Round 105

Handling Ambiguous Missing Data in Health Studies

A longitudinal study on lifestyle interventions and cardiovascular health is missing 15% of its 'Physical Activity' data points. Missingness is not entirely random; participants with higher BMI were less likely to sync their wearable devices. We must decide on a primary imputation and handling strategy for the final analysis. The goal is to maximize statistical power without introducing systematic bias or overstating the certainty of the findings. The final report will influence public health guidelines, making transparency and robustness critical.

Dashboard

Status

DECIDED

Winner

B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR).

Majority

B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR).

Duration

10695 ms

Topic

Options

B Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR).
1.91 of 3 PPV winner
C Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself.
1.09 of 3
A Adopt a 'Worst-Observation-Carried-Forward' approach for missing values to ensure the intervention's efficacy is not overstated, prioritizing conservative estimates for public safety.
0.00 of 3
D Execute a Maximum Likelihood Estimation (MLE) within a structural equation framework to utilize all available data without generating synthetic individual data points.
0.00 of 3
E Perform a Complete Case Analysis but apply Inverse Probability Weighting (IPW) to adjust for the bias of participants excluded due to non-syncing.
0.00 of 3

Checks

Baselines

PPV no gold answer
Majority no gold answer
Comparison PPV matched majority
k samples8
Agents3
Parsed samples 24 / 24
Quality split agent disagreement

PPV

Top Influences

Claude Sonnet 5 · delegate 1.332
GPT 5.4 mini · delegate 1.332
Gemini 3 Flash Preview · delegate 1.236

Samples

Answer Distribution

Claude Sonnet 5 C: 7 B: 1
GPT 5.4 mini B: 7 C: 1
Gemini 3 Flash Preview B: 4 C: 4

PPV

Influences

Label Role Score
Claude