Bayesian Modeling Approach
Background
Reliable information on health coverage indicators is essential for monitoring progress, informing programs, and guiding policy decisions. However, relying on survey and routine data alone is often challenging. Routine data from facilities may suffer from underreporting or inconsistent data quality, while survey data may be uncertain or not recent.
To address these challenges, statistical models can be used to produce estimates and forecasts over time, combining multiple data sources and accounting for their limitations. This results in estimates of coverage every year (between data points and past data) with an indication of how certain/uncertain we are about each year. As a result, models enable more complete, accurate, and timely assessments of health coverage, especially in data-limited settings.
Producing Estimates and Short-Term Forecasts
We developed a statistical model to estimate health coverage at the national level and for subnational regions up to the most recent year with data, and to make short-term forecasts for the years ahead.
The model looks at the available data and identifies different ways coverage could have changed over time. Each of these possible paths is called a trajectory (see Figure 1).
For each year, we report a best estimate (the middle value across all trajectories) and a range that shows the uncertainty (leaving out the most extreme possibilities at the edge).
Informed by global analyses, the model captures that over time coverage usually rises from low to high levels, following an S-shaped trend, with periods of faster or slower progress along the way depending on what the data indicates. It uses survey and routine data to choose trajectories that match what has been observed. The model also draws on trends seen in other areas with similar coverage levels.
How are survey data used?
Survey data help us understand coverage, but they come with some uncertainty. This happens because surveys only include a sample of the population, not everyone, and there can be errors during data collection.
To best use survey data, the model tries to strike the right balance—smoothing out random ups and downs that are probably not real, while still capturing important patterns in the data. To do this, the model looks at how uncertain each data point is:
- High uncertainty: If a data point is very uncertain, it will have less impact on estimated coverage (the model gives it less weight and is more likely to smooth over it).
- High reliability: If a data point is more reliable, estimates will align closer to that value.
For subnational regions, the model uses survey data from the specific region when available.
How are routine data used?
The coverage estimates from routine data can be biased, so the model treats it differently from survey data. For surveys, the model uses the actual coverage levels. For example, if a survey indicates coverage at 60% for a particular year, the model uses that value directly.
In contrast, routine data can be biased due to issues such as incomplete reporting and data collection inconsistencies. Due to this, the model does not rely on coverage levels observed in routine data. Instead, the model focuses on the trend over time—specifically, how coverage changes from year to year.
- Example: If routine data shows coverage increasing from 50% in 2020 to 53% in 2021, the model interprets this as a 3 percentage point increase. If the routine data shows faster or slower changes than expected, the model adjusts the estimates—but only as much as the data can be trusted.
Accounting for Data Quality
The model accounts for routine data quality by adjusting the uncertainty of the trend estimates. Observations with lower data quality are treated as more uncertain and given less weight in determining true rates of change. Specifically, uncertainty in the estimated rate of change increases as the Countdown mean data quality score decreases. Consequently, lower-quality data exerts less influence on the modeled rate of change.
Illustrative Examples
Estimates are produced for:
- The proportion of women who receive the recommended minimum of at least four antenatal care visits during pregnancy (ANC4).
- The proportion of live births that take place in a health facility (Institutional deliveries).
- The proportion of children who receive the recommended three doses of pentavalent vaccine (Vaccination coverage).
Example 1: ANC4 coverage
- An example of the output for ANC4 coverage at the national level is shown in the figure below. The graph displays survey data and routine data as dots (grey for routine data, red for survey data).
- The red line represents the modeled point estimates, and the red shaded areas represent the 95% uncertainty intervals.
Example 2: ANC4 Subnational Coverage
Example outputs for subnational coverage estimation for 2025 are shown in Figure 4.
Red dots represent point estimates, and horizontal lines represent 95% uncertainty intervals.
Example 3: Data and Bayesian estimates
The figure below shows example data and estimates obtained from the model for a coverage indicator in four different regions.
** Interpretation**
- Survey data from DHS and MICS are shown in red and blue, with vertical bars indicating how uncertain each survey point is. Routine data are shown in black. The lines represent the model’s point estimates with shaded areas highlighting uncertainty (in red if routine data were included, black/green otherwise).
- The plots show that the model’s estimates usually follow the survey data, unless a data point is very uncertain and does not match the overall trend.
- For example, in Region B, the most recent MICS survey point is lower than expected and very uncertain, so the model’s recent estimates do not exactly align with this survey.
- We also see that routine data help inform how quickly coverage is changing over time, particularly after the most recent survey, when no new survey data is available.
- Region C: The routine data show an increase in coverage. As a result, the estimates that include routine data show a faster rate of change during that period compared to the estimates based only on survey data.
- Region D: Routine data suggest that coverage has not increased recently, and estimates that include routine data reflect that information.