution for the latent True Status Ti

At each iteration, the True Status of subject i, Ti, is updated/resampled. Note that Ti appears in the likelihood 

terms LTi, LXi, and LWi when subject i was administered a dichotomous test (Western Blot or line 

immunoassay). Hence, the full conditional posterior distribution for Ti; i = 1, 2, ..., N can be written as a 

product of terms exponentiated with either Ti or 1-Ti, that is 

f(Ti| Xi, θ) ∝ (∏ aij

j

)

Ti

(∏ bij

j

)

1− Ti

= ai

Tibi1−Ti

⇒ Ti| Xi, θ ~ Bernoulli ( ai

ai + bi

)

Full conditional posterior distribution for the prevalence

The full conditional posterior distribution for prevalence is the easiest to derive, because prevalence is only 

present in the likelihood component LTi. Its posterior distribution is thus given by: 

f(π | X, θ−π) ∝ ∏ πTi

 (1 − π)1−Ti παπ−1(1 − π)βπ−1

i

= π∑ Ti+απ−1(1 − π)

N− ∑ Ti+βπ−1

~ Beta (∑ Ti + απ , N − ∑ Ti + βπ)

Full conditional posterior distributions for the sensitivities and specificities of the 

dichotomous tests 

In surveys where a dichotomous test was used, we update its sensitivity and specificity values by 

sampling values from their respective full conditional posterior distributions at each iteration. Since these 

tests contribute to the likelihood term and their parameters’ prior distributions are Beta distributions, their 

respective full conditional posterior distributions are also Beta distributions. In cases where a truncated 

prior is used, the full conditional posterior density will be a truncated beta density, that is, a beta density 

over a range narrower than [0, 1]. The full conditional posterior distributions are: 

f(sW | data, other parameters) ∝ ∏[sW

wi

(1 − sW)

1−wi]

Ti

sW

αs−1(1 − sW)

βs−1

i

= sW

∑i Tiwi+ αs−1(1 − sW)

∑ Ti(1−wi i)+ βs−1

and f(cW | data, other parameters) ∝ ∏[(1 − cW)

wicW

1−wi

]

(1−Ti)

cW

αc−1(1 − cW)

βc−1

i

= cW

∑ (1−Ti

)(1−wi i)+ αc−1(1 − cW)

∑ (1−Ti i)wi+ βc−1

Updating censored values 

In some surveys, high score values (i.e., S/CO) were censored. At each iteration, these censored values are 

imputed a S/CO from the corresponding score’s conditional distribution. 
61

For example, in a type 3 survey, we remind that the scores Xi = ( Xi1, Xi2, Xi3, Xi4)

⊤ ~ N(μs

, Σs

). If the 

first score - that is, Xi1 of sample i was censored, then we impute a value - greater than the censored value 

for that score based on the distribution of Xi1 conditional on (Xi2, Xi3, Xi4). That conditional distribution is 

easily obtained. Indeed, if U and V are two vectors (block variables) such that: 

(U, V) ~ N (μ = (μ = (μU, μV

)

⊤, Σ = (

ΣU Σ′UV

ΣUV ΣV

)))

then U|V ~ N (μU + Σ′UVΣV

−1(V − μV

), Σ = ΣU − Σ′UVΣV

−1ΣUV)

The conditional distribution of Xi1 given (Xi2, Xi3, Xi4) is a particular case of the above (where U = Xi1 is of 

length 1) and can thus be easily calculated. The conditional distribution of Xi2, Xi3 or Xi4 given the other Xi* 

scores can be obtained along the same lines. We first left-multiply the vector Xi by the appropriate 

permutation matrix P to make the component Xij of interest become the first component of Xi

* = PXi, from 

which it follows that Xi

*

~ N (Pμ, P’ΣP) and then obtain the conditional distribution for Xij along the lines 

elicited above.