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Application of Propensity Score Methods to Address Missing Data in a Trial on the Effect of Energy Protein Supplementation Among Pulmonary TB-HIV Patients in Mwanza, Tanzania

This study evaluated propensity score inverse probability weighting (PS-IPW) and multiple imputation (MI) against complete case analysis for handling monotonic missing data in a pulmonary TB-HIV supplementation trial in Tanzania, finding that while both advanced methods outperformed traditional analysis in bias and efficiency, none revealed statistically significant treatment effects.

Original authors: Auson B. Magige, Benson Kidenya, Jeremiah Kidola, Eveline Konje, Jim Todd, Farida Iddi Mkassy, Neema Mosha

Published 2026-06-28

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CC BY 4.0

Original authors: Auson B. Magige, Benson Kidenya, Jeremiah Kidola, Eveline Konje, Jim Todd, Farida Iddi Mkassy, Neema Mosha

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 Nutrition Experiment with a Missing Puzzle

Imagine a group of researchers in Mwanza, Tanzania, trying to figure out if giving extra "energy-protein" cookies to people suffering from both Tuberculosis (TB) and HIV helps them get stronger and gain weight.

They set up a fair test (a clinical trial) with 354 patients. Half got a big, nutritious daily snack (the Intervention Group), and the other half got a tiny, plain biscuit (the Control Group). They checked their weight, arm size, and hand strength at the start, after two months, and after five months.

The Problem:
Just like a game of musical chairs where some people leave the room before the music stops, many patients dropped out of the study before it ended. By the five-month mark, about 19% of the participants were missing. This left the researchers with a puzzle: How do you calculate the final results when a big chunk of the puzzle pieces is missing?

If you just ignore the missing people (a method called Complete Case Analysis or CCA), you might be looking at a distorted picture. Maybe the people who dropped out were the ones who felt the worst, or maybe they were the ones who felt the best. If you don't account for this, your conclusion could be wrong.

The Three Tools Used to Fix the Missing Pieces

To solve this "missing puzzle" problem, the researchers tried three different mathematical tools to see which one gave the most honest answer.

1. The "Ignore the Missing" Method (Complete Case Analysis - CCA)

The Analogy: Imagine you are judging a race, but 20 runners quit halfway. This method says, "Let's only count the runners who finished the whole race."
The Flaw: If the runners who quit were the slowest ones, you might think the race was faster than it really was. If they were the fastest, you might think it was slower. It's risky because it assumes the missing people were just like the ones who stayed.

2. The "Fill in the Blanks" Method (Multiple Imputation - MI)

The Analogy: Imagine you have a crossword puzzle with missing words. Instead of leaving them blank, you look at the clues from the words you do have and make your best guess to fill in the empty squares. You do this many times (20 times!) with slightly different guesses to see how the answer changes.
The Logic: This method assumes that if we know a person's age, job, and how they felt at the start, we can make a smart guess about what their weight would have been at the end. It fills in the missing data based on patterns it sees in the data that is there.

3. The "Weighted Scale" Method (Propensity Score Inverse Probability Weighting - PS-IPW)

The Analogy: Imagine you are weighing a bag of apples, but some apples are missing. Instead of guessing what the missing apples weigh, you look at the apples you do have. If you notice that the apples you have are mostly small ones, you give the small apples "extra weight" on the scale to represent the missing big ones.
The Logic: This method calculates the "probability" of a person dropping out based on their background. If a person with a specific profile (e.g., a farmer with low weight) was likely to drop out, the researchers give the data from the few farmers who stayed extra importance (weight) to represent the ones who left.

What Did They Find?

After running the numbers with all three methods, the results were surprisingly consistent:

No Magic Bullet: Whether they ignored the missing people, filled in the blanks, or used the weighted scale, the answer was the same. The special energy-protein cookies did not significantly help patients gain weight, grow their arm muscles, or get stronger compared to the plain biscuits.
The "Missing" Pattern: The researchers found that the missing data wasn't random (like people just forgetting to show up). It followed a pattern: people who were missing at the end were often similar to people who were missing earlier. This confirmed that the "Fill in the Blanks" (MI) and "Weighted Scale" (PS-IPW) methods were the right tools to use, as they are better at handling these specific patterns than just ignoring the missing people.
A Glimmer of Hope: While the weight and arm size didn't change much, there was a small, consistent trend that hand strength improved slightly in the group that got the big cookies. However, this improvement wasn't strong enough to be called a "statistical victory" (it could have been luck).

The Conclusion

The study concludes that for these specific patients in Tanzania, a short-term boost of energy-protein snacks didn't make a huge difference in their physical recovery.

The Big Lesson for Science:
The most important takeaway isn't just about the cookies; it's about how to handle missing data. The researchers showed that ignoring missing people (CCA) is risky. Using smarter methods like filling in the blanks (MI) or weighting the remaining data (PS-IPW) gives a more accurate and fair picture, even if the final answer is "the treatment didn't work."

In short: The cookies didn't work, but the math used to figure that out was solid and reliable.

Technical Summary: Application of Propensity Score Methods to Address Missing Data in a Trial on Energy-Protein Supplementation Among PTB-HIV Patients

Problem Statement
Missing data is a pervasive challenge in clinical research, particularly in resource-limited settings with high patient attrition rates, such as trials involving Pulmonary Tuberculosis (PTB) and HIV co-infected patients. In the specific context of a randomized controlled trial (RCT) conducted in Mwanza, Tanzania, assessing energy-protein supplementation, attrition rates reached 12.2% at two months and 19.1% at five months. Traditional methods for handling missing data, such as Complete Case Analysis (CCA) or single imputation techniques (e.g., Last Observation Carried Forward), often rely on assumptions (like Missing Completely at Random, MCAR) that rarely hold in real-world clinical scenarios. When these assumptions are violated, estimates of treatment effects can become biased, compromising the internal validity of the trial. While Multiple Imputation (MI) and Propensity Score (PS) methods, specifically Inverse Probability Weighting (IPW), offer more robust alternatives, there is a need for empirical comparison of their performance in high-attrition clinical trials where Missing Not at Random (MNAR) mechanisms are suspected.

Methodology
This study performed a secondary data analysis of a previously published RCT involving 354 PTB-HIV co-infected participants randomized to receive either energy-protein supplementation (intervention) or a control supplement. The study aimed to evaluate the impact of supplementation on weight, arm circumference, and handgrip strength at 2 and 5 months.

The analytical approach involved three distinct phases:

Missing Data Characterization: The pattern and mechanism of missingness were assessed using Little's MCAR test and binary logistic regression. Missingness indicators were regressed against baseline covariates and prior outcome values to determine if data were MCAR, Missing at Random (MAR), or MNAR.
Comparative Analysis of Handling Methods: Three analytical strategies were applied to the dataset:
- Complete Case Analysis (CCA): A linear regression model assuming MCAR, excluding any participant with missing outcome data.
- Multiple Imputation (MI): Utilizing Multiple Imputation by Chained Equations (MICE) with 20 imputations and predictive mean matching, assuming a MAR mechanism.
- Propensity Score Inverse Probability Weighting (PS-IPW): A logistic regression model estimated the probability of having observed data (propensity score) based on baseline covariates. Stabilized weights were generated and applied to a weighted regression model to correct for systematic differences between those with and without observed outcomes.
Performance Evaluation and Sensitivity Analysis: The effectiveness of PS-IPW and MI was compared against CCA using Mean Squared Error (MSE), Bias, and Relative Efficiency (RE). To assess robustness against violations of the MAR assumption, a sensitivity analysis was conducted using a pattern-mixture model under MNAR scenarios, applying delta values (0, -0.5, -1, -2) to simulate progressively worse unobserved outcomes.

Key Results

Missing Data Mechanism: The missing data followed a monotonic pattern, increasing over time. Statistical tests rejected the MCAR assumption ( $p < 0.001$ ). Logistic regression indicated that missingness at 5 months was associated with values at 2 months, supporting a MAR mechanism with little evidence of MNAR.
Treatment Effects: Across all three methods (CCA, MI, and PS-IPW), the energy-protein supplementation showed no statistically significant effects on weight, arm circumference, or handgrip strength at either 2 or 5 months.
- At 5 months, CCA showed a non-significant weight reduction of 0.75 kg ( $p=0.145$ ).
- MI estimated a weight decline of 0.78 kg ( $p=0.107$ ).
- PS-IPW estimated a weight decline of 0.70 kg ( $p=0.181$ ).
- Similar non-significant trends were observed for arm circumference and grip strength, though grip strength showed a consistent positive direction of effect across methods.
Methodological Performance:
- Bias and Efficiency: Both MI and PS-IPW generally outperformed CCA in terms of bias reduction and efficiency. MI demonstrated higher relative efficiency (lower MSE) across most outcomes, while PS-IPW provided more stable bias control for specific outcomes (e.g., weight and grip strength).
- Sensitivity: The MNAR sensitivity analysis revealed that results remained stable under mild to moderate departures from MAR, reinforcing the robustness of the primary findings.

Significance and Claims
The paper claims that while the specific intervention (short-term energy-protein supplementation) did not yield statistically significant improvements in the measured anthropometric and functional outcomes for PTB-HIV patients in this setting, the methodological approach offers critical insights for clinical trial analysis.

Validation of Robust Methods: The study demonstrates that in high-attrition trials, robust missing data handling strategies (MI and PS-IPW) are superior to traditional CCA. These methods reduce bias and improve precision, ensuring that conclusions are not distorted by the exclusion of incomplete cases.
Consistency of Findings: The concordance of results across CCA, MI, and PS-IPW suggests that the lack of significant treatment effect is a genuine finding rather than an artifact of missing data handling. The similarity in effect estimates indicates that missingness did not substantially bias the main conclusions.
Contextual Relevance: The findings align with broader evidence suggesting that nutritional support alone may yield limited or mixed effects on clinical outcomes in TB-HIV populations, potentially due to the short duration of the intervention or persistent catabolic stressors.
Methodological Contribution: By empirically comparing PS-IPW and MI in a real-world clinical trial context, the study underscores the importance of moving beyond CCA. It highlights that while MI may offer greater efficiency, PS-IPW provides valuable bias control, advocating for the use of complementary methods to ensure valid conclusions in global health research.

The authors conclude that future research in this population should incorporate longer-term interventions and integrated social support, while strictly adhering to robust statistical plans for handling missing data to maintain the integrity of clinical trial results.