High-Resolution District Level Contraceptive Prevalence in Pakistan Using a Bayesian Small Area Estimation Approach

This study employs a two-stage Bayesian small area estimation framework that integrates routine commodity data, census figures, and national survey benchmarks to generate high-resolution, statistically robust district-level estimates of contraceptive prevalence in Pakistan, thereby addressing data gaps and enabling more targeted family planning interventions.

The Gist

Imagine you are trying to bake a giant cake for a whole country, but you only have a recipe that tells you how much sugar to use for the entire country or for each province. You don't know how much sugar the specific neighborhood in the city needs, or the tiny village in the mountains. If you just guess based on the big numbers, some neighborhoods might get a cake that's too sweet, while others get a bland, dry mess.

This is exactly the problem the researchers in this paper faced with family planning in Pakistan.

The Problem: The "Blurred Map"

For years, Pakistan has had great surveys that tell them how many women use birth control at the national level or the provincial level (like Punjab or Sindh). But these surveys are like looking at the country through a foggy window. They give a good average, but they hide the details.

• The Reality: In one city district, almost half the women might use birth control. In a neighboring rural district, it might be only 10%.
• The Issue: If the government only looks at the "Provincial Average," they might send too many supplies to the city (where they aren't needed as much) and not enough to the rural area (where people are desperate for them).

They also have "logistics data" (records of how many pills and condoms were shipped to districts), but this data is messy. It's like a delivery driver's notebook that has scribbles, missing pages, and counts boxes instead of actual people using them. It's noisy and unreliable on its own.

The Solution: The "Smart Detective" (Bayesian Small Area Estimation)

The authors created a clever statistical tool called a Bayesian Small Area Estimation (SAE) model. Think of this model as a super-smart detective who solves the mystery of "Who is using birth control where?" by combining three different clues:

1. The Big Picture Clue (Surveys): The reliable but blurry national/provincial averages.
2. The Supply Clue (Logistics): The messy delivery records of how many condoms and pills were sent to each district.
3. The Context Clue (Census & Demographics): Information about the people living there (education levels, income, how many women are of childbearing age).

How the Detective Works:
Imagine the detective is trying to guess the birth control usage in a remote village where the delivery records are missing.

• The detective looks at the Provincial Average (Clue 1) to get a baseline.
• Then, they look at the Village's characteristics (Clue 3). If the village has high poverty and low education, the detective knows usage is likely lower than the average. If it's a wealthy, educated city, usage is likely higher.
• Finally, they check the Delivery Records (Clue 2). Even if the records are messy, if they show a sudden spike in pill shipments to that village, the detective adjusts their guess.

By "borrowing strength" from the reliable data of neighboring areas and the known characteristics of the village, the detective can make a very educated guess for every single district, even the ones with bad data.

What They Found: The Hidden Inequalities

Once the detective finished the work, they produced a high-resolution map of Pakistan with 121 districts. The results were eye-opening:

• The Gap is Huge: The difference between the best district and the worst district was massive. Some districts had a usage rate of 46%, while others were as low as 8%.
• Urban vs. Rural: Cities like Karachi and wealthy parts of Punjab had high usage. Remote, mountainous, or very poor rural areas had very low usage.
• The "Fog" Lifted: The old provincial averages were hiding these huge gaps. The new map shows exactly where the "blind spots" are.

Why This Matters

This isn't just about math; it's about saving lives and helping families.

• Before: The government was like a doctor prescribing the same medicine to every patient in a hospital, regardless of their specific illness.
• Now: They have a detailed chart showing exactly which "patient" (district) needs more help.

If a district has low usage but high poverty, the government knows they need to build better roads and schools first. If a district has high demand but no supplies, they know to send more trucks immediately.

The Bottom Line

The researchers took messy, incomplete data and used a smart statistical "recipe" to create a clear, detailed map of family planning in Pakistan. They turned a blurry, low-resolution photo into a high-definition picture, allowing leaders to stop guessing and start helping the specific communities that need it most. It's a way to make sure no one is left in the dark.

Technical Summary

1. Problem Statement

National and provincial surveys in Pakistan (such as the Pakistan Social and Living Standards Measurement Survey - PSLM, and the Demographic and Health Survey - DHS) provide reliable data on Contraceptive Prevalence Rate (CPR) but lack district-level granularity.

• The Gap: Provincial averages mask significant local heterogeneity, obscuring geographic inequities and hindering targeted public health planning.
• Data Limitations: While administrative data (specifically the Contraceptive Logistics Management Information System, cLMIS) is available at the district level, it is rarely used for prevalence estimation due to concerns regarding reporting completeness, measurement error, lack of private-sector coverage, and the absence of direct user counts (it tracks supply/dispensation, not users).
• Need: There is a critical need for a methodology that can statistically integrate sparse survey benchmarks with noisy administrative supply data to generate high-resolution, statistically coherent district-level estimates.

2. Methodology

The study employs a two-stage Bayesian Small Area Estimation (SAE) framework to generate estimates for 121 districts across Pakistan.

