Treatmentseeking behaviour in low and middleincome countries estimated using a Bayesian model
 Victor A. Alegana^{1, 2}Email author,
 Jim Wright^{1},
 Carla Pezzulo^{1, 2},
 Andrew J. Tatem^{1, 2} and
 Peter M. Atkinson^{1, 3, 4}
DOI: 10.1186/s1287401703460
© The Author(s). 2017
Received: 3 January 2017
Accepted: 12 April 2017
Published: 20 April 2017
Abstract
Background
Seeking treatment in formal healthcare for uncomplicated infections is vital to combating disease in low and middleincome countries (LMICs). Healthcare treatmentseeking behaviour varies within and between communities and is modified by socioeconomic, demographic, and physical factors. As a result, it remains a challenge to quantify healthcare treatmentseeking behaviour using a metric that is comparable across communities. Here, we present an application for transforming individual categorical responses (actions related to fever) to a continuous probabilistic estimate of fever treatment for one country in SubSaharan Africa (SSA).
Methods
Using nationally representative household survey data from the 2013 Demographic and Health Survey (DHS) in Namibia, individuallevel responses (n = 1138) were linked to theoretical estimates of travel time to the nearest public or private health facility. Bayesian Item Response Theory (IRT) models were fitted via Markov Chain Monte Carlo (MCMC) simulation to estimate parameters related to fever treatment and estimate probability of treatment for children under five years. Different models were implemented to evaluate computational needs and the effect of including predictor variables such as rurality. The mean treatment rates were then estimated at regional level.
Results
Modelling results suggested probability of fever treatment was highest in regions with relatively high incidence of malaria historically. The minimum predicted threshold probability of seeking treatment was 0.3 (model 1: 0.340; 95% CI 0.155–0.597), suggesting that even in populations at large distances from facilities, there was still a 30% chance of an individual seeking treatment for fever. The agreement between correctly predicted probability of treatment at individual level based on a subset of data (n = 247) was high (AUC = 0.978), with a sensitivity of 96.7% and a specificity of 75.3%.
Conclusion
We have shown how individual responses in national surveys can be transformed to probabilistic measures comparable at population level. Our analysis of household survey data on fever suggested a 30% baseline threshold for fever treatment in Namibia. However, this threshold level is likely to vary by country or endemicity. Although our focus was on fever treatment, the methodology outlined can be extended to multiple health seeking behaviours captured in routine national survey data and to other infectious diseases.
Keywords
Bayesian hierarchical model Treatmentseeking behaviour Item response theory Markov Chain Monte CarloBackground
Delay in seeking treatment for ill health in low and middleincome countries (LMICs) affects disease progression, management and outcomes [1–3]. Most infectious diseases in LMICs are preventable by using costeffective interventions and treatable at peripheral health facilities [4]. However, weak health systems affect the delivery of most interventions [5] and socioeconomic and physical barriers that modify healthseeking behaviour compound this, leading to underutilisation of health facilities [6]. Encouraging appropriate treatmentseeking behaviour for uncomplicated infections is vital to further reduce disease burden in these countries or for successful elimination. For malaria, for example, the current World Health Organisation (WHO) recommendation is for malaria treatment to be sought in the formal healthcare sector within 24 hours of fever onset and other malariarelated symptoms [7]. This is because patients who seek treatment through the formal sector are likely to receive an appropriate diagnosis and effective management [8]. However, there are many factors influencing population treatmentseeking behaviour including, but not limited to; availability of healthcare providers, proximity or travel time to healthcare facilities, condition severity and perception, and the sociodemographic profile of the population at risk [9].
Studies on treatmentseeking behaviour can be grouped into two categories of approach. The first is a qualitative description of steps undertaken by the population in different settings [10–12] while the second is a quantitative association between determinants (factors) and choice of health service use [13–18]. Although these approaches are used widely in biomedical research, they usually do not examine the latent (i.e. theoretical) characteristics such as individuallevel traits to estimate variation at population level. In addition, comparability is not simply guaranteed with the same questionnaire because of differential item functioning problem i.e. the varying behavioural response to the same question depending on the respondent [19]. Such variation can then be translated to spatially explicit applications that can be combined with existing spatial data on populations [20] and disease incidence to inform and optimise targeting of communitybased interventions.
Modelbased geostatistical methods have already been used to predict and estimate disease incidence at fine spatial resolution [21, 22]. This has been aided by public health intelligence data that are increasingly becoming available across space and time from geolocated nationally representative household surveys. These include the Malaria Indicator Surveys (MIS) [23], Demographic and Health Surveys (DHS) [24], and Multiple Indicator Cluster Surveys (MICS) [25]. These nationally representative household surveys also collect information on selfreported health behaviour such as fever management [14]. However, how can responses concerning fever treatment from household surveys be compared across populations with varying access, demographics, cultures, and disease burdens? Item response theory (IRT) has been widely used to examine surveys items (questions) and person characteristics in psychology and education [26–28]. In education, for example, it has been used to estimate the personlevel traits (such as ability) or itemlevel difficulty in an examination [29–31]. IRT concepts can be extended to health as applied previously in delirium screening [32], longitudinal data analysis [33], and interpreting medical codes from patient records [34]. IRT approaches are essentially probit models with additional regression effects used to aid estimation of item characteristics [35]. Extending this to a Bayesian framework has the advantages of incorporating uncertainty in estimating latent traits and prior distributions can be imposed on the Bayesian probability model to capture many aspects of data not included in descriptive or quantitative frequentist approaches [36]. Although Imputation techniques can be used to handle missing data, this was beyond the current scope of this manuscript.
