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Evaluating Technical Efficiency of Voluntary Medical Male Circumcision Service Delivery In Zambia: Data Envelopment Analysis Approach

A study of 67 Zambian health facilities using Data Envelopment Analysis reveals substantial technical inefficiency in Voluntary Medical Male Circumcision service delivery, indicating that optimizing resource utilization and management interventions could significantly increase service output without requiring additional funding.

Original authors: Nanzaluka Hatontola, Wilbroad Mutale, Chris Mweemba, Mwimba Chewe

Published 2026-06-24

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CC BY 4.0

Original authors: Nanzaluka Hatontola, Wilbroad Mutale, Chris Mweemba, Mwimba Chewe

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 Picture: A "Kitchen" Efficiency Check

Imagine Zambia has a network of 67 different kitchens (health facilities) tasked with a specific job: performing voluntary medical male circumcisions (VMMC). This is a crucial health service that helps prevent HIV transmission.

The researchers wanted to answer a simple question: Are these kitchens using their ingredients and staff to make the most meals possible?

With money for HIV programs getting tighter, the country can't just keep building more kitchens or hiring more chefs. They need to make sure the existing ones are working as hard and as smart as they can. This study used a mathematical tool called Data Envelopment Analysis (DEA) to act like a "kitchen inspector" to see which facilities are running efficiently and which ones are wasting resources.

How They Measured Efficiency (The Recipe)

To judge a kitchen, you need to look at what goes in (Inputs) and what comes out (Outputs).

The Ingredients (Inputs):

Open Days: How many days a week the kitchen is open for business.
Flyers & Visits: How often the staff went out into the community to invite people in (outreach).
Helpers: The number of community volunteers helping to organize things.

The Meals Served (Outputs):

Surgeries Performed: The total number of circumcisions done.
Follow-up Visits: The number of patients who came back to check their healing (ensuring the job was done safely).

The Findings: Who is Cooking Best?

The researchers compared all 67 kitchens against each other to find the "Best Practice Frontier"—the theoretical limit of what is possible with the current resources.

The "Half-Empty" Problem:
The study found that more than half of the facilities (about 57%) were operating at less than 50% efficiency.
- The Analogy: Imagine a bakery that has enough flour, ovens, and bakers to bake 100 loaves of bread a day, but they are only baking 40. They aren't running out of ingredients; they just aren't using them well.
The "Size" vs. "Skill" Distinction:
The researchers checked two things:
- Is the kitchen too big or too small? (Scale Efficiency).
- Is the kitchen manager doing a good job? (Technical Efficiency).
- The Result: Most kitchens were actually the right size. They weren't too big or too small. The problem wasn't the building; it was the management. The "chefs" weren't organizing the workflow, scheduling, or community outreach effectively.
The "Star Chefs" (Benchmarking):
Only a small group of facilities (about 12%) were running at 100% efficiency.
- The Analogy: One specific facility (Facility #51) was the "Star Chef." It appeared as the role model for 21 other struggling facilities. This means Facility #51 figured out how to get the most done with the same amount of ingredients. The other kitchens could learn exactly how to do this by copying Facility #51's methods.

Why Are Some Kitchens Struggling?

The paper suggests two main reasons for the low efficiency:

Internal Messiness: The way services are organized, how staff time is used, and how volunteers are coordinated could be improved.
Empty Seats: Some kitchens might have great staff and open hours, but not enough people are walking through the door. This isn't necessarily the kitchen's fault; it could be because the community doesn't know about the service, or people are afraid to come.

The Bottom Line

The study concludes that Zambia doesn't necessarily need to spend more money to get more circumcisions done. Instead, they need to reorganize.

The Solution: The struggling facilities should look at the "Star Chefs" (the efficient ones) and copy their playbook. If they can fix their management and coordination, they could likely double their output without hiring a single new person or buying new equipment.

In short: The engines are there, the fuel is there, but the drivers need to learn how to drive better.

Technical Summary: Evaluating Technical Efficiency of Voluntary Medical Male Circumcision Service Delivery in Zambia

Problem Statement
Despite Voluntary Medical Male Circumcision (VMMC) being a proven intervention that reduces female-to-male HIV transmission by 50–60%, coverage in Zambia remains below the 80% target. As global donor funding stabilizes and Zambia assumes greater financial responsibility for its HIV response, maximizing the utility of existing resources is critical. While multi-country studies have highlighted wide variations in VMMC unit costs and the potential for efficiency gains through task shifting and integration, no systematic assessment had previously evaluated the technical efficiency of VMMC service delivery at the facility level in Zambia. This study addresses the gap by quantifying how efficiently Zambian health facilities convert available inputs into service outputs.

Methodology
The study employed a cross-sectional quantitative design using secondary data from the Global Fund TB/HIV 2023 survey, covering 67 health facilities across all ten Zambian provinces that provided VMMC services in 2022. The analysis utilized Data Envelopment Analysis (DEA), a non-parametric linear programming technique, to measure the relative technical efficiency of each facility (treated as Decision-Making Units or DMUs).

Model Orientation: An input-oriented model was selected to align with the policy objective of minimizing inputs required to achieve a given level of service output in a resource-constrained setting.
Models Estimated:
- Constant Returns to Scale (CRS; CCR model): Measures overall technical efficiency, combining managerial competence and scale effects.
- Variable Returns to Scale (VRS; BCC model): Measures pure technical efficiency (PTE), isolating managerial ability from scale effects.
- Scale Efficiency (SE): Calculated as the ratio of CRS to VRS scores to determine if facilities are operating at an optimal size.
Variables:
- Inputs: Number of days per week VMMC services were offered ( $X_1$ ), frequency of outreach activities ( $X_2$ ), and the number of community-based volunteers assigned ( $X_3$ ).
- Outputs: Total number of circumcisions performed ( $Y_1$ ) and the number of post-operative follow-up visits completed ( $Y_2$ ).
Analysis: Statistical analyses were performed using R version 4.5.1 and the rDEA package. Benchmarking analysis identified efficient facilities forming the production frontier to serve as peer comparators for inefficient units.

Key Results
The analysis of 67 facilities revealed substantial technical inefficiency in VMMC service delivery:

Service Volume: Facilities performed a mean of 584 circumcisions (median = 298) and 486 follow-up visits (median = 168) annually, with high variability across sites.
Technical Efficiency (VRS): Under the Variable Returns to Scale model, which isolates managerial performance, 38 facilities (56.7%) scored below 0.50, indicating they were operating at less than half the potential output of their inputs. Only 14 facilities (20.9%) achieved full efficiency (score = 1.00).
Technical Efficiency (CRS): The Constant Returns to Scale model showed even greater inefficiency, with 45 facilities (67.2%) scoring below 0.50 and only 8 facilities (11.9%) achieving full efficiency.
Scale Efficiency: In contrast to technical efficiency, scale efficiency was relatively high. 55 facilities (82.1%) scored between 0.50 and 0.99, and only 4 facilities (6.0%) scored below 0.50. This indicates that the majority of facilities are operating at an appropriate size, and the primary source of inefficiency is not scale-related but rather managerial or operational.
Benchmarking: Thirteen facilities appeared in the efficiency reference sets. Facility 51 was the most influential benchmark, serving as a peer target for 21 other facilities, followed by Facility 68 (18 references). This suggests that best practices are localized within a small cluster of high-performing sites.

Key Contributions

First Facility-Level DEA in Zambia: This study provides the first systematic, facility-level assessment of technical efficiency for VMMC services in Zambia.
Decomposition of Inefficiency: By comparing CRS and VRS scores, the study distinguishes between managerial inefficiency and scale inefficiency, finding that the former is the dominant driver of underperformance.
Identification of Benchmarks: The study identifies specific high-performing facilities that serve as realistic, domestically grounded targets for underperforming sites, moving beyond theoretical ideals to practical peer comparisons.

Significance and Claims
The paper claims that VMMC service delivery in Zambia is characterized by suboptimal resource utilization driven by operational and managerial factors rather than inappropriate facility size or infrastructure shortages.

The authors assert that significant improvements in VMMC output can be achieved without additional resource investment by:

Reorganizing service delivery based on the operational models of the identified efficient facilities.
Targeting management interventions at underperforming facilities to improve the conversion of inputs (service days, outreach, volunteers) into outputs (procedures, follow-ups).
Utilizing peer learning mechanisms, such as exchange visits and mentorship from the identified benchmark facilities (e.g., Facility 51 and 68).

The study concludes that Data Envelopment Analysis is a valuable tool for identifying performance gaps and guiding evidence-based resource allocation, particularly as Zambia transitions toward greater domestic financing of its HIV response. The findings suggest that the "low-hanging fruit" for increasing coverage lies in optimizing existing systems rather than expanding physical capacity.