Data Sources

The model integrates four complementary data sources:

1. PSLM (2018-19): Provides provincial-level CPR and modern CPR (mCPR) benchmarks.
2. cLMIS (2020): Provides district-level contraceptive dispensation data (supply side).
3. PSLM (2019-20): Provides district-level socioeconomic covariates (education, income, sectoral composition).
4. 2023 Population Census: Provides demographic denominators (Married Women of Reproductive Age - MWRA).

Stage 1: Crude District Estimates

• Conversion: cLMIS dispensation data is converted into estimated "users" using method-specific conversion factors.
• Normalization: Users are normalized by district MWRA counts.
• Scaling: District-level ratios are adjusted to align with provincial PSLM benchmarks.
• Uncertainty Quantification: Standard errors are calculated by combining provincial sampling uncertainty with within-province variability. To prevent over-constraint, minimum standard error thresholds (1.5% for CPR, 2.0% for mCPR) are imposed.

Stage 2: Hierarchical Bayesian Model

A bivariate hierarchical Bayesian model is constructed to jointly estimate CPR and mCPR, borrowing strength across districts and provinces.

• Model Structure:
  • Linear Predictors: Logit-scale models incorporating fixed effects (covariates: education index, income index, fertility rate <25, agriculture/manufacturing proportions) and random effects (province-specific).
  • Bivariate Joint Estimation: The model estimates overall CPR and mCPR simultaneously, allowing for cross-indicator information borrowing while constraining the correlation between provincial random effects to near zero to maintain distinct patterns for traditional vs. modern methods.
• Measurement Error Modeling: The cLMIS data is treated as a noisy proxy. The model uses a dual proxy structure with:
  • Elasticity Parameters: Allowing deviation from unit elasticity between supply and prevalence.
  • Heteroskedastic Errors: Error variance is modeled as a function of district characteristics (e.g., higher error in agricultural/rural districts, lower in industrial/urban districts).
  • Robustness: Errors follow a t-distribution to handle outliers.
• Constraints:
  • Provincial Anchoring: District estimates are constrained so that MWRA-weighted aggregates match PSLM provincial benchmarks.
  • Soft Constraints: Modern CPR is centered on province-specific ratios relative to overall CPR to ensure demographic plausibility.

Validation

• Internal: Demographic coherence checks, sectoral correlation validation, and proxy model fit ($r > 0.7$).
• External: Comparison with independent district-level surveys (Mean Absolute Deviation $\approx$ 4 percentage points) and aggregation checks against PSLM benchmarks (difference $\leq$ 0.6 percentage points).

3. Key Contributions

• Methodological Innovation: Moves beyond treating administrative data as mere covariates; instead, it treats logistics data as a primary signal while explicitly modeling its measurement error via a heteroskedastic proxy structure.
• Bivariate Framework: Introduces a joint estimation approach for CPR and mCPR, improving stability in data-sparse districts without conflating traditional and modern method patterns.
• High-Resolution Output: Generates the first statistically coherent, district-level estimates for 121 districts in Pakistan, covering areas previously unmeasured or reliant on outdated snapshots.
• Dynamic Monitoring Pathway: Demonstrates a replicable framework for shifting from episodic survey-based assessment to routine, dynamic monitoring using administrative data.

4. Key Results

• Estimates:
  • CPR Range: 8.6% (Dera Bugti) to 46.0% (Rawalpindi/Jhelum).
  • mCPR Range: 6.0% (Dera Bugti) to 35.4% (Central Karachi).
  • National Median: CPR 28.9%, mCPR 20.2%.
• Geographic Disparities:
  • High Prevalence: Concentrated in North-Eastern Punjab (urbanized, educated) and Karachi districts.
  • Low Prevalence: Found in Southern Punjab, interior Sindh, mountainous/merged districts of Khyber Pakhtunkhwa (KP), and uniformly low across Balochistan.
• Model Performance:
  • Convergence: Excellent diagnostics ($R$-hat $\leq$ 1.003, high ESS, no divergent transitions).
  • Validation: Aggregated provincial estimates differed from PSLM benchmarks by only 0.1–0.6 percentage points.
  • External Validation: 8 out of 12 districts compared to independent literature showed deviations under 5 percentage points.
• Uncertainty: Confidence intervals were narrower (3–5%) in data-rich urban districts and wider (7–8%) in remote, data-sparse districts (e.g., Balochistan, merged KP), correctly reflecting data quality.

5. Significance and Policy Implications

• Targeted Interventions: The granular data reveals that provincial averages mask localized disadvantage. Policymakers can now distinguish between districts needing service-delivery optimization (moderate capacity, low use) versus those requiring broader infrastructure and social investments (structurally disadvantaged).
• Resource Allocation: Enables evidence-based prioritization of underserved districts, moving away from "one-size-fits-all" provincial planning.
• Scalability: The framework offers a cost-effective solution for Low- and Middle-Income Countries (LMICs) to generate subnational health indicators without waiting for expensive, large-scale household surveys.
• SDG Alignment: Directly supports Sustainable Development Goal 3 (Good Health and Well-Being) by improving the monitoring of reproductive health indicators in data-constrained environments.

Limitations Noted: The model relies on supply-side data (missing private sector/traditional methods), uses Census denominators (potential local misreporting), and anchors to PSLM benchmarks (inheriting any provincial-level survey bias). However, the integrated approach is deemed superior to single-source estimates.