Here, the aim was to demonstrate the application of IRT to fever treatmentseeking modelling using data from a low malaria transmission setting, the Namibia 2013 DHS. We analyse fever treatmentseeking behaviour at a national level and derive response characteristic curves based on travel times to the nearest facilities. The rest of this paper is organised as follows. Section 2 provides an overview of household survey data in LMICs and the proposed modelling approach. We then present treatmentseeking behaviour model outputs in section 3, including evaluation of model performance. The paper concludes with a brief discussion in sections 4 and 5.
Methods
Data characteristics in low and middle income countries
Distance or proximity to healthcare provider is an important parameter in the choice of treatment by patients in many LMICs [37–39]. In these countries, the majority of people access facilities by walking. Therefore, it is preferable to use a facility close to the place of residence because it is less costly compared to travelling greater distances requiring motorised transport [40]. Other factors that influence utilisation patterns include: age, gender, healthcare costs, socioeconomic status, residence (urban or rural), familiarity with health personnel, fever severity, and quantity as well as quality of services at peripheral facilities [41, 42]. In some cases, however, the phenomenon of bypassing the nearest healthcare facility can be encountered, even for mild fever conditions [43, 44]. Empirical data are not always available to model such nuances and we therefore assume use of the nearest facility in this case study.
Estimation of travel times to the nearest formal healthcare treatment provider
Estimating travel times between population centres and formal healthcare providers has already been considered in previous research [14]. In brief, this requires a combination of mode of travel (walking or motorised) and an impedance surface that is constructed based on multiple data layers, including the various land use and land cover characteristics, elevation, and roads [45]. Travel time to nearest healthcare facility is a useful measure because it is relatively easy to estimate and to relate travel times in different settings compared to estimating the actual physical distance. The approach in Alegana et al. [14] shows how travel times for Namibia were derived.
Quantification of formal healthcare use based on national representative household surveys
To estimate the utilisation of healthcare facilities, this study used the reported use of formal healthcare for fever treatment from the DHS. These surveys are conducted in 90 countries worldwide, and 44 in SSA, providing information on reproductive health, fertility, population demographics and general health status, nutrition, household characteristics, socioeconomic status and infant and child mortality rates [46]. The surveys are based on a random twostage cluster sampling design in which clusters are usually first sampled within a region on a probabilityproportionaltosize basis and thereafter, within each cluster, households are sampled randomly [47, 48]. Cluster sizes usually vary, but are typically approximately 15 to 30 households. The household survey provides information on health and the sociodemographic profile of consenting participants including their treatmentseeking behaviour for conditions such as malariaassociated fever.
Application of Bayesian probit models to healthcare utilisation research
Item response modelling was proposed in the 1960s [54–56] and is commonly applied to studies in education and psychology to estimate item characteristics [28]. The first applications of IRT used maximum likelihood estimation [57, 58]. Bayesian extensions were proposed for one and twoparameter models [59] and extended to the threeparameter logistic model [60]. Fitting via Gibbs sampling became popular using data augmentation (DAG) techniques in the 1990s particularly for application to the normalogive models [61–63]. Fu et al. [64] provided some extensions to the threeparameter model following Sahu’s DAG approach [63] and compared Gibbs sampling to BILOGMG software [65] using likelihood estimation. There have also been other innovations in parameter estimation [62], including extension to a multilevel approach [26–28] and comparison with maximum likelihood methods [66]. Here, a unidimensional threeparameter model with a hierarchical structure was used, its parameters estimated, and prior sensitivity checked by comparing model goodnessoffit statistics. The main objective was to estimate the probability of a positive response to choice of treatment for persons with fever associated with malaria at a household level.
The likelihood and posterior specification
Goodnessoffit statistics, prior specification and Markov chain Monte Carlo implementation
The same notation was used for the item discrimination parameter, witha _{ i } > 0, where a halfnormal or truncated normal prior was used such that a _{ i } ~ N(μ _{ a }, σ _{ a } ^{2} )I(a _{ i } > 0)and I(⋅) is an indicator function. The rationale for this specification is to ensure that the parameter estimate is positive. The probability threshold parameter was constrained on c ∈ (0, 1] using a beta distribution such that π(c _{ k }; κ, τ)αc _{ k } ^{ κ − 1} (1 − c _{ k })^{ τ − 1} for suitable parameters values \( {\kappa}_{c_k} \)and\( {\tau}_{c_k} \). The recommended procedure for selecting suitable estimates of these parameters is such that the E(c) = κ/(κ + τ) and weakly informative priors may be used for parameters of beta distribution.
Results
We used the Namibia 2013 DHS data to estimate the probability of fever treatment in the formal sector (reported fever treatment in public and private sectors) for children under five years. There were 4818 children under five years enumerated, of which 1138 (23.6%) reported at least one fever episode in the preceding fortnight. Of those that reported a fever episode, 726 (63.8%) sought treatment in the formal sector (public and private sector excluding traditional healers). Overall, the proportion of children with reported fever was fairly homogeneous across all the regions surveyed but varied by estimated travel times. Estimation of probability of treatment focussed on children reporting fever (n = 1138) rather than all children examined in the crosssectional survey.
Model comparison based on goodnessoffit statistics
Model  DIC  PD  Inverse log likelihood  Number of chains 

