An exploration of multilevel modeling for estimating access to drinking-water and sanitation

Monitoring progress towards the targets for access to safe drinking-water and sanitation under the Millennium Development Goals (MDG) requires reliable estimates and indicators. We analyzed trends and reviewed current indicators used for those targets. We developed continuous time series for 1990 to 2015 for access to improved drinking-water sources and improved sanitation facilities by country using multilevel modeling (MLM). We show that MLM is a reliable and transparent tool with many advantages over alternative approaches to estimate access to facilities. Using current indicators, the MDG target for water would be met, but the target for sanitation missed considerably. The number of people without access to such services is still increasing in certain regions. Striking differences persist between urban and rural areas. Consideration of water quality and different classification of shared sanitation facilities would, however, alter estimates considerably. To achieve improved monitoring we propose: (1) considering the use of MLM as an alternative for estimating access to safe drinking-water and sanitation; (2) completing regular assessments of water quality and supporting the development of national regulatory frameworks as part of capacity development; (3) evaluating health impacts of shared sanitation; (4) using a more equitable presentation of countries’ performances in providing improved services. doi: 10.2166/wh.2012.107 Jennyfer Wolf (corresponding author) Sophie Bonjour Annette Prüss-Ustün Department for Public Health and Environment, Evidence and Policy on Environmental Health, World Health Organization, 20 Avenue Appia, CH-1211, Geneva 27, Switzerland E-mail: wolfj@who.int


INTRODUCTION
Providing universal access to safe water and sanitation ser- . Therefore we developed estimates for access to improved water sources and improved sanitation facilities using advanced modeling methods and reconsidered the definition of the access indicators depending on safety for health. The JMP task force on methods recommended that the JMP method be reviewed ( JMP b). The content of this paper may contribute to these discussions.
This article presents trends in access to safe water and sanitation over 25 years using available survey information and a sound modeling approach. Furthermore, we discuss the inclusion of water quality, different ways to consider shared sanitation and the potential impact such changes would have. Finally, we propose an alternative indicator to monitor the MDG targets which would more equitably represent the performance of countries.

Data compilation and classification
We used the JMP database on access to improved water sources and improved sanitation facilities. It contains datasets collected through nationally representative household surveys and censuses (JMP a). The data represent percentages of households using different improved sources/ facilities, disaggregated by urban and rural population. For the national level (urban and rural combined), nearly 1,100 data points for both water and sanitation were included. Detailed information about data sources and classification of a facility as improved or unimproved can be found in the JMP reports ( JMP a, a JMP classificationthe seat was indeed uncovered, but the pit itselfwhich matters for the JMP definitionwas actually covered. Recent discussions with Chinese survey authorities revealed the reasons for these differences.
Adjustments not only changed Chinese sanitation coverage but had a significant impact on global figures.
In general, JMP harmonization exercises led to internationally adopted and harmonized core questions and response categories and hence to greater data comparability and accuracy of estimates. Additionally, recent surveys provide more disaggregation, and therefore less ambiguity.
Several initiatives are contributing to the 'reconciliation' between past and recent datasets, such as the Accelerated Data Programme of the International Household Survey Network, which was established to improve the coordination and effectiveness of surveys (International Household Survey Network ). However, harmonization between historical and recent data remains a challenge and not always completely achievable.

Modeling approach
Criteria for model selection included: (a) closeness of modeled estimates to the survey points without following all within-country variability which might be partly due to systematic and non-systematic error; (b) transparency, simplicity and reproducibility of the model; and (c) ability to estimate for countries with little or no information. We therefore applied a linear two-level model with a logittransformation of the dependent variable (access to improved water sources or improved sanitation), a cubic spline transformation of the main predictor (time), region ing an intercept and regression slope separately for each country as is currently done in JMP, the multilevel model estimates an average intercept and an average slope with residual variances across countries. In practice, countries are assumed to follow the regional mean in case the trend information for the country is scarce or absent. When there is reliable information for a specific country (i.e. many data points and little within-country variability) the country curve will closely follow the country survey points, whereas for unreliable information (i.e. few country data points or high within-country variability) the estimates will still be close to the survey points but the trend will tend to follow the overall mean (Goldstein ; Hox ; Steele ).
We applied a two-level model allowing a random intercept and slope by country. The model was applied separately to the total, the rural and the urban population. Estimates were derived using maximum likelihood. The dependent variable was logit-transformed to restrict estimates and confidence intervals between zero and one (or 100%) and to use the specific shape of the logit curve with a slower increase when access approaches 100%. The logit transformation leads to increasingly asymmetric and narrow confidence intervals close to zero or 100% (De Onis et al. ). Likelihood ratio test and the Akaike Information Criterion (AIC) were used to decide the inclusion of random and fixed effects. We assumed unstructured covariance between the random intercept and random slope. Random effects and the dependent variable (after transformation) followed normal distributions (Quené &  int/quantifying_ehimpacts/en/index.html). Knots, which determine the flexibility of the curve, were set after 25, 50 and 75% of data points. Sensitivity analyses were performed with different transformations of the dependent and independent variable (different splines and random/fixed effects, non-logit transformation) and the choice of the final model was based on likelihood ratio tests, the AIC and inspection of the curves. For countries with no information, the regional mean trend was taken as the best estimate. Confidence intervals on the national level were calculated as the square root of the combined fixedand random-level variances, which were assumed to be independent. The regional estimates in Tables 1-3 were calculated as the population weighted average of the country estimates.
The global estimate was calculated accordingly as the population weighted average of the regional estimates.
Confidence intervals for regional and global estimates were calculated using regional and global standard errors derived as the square root of the weighted country variances. The country variances on the natural scale were estimated from the country logit variances using the delta method, which has been applied before and described in We present estimates for WHO regions (Sub-Saharan Africa, the Americas, Eastern Mediterranean, Europe, South-East Asia, and Western Pacificwith high income countries (HIC) grouped separately (WHO )) and, furthermore, disaggregated in urban and rural areas (Tables 1 and 2).
For all analyses discussed in this paper, Equatorial Guinea was not considered a high income country but grouped with other Sub-Saharan African countries. All analyses were per-

