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Improving the reliability of district-level estimates ofteenage pregnancy in Malawi using small area estimation

This study enhances the reliability of district-level teenage pregnancy estimates in Malawi by applying a Fay-Herriot small area estimation model to 2024 survey data and 2018 census auxiliary variables, thereby providing a more stable evidence base for decentralized policy and targeted interventions.

Original authors: Evaristar Kudowa, Samuel O. Manda, Marc Y.R Henrion

Published 2026-07-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Evaristar Kudowa, Samuel O. Manda, Marc Y.R Henrion

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: Guessing the Weather in a Tiny Village

Imagine you are trying to figure out how much it rains in every single village in Malawi. You have a giant weather report (a national survey) that gives you a very accurate picture of the whole country. However, when you try to look at just one small village, the report is shaky.

Why? Because the survey didn't ask enough people in that specific village. It's like trying to guess the average height of a whole class by measuring just two students. If you happen to pick two basketball players, you'll think the whole class is tall. If you pick two jockeys, you'll think they are short. The answer is unreliable because the "sample size" is too small.

In Malawi, the government wants to know exactly how many teenage girls (ages 15–19) are pregnant in each of the 32 districts. This is crucial for planning schools, clinics, and support programs. But the national survey didn't interview enough girls in every single district to give a trustworthy number. Some districts had only 5 or 20 girls surveyed, making the numbers jump around wildly and look unreliable.

The Solution: The "Smart Neighbor" Method

The researchers used a statistical trick called Small Area Estimation (SAE). Think of this as a "Smart Neighbor" method.

If you want to know the average height of a specific small village, but you only measured two people, you can't trust that number alone. However, if you know that this village is next to a big city where everyone is tall, and you know the village has similar schools and poverty levels to that city, you can use that "neighbor" information to make a better guess.

The researchers did this by combining two things:

The Direct Survey: The shaky numbers they got from actually asking girls in the district.
The "Neighbor" Data (Auxiliary Variables): Reliable data from the 2018 Census about things that usually cause teenage pregnancy, such as:
- How many people live in rural areas.
- How many girls got married before age 18.
- How many households are run by women.
- How crowded the area is.

The Magic Tool: The Fay-Herriot Model

To mix these two sources of information, they used a mathematical recipe called the Fay-Herriot (FH) model.

Imagine you are baking a cake.

Ingredient A is the direct survey data (the raw flour). It's real, but it's a bit lumpy and inconsistent because there's so little of it.
Ingredient B is the Census data (the sugar and eggs). It's very smooth and consistent, but it doesn't tell you about the specific village directly.

The FH model is the mixer. It takes the lumpy flour and the smooth sugar and blends them together perfectly. It says, "Okay, the survey says 40%, but because this district has a lot of early marriages and lives in a rural area (based on the Census), the real number is probably closer to 35%."

The result is a composite estimate: a number that is still based on the real survey, but "stabilized" by the reliable Census data.

What Happened? (The Results)

The researchers tested this method and found that it worked like a charm:

Less Shaking: The direct survey numbers were jumping all over the place (some districts looked like 42% pregnant, others 13%). The new model-based numbers were much smoother and more consistent.
More Confidence: The "error bars" (the margin of doubt) got much smaller. Before, they weren't sure if a district's rate was 20% or 40%. Now, they are much more confident it's around 30%.
No Magic, Just Math: The model didn't invent new numbers. It just took the shaky survey data and "borrowed strength" from the reliable Census data to make the shaky numbers stand up straight.

Why This Matters for Malawi

Malawi is moving toward a system where local districts make their own decisions about health and education. But you can't make a good plan if your map is blurry.

Before: District leaders looked at the survey and saw wild, unreliable numbers. They didn't know where to send help.
After: They now have a clear, reliable map. They can see exactly which districts need more support for teenage pregnancy prevention.

The Bottom Line

This paper shows that when you don't have enough data for a small area, you don't have to give up. By using a smart mathematical model to combine your small survey with big, reliable census data, you can create a clear, trustworthy picture of what is happening in every district. This helps the government stop guessing and start helping the right girls in the right places.

Technical Summary: Improving the Reliability of District-Level Estimates of Teenage Pregnancy in Malawi Using Small Area Estimation

Problem Statement
Malawi is transitioning toward a decentralized decision-making system, necessitating reliable local health indicators for district-level planning and resource allocation. While national and regional estimates of teenage pregnancy are available through household surveys like the Demographic and Health Survey (DHS), direct estimates at the district level are often unreliable. This unreliability stems from small sample sizes and high sampling variability inherent in survey designs not powered for granular administrative units. Consequently, direct estimates exhibit large coefficients of variation (CV), limiting their utility for evidence-based policy and targeted interventions. The study addresses the need for a statistical framework to stabilize these estimates without losing coherence with survey-based measures.

Methodology
The study employs a model-based Small Area Estimation (SAE) approach using an area-level Fay–Herriot (FH) model to improve the precision of teenage pregnancy prevalence estimates across Malawi's 32 administrative districts.

Data Sources: The primary data comes from the 2024 Malawi Demographic and Health Survey (MDHS), focusing on females aged 15–19. Teenage pregnancy is defined as the proportion of girls in this age group who are currently pregnant or have ever experienced a pregnancy (including pregnancy loss). Auxiliary variables were derived from the 2018 Malawi Population and Housing Census and the Integrated Household Survey (IHS5).
Variable Selection: An initial pool of 18 district-level auxiliary variables was assessed. Using Least Absolute Shrinkage and Selection Operator (LASSO) regression with 10-fold cross-validation, four key predictors were selected for the final linking model:
1. Proportion of females living in rural areas.
2. Proportion of females married before age 18.
3. Proportion of female-headed households.
4. Log-transformed population density.
Statistical Model:
- Direct Estimation: Design-based direct estimators ( $\hat{p}^{DIR}_i$ ) and their sampling variances ( $\psi_i$ ) were calculated using survey weights and Taylor linearization.
- Transformation: To satisfy the linearity and normality assumptions of the FH model, a logit transformation was applied to the direct estimates, with a continuity correction (0.5) for boundary values (0 or 1).
- Fay–Herriot Model: A two-level model was constructed:
  - Sampling Model: $\hat{p}_i = p_i + e_i$ , where $e_i \sim N(0, \psi_i)$ .
  - Linking Model: $p_i = \mathbf{x}^\top_i \boldsymbol{\beta} + u_i$ , where $u_i \sim N(0, \sigma^2_u)$ represents area-specific random effects.
- Estimation: The model was fitted using Restricted Maximum Likelihood (REML) to estimate variance components. The resulting Empirical Best Linear Unbiased Predictor (EBLUP) serves as a weighted composite of the direct estimator and a regression-based synthetic estimator.
- Back-Transformation: Bias-corrected back-transformation was applied to return estimates to the original probability scale.
- Precision Assessment: Mean Squared Error (MSE) and Coefficients of Variation (CV) were estimated using a parametric bootstrap procedure (200 iterations).

Key Results

Model Performance: The linking model explained a significant portion of the between-area variability, with an adjusted $R^2$ of 0.666 and an FH-specific $R^2$ of 0.878. The estimated variance of the random effects was 0.00785 on the logit scale.
Stability and Precision: The model-based EBLUP estimates demonstrated reduced variability compared to direct survey estimates.
- Direct Estimates: Mean = 0.3070, SD = 0.0752, Range = 0.130–0.421.
- EBLUP Estimates: Mean = 0.3066, SD = 0.0628, Range = 0.151–0.385.
- The interquartile range for EBLUPs was narrower, indicating greater stability.
Error Reduction: The MSE of the EBLUP estimates was lower than that of the direct estimates in all 32 districts. The Coefficient of Variation (CV) was consistently lower for the model-based estimates across all districts, confirming a gain in efficiency.
Diagnostics: Residual analysis (Q-Q plots, Shapiro-Wilk tests) confirmed that assumptions of normality and independence were met. A strong positive correlation ( $r=0.81$ ) was observed between direct and EBLUP estimates, indicating that the model-based approach remained coherent with the survey data while reducing noise.
Specific Adjustments: The model moderated extreme direct estimates. For instance, the direct estimate for Chikwawa district decreased from 42.1% to 33.5%, while Zomba district's estimate increased from 26.3% to 32.0%, reflecting the "borrowing of strength" from auxiliary variables and neighboring areas.

Significance and Claims
The paper claims that the application of the area-level Fay–Herriot model successfully addresses the limitations of small sample sizes in district-level surveys. By integrating survey data with auxiliary census information, the study produces more stable and reliable estimates of teenage pregnancy prevalence.

The authors assert that these improved estimates provide a more robust evidence base for Malawi's decentralized health system. Specifically, the results support the planning, monitoring, and evaluation of national policies such as the National Youth Friendly Health Services Strategy and the National Strategy on Ending Child Marriage. The study concludes that SAE methods are particularly valuable in low-income settings where survey sample sizes are insufficient for direct subnational estimation, enabling more consistent targeting and allocation of reproductive health interventions. The authors note that while the model improves precision, its accuracy is dependent on the quality of auxiliary variables, and future work could extend this methodology to multivariate spatio-temporal models.