M1^{a}  3615.9  2178.9  −0.001  3 
M2^{a}  3685.1  2256.1  −0.001  3 
M3  5098.7  3693.1  −0.001  3 
M4  23874.1  22754.0  −0.002  3 
Estimated summary statistics and the 95% Bayesian credible intervals of parameters based on all four models
Model  Estimate  a  b  c  α  β  Corr (α, β) 

M1  Mean  0.704  0.807  0.340  −0.084  −0.098   
Median  0.556  0.850  0.326  −0.087  −0.112    
95% CI  [0.016–2.194]  [1.044–2.346]  [0.1554–0.597]  [0.682–0.523]  [0.439–0.394]    
GelmanRubin Convergence estimate  1.000  1.000  1.000  1.000  1.000    
GelmanRubin Convergence upper CI  1.000  1.010  1.000  1.000  1.030    
M2  mean  0.784  1.060  0.352  −0.080  −0.123   
median  0.654  0.978  0.344  −0.081  −0.121    
95% CI  [0.042–2.243]  [0.100–2.452]  [0.172–0.572]  [0.661–0.518]  [0.417–0.218]    
GelmanRubin Convergence estimate  1.001  1.000  1.001  1.001  1.020    
GelmanRubin Convergence upper CI  1.010  1.000  1.000  1.000  1.040    
M3  mean  0.789  0.977  0.376  −0.582  −0.140   
median  0.660  0.895  0.372  −0.581  −0.150    
95% CI  [0.046–2.225]  [0.055–2.423]  [0.176–0.597]  [2.208–1.069]  [0.434–0.248]    
GelmanRubin Convergence estimate  1.000  1.000  1.000  1.000  1.000    
GelmanRubin Convergence upper CI  1.000  1.000  1.000  1.000  1.000    
M4  mean  0.870  1.003  0.313  −0.133  −0.008  −0.011 
median  0.768  0.912  0.311  −0.152  −0.012  0.006  
95% CI  [0.059–2.244]  [0.063–2.477]  [0.095–0.527]  [0.665–0.501]  [0.880–0.873]  [0.957–0.952]  
GelmanRubin Convergence estimate  1.000  1.000  1.000  1.010  1.000  1.010  
GelmanRubin Convergence upper CI  1.000  1.000  1.010  1.040  1.000  1.050 
Estimated probability for fever treatment (mean and 95% Bayesian Credible Interval) at the nearest health facility
Region  Population estimate 2015^{a}  Estimated mean malaria incidence per 1000 population in 2014^{b}  Estimated Average travel time to nearest health facility (minutes)  Probability of using a dispensary or clinic for fever treatment mean (95% CI)  Probability of using a health centre for fever treatment mean (95% CI)  Probability of using a Regional or district hospital for fever treatment mean (95% CI) 

Zambezi  105,804  1.612  23.0  0.546 (0.369–0.671)  0.537 (0.369–0.667)  0.531 (0.369–0.661) 
Kavango  259,984  1.467  29.7  0.513 (0.368–0.649)  0.498 (0.368–0.633)  0.503 (0.368–0.638) 
Ohangwena  283,188  1.426  29.3  0.522 (0.368–0.650)  0.494 (0.367–0.630)  0.497 (0.368–0.632) 
Oshikoto  210,881  1.256  37.3  0.504 (0.368–0.644)  0.492 (0.367–0.633)  0.496 (0.367–0.637) 
Otjozondjupa  167,186  1.227  31.8  0.504 (0.368–0.643)  0.486 (0.367–0.623)  0.499 (0.368–0.637) 
Omusati  281,050  1.131  35.6  0.513 (0.368–0.650)  0.497 (0.367–0.637)  0.498 (0.367–0.638) 
Omaheke  82,441  1.126  38.3  0.490 (0.367–0.631)  0.496 (0.367–0.637)  0.493 (0.367–0.634) 
Oshana  207,218  1.096  17.6  0.561 (0.369–0.677)  0.545 (0.369–0.661)  0.547 (0.369–0.663) 
Kunene  102,986  0.967  146.4  0.433 (0.364–0.614)  0.426 (0.364–0.608)  0.429 (0.364–0.612) 
Khomas^{c}  418,742    43.9  0.487 (0.367–0.636)  0.483 (0.367–0.631)  0.482 (0.367–0.631) 
Karas^{c}  88,977    110.2  0.447 (0.365–0.619)  0.440 (0.365–0.613)  0.446 (0.365–0.618) 
Hardap^{c}  93,447    86.7  0.471 (0.366–0.628)  0.470 (0.366–0.626)  0.461 (0.366–0.616) 
Erongo^{c}  180,672    98.4  0.443 (0.365–0.620)  0.440 (0.365–0.618)  0.440 (0.365–0.617) 
Discussion
Characterising treatmentseeking behaviour in LMICs is valuable because it varies by geographic location, type of disease and severity, person characteristics including age and gender, as well as health system based factors such as availability, cost among other enabling factors [9, 75, 76]. Here, the focus was on the estimation of latent parameters of a survey question on fever and estimating the probability of seeking treatment based on a dichotomous response. We used data from a nationally representative household survey from the DHS in one country to estimate fever treatment latent characteristics using a Bayesian IRT approach. By using this method, we estimated the parameters of fever response curves that characterise geographical decay in the use of formal health care based on travel time to the nearest facility. The method is particularly appealing because of the joint estimation of IRT parameters related to fever treatment with uncertainties incorporated in prior distributions and the ability to extract the full posterior distribution compared to point estimates from maximum likelihood approaches [26, 61]. This is important because estimates from such probabilistic modelling can then be applied in estimating numbers of symptomatic infections (treatment burden) when such probabilistic estimates are transformed into gridded metrics that vary spatially [77, 78]. The modelling approach can also be extended to other items in household surveys to further understand human behaviour response to health conditions.
The lower limit probability estimated here, related to the threshold parameter (e.g. from Table 2 model 1: 0.340; 95% CI 0.155–0.597), for Namibia suggests that even at large distances from health facilities, there was still a 30% chance of individuals seeking fever treatment. We suggest that this is an important property in treatmentseeking behaviour for individuals living far from health facilities in Namibia, although this threshold may be different by country or endemicity and was not explored further in this analysis. In this study, estimates of probability of fever treatment at the regional level showed that the mean probability was highest in regions with relatively high incidence of malaria historically (Table 3). Another operational application of the probability response characteristics curves, derived from the latent parameters in Fig. 3a, could be in identifying areas where community health workers could be deployed [79, 80]. This, however, requires definition of a cutoff probability (yaxis on Fig. 3a), currently not established for malaria transmission settings, to delineate areas with limited access. Constraining the b parameter (item parameter) did not influence estimates of the individuallevel traits and the threshold parameters. This is primarily because only one item was used in this application resulting in similar parameter estimate for the location parameter.
In extending the model to a multilevel framework, travel times were used as predictors. Comparison between constant intercept and slope model parameters with a random parameter model showed that the former resulted in shorter MCMC runs and better model fit compared to the latter (i.e., the random slope and intercept), which experienced slow convergence as the number of effective parameters increased exponentially. We are not discouraging use of a more complex modelling approach while estimating IRT parameters, but this highlights the increasing computational demands and efficiency related to increased complexity.
MCMC techniques were used to estimate and jointly interpret IRT parameters. The threeparameter logistic model [60] was particularly useful compared to the twoparameter model [59], because, the third parameter c represents the threshold probability on the fever response curve, ensuring that probability is always greater than or equal to zero. Despite the known benefits of IRT in other fields [28], this approach has seldom been applied to modelling human behavioural aspects for treatmentseeking behaviour. The current study was confined to patients’ responses to a fever question in household survey data and how latent (rather than observed) properties can be quantified in relation to patient behaviour and travel time. Dichotomous responses are common in many health surveys in LMICs and methods used here can be extended to other health conditions. Although we did not have to deal with missing data (NAs), several data imputation techniques can be used for nonignorable NAs [81]. These may arise when there is lack of response, or, associated with refusal to participate or simply unobserved variable for survey items. When NAs are imputed into the data matrix, for example, these do not usually contribute to likelihood estimation [82] of the ability parameter and the higher the number of missing values the more likely that there will be an increase in uncertainty for the parameter estimate.
There exist some additional limitations aside from those related to computational speed and efficiency. While fever in the Namibia 2013 DHS was associated with malaria treatment, the survey data did not include a laboratory confirmation of malaria infection [83]. Moreover, the sampling methodology for children with fever in the DHS may be inferior because the survey is not powered for fever detection [47]. Most current surveys however incorporate rapid diagnostic tests (RDTs) and future identification of febrile cases could include laboratory results as a preprocessing step in identifying malariarelated fever cases. In addition, although prior specifications introduce a measure of uncertainty in a hierarchical way, assumptions in generating input data such as use of the nearest facility may not be sufficient in understanding treatmentseeking behaviour. It has been shown in separate population surveys that patients may bypass the nearest health centre due to various individual or supplybased factors such as quality [84]. While an obvious recommendation is to include such effects, increasing model complexity to capture such differences may have an impact on computational efficiency as seen in model 3 and model 4. More importantly, identifying measures of quality of care in public or private health sectors can be challenging [40].
Conclusion
In the context of fever treatment, we have demonstrated that there is potential to use nationally representative household data to provide a probabilistic measure of treatment using a Bayesian method. Our estimates of threshold probability apply to one low malaria transmission country and may be different in other countries with varying malaria endemicity. Future studies will aim to conduct such comparative analysis between and within countries via spatially varying parameters. The methodology can be extended to multiple human behavioural questions (items) related to health and demographics in the routine national survey data.
Abbreviations
 AUC:

Area under curve
 CHW:

Community health worker
 DAG:

Data augmentation
 DHS:

Demographic health surveys
 DIC:

Deviance information criterion
 iCCM:

Integrated communitycase management
 IRT:

Item response theory
 LMICs:

Low and middleincome countries
 MCMC:

Markov chain Monte Carlo
 MICS:

Multiple indicator cluster surveys
 MIS:

Malaria indicator surveys
 ROC:

Receiveroperating characteristics
 SSA:

SubSaharan Africa
 WHO:

World Health Organization
Declarations
Acknowledgements
We would like to thank Professor Sujit Sahu (University of Southampton) and Dr Linus Bengtsson (Flowminder codirector) for comments on the earlier version of the manuscript.
Funding
Andrew J Tatem is supported by a Wellcome Trust Sustaining Health Grant [grant number 106866/Z/15/Z] and Bill and Melinda Gates Foundation [grant numbers OPP1106427, 1032350, OPP1134076].
Availability of data and materials
DHS data available in the public domain at http://dhsprogram.com/data/availabledatasets.cfm.
Authors’ contributions
VA, PMA, and AJT were responsible for study design, analysis, interpretation, and production of final manuscript. CP and JW contributed to data assembly and management, interpretation and production of final manuscript. All authors have read and approved the final version of the manuscript.
Competing interests
The authors declare that they have no competing interests.
Consent for publication
Not Applicable.
Ethics approval and consent to participate
University of Southampton (17263).
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Authors’ Affiliations
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