Water quality
Not all water sources that are classified as improved provide water with a quality that complies with WHO drinking water quality guidelines (WHO ) or are safe for health.
Hence, the currently used MDG estimates should be cor- We also used similar assessments performed in China and India. In the Chinese assessment 1,604 and in the Indian 11,757 water sources were tested. Chinese RADWQ, however, covered one region only and tested total rather than thermotolerant coliforms. The Indian assessment was not conducted as an official RADWQ but followed the same methodology. It examined compliance to BIS 10500 (Bureau of Indian Standards ), which is based on WHO and national guidelines on drinking water quality. We only used the value for microbial water quality from the Indian RADWQ as chemical water quality testing was not done for arsenic. A systematic literature search in Medline and the internet did not yield any additional significant country representative data on water quality at point of use for low income countries. The total information on water quality, therefore, does not exceed one or two country representative surveys per large geographical region.
We compiled water quality estimates for piped to the household and non-piped improved sources from the above described assessments. We then extrapolated these water quality estimates from the respective countries to other countries in the same region (WHO region). We estimated piped water using MLM (see Supplemental material for details, available online at http://www.iwaponline. com/jwh/011/107.pdf) and non-piped improved sources as the difference between total improved and piped sources by country. We then multiplied the respective water quality proportions with those national estimates on piped and nonpiped sources to estimate the population proportion without access to safe water in 2010. Water quality from unimproved

RESULTS
The complete time series  for each country is available at www.who.int/quantifying_ehimpacts/en/index.
html. This site also contains additional information (number of surveys per time period and region, model equations, model evaluation, etc.) under 'Supplemental material'.

Country, regional and global trends
Complete data series between 1990 and 2015 for access to improved water sources and sanitation were generated for 193 WHO Member States. We estimate that, globally, the proportion of people without access to an improved water source will be reduced from 23% in 1990 to 10% in 2015.
The number of unserved people, however, will be reduced by only 40%. Sub-Saharan Africa and the Eastern Mediterranean region will not halve their proportion of the unserved population. Furthermore, the number of people without access to an improved water source in these two regions is projected to increase by an additional 46 million people (Tables 1 and 3).
The global proportion of people without access to improved sanitation will be reduced from 50% in 1990 to 34% in 2015. The number of unserved people will decline only by little more than 200 million. If we were to apply the MDG target to regions, only Western Pacific would achieve the sanitation target by 2015 (Tables 2 and 3).   Access to services is consistently higher for urban compared to rural areas. However, the decrease in the proportion of the urban population without access to improved services between 1990 and 2015 was slower compared to the rural population (Tables 1 and 2). The total number of the urban population without access will rise globally between 1990 and 2015 from 109 to 130 million (access to an improved water source) and from 548 million to 765 million (access to improved sanitation).

Taking water quality into account
After adjusting our estimates with summary microbial and overall water quality (Table 4), calculated as described above, the proportion of the world's population without access to safe water in 2015 rose from 12 to 30% for microbiologically unsafe water and to 33% for overall unsafe water (Table 5).

Differing classifications of shared sanitation
Our final estimates on access to improved sanitation in Tables 2 and 3 (Table 6).

Results
The MDG drinking-water target has been met if access to improved water sources is equated with sustainable access  to 'safe' water. We estimate that in 2015 only 10% of the world population will not have access to an improved water source. However, the sanitation target will be missed substantially if current trends continue. Alarmingly, the number of people without access to an improved water source or improved sanitation increased over time in some regions. This shows that the rates of improvement in access are generally not keeping up with population growth, especially in urban areas.
Generally, urban populations are considerably better served. Urbanization can facilitate the provision and lower the costs of facilities (Satterthwaite ). However, the comparatively small progress in those areas indicates that service provision is increasingly lagging behind population growth and rapid urbanization (JMP a).

Modeling approach
We believe that MLM offers several advantages over tra-   years after the latest point and subsequently extends it horizontally (JMP c). This leads to a sudden step in the estimates which is unlikely to happen in reality (Figures 3   and 4). Although global estimates of MLM differ only slightly from JMP estimates, they can differ substantially for individual countries, with up to 14 percentage points for access to an improved water source and 49 percentage points for access to improved sanitation. Furthermore, MLM proposes approximate estimates based on the regional mean for nine countries for water and 21 countries for

Additional measure for progress
Halving a high proportion without access is much harder compared to halving a low one. This measure is, however, used to monitor the MDG target at global level (JMP a).

ACKNOWLEDGEMENT
We thank Abdou-Salam Savadogo for his valuable contribution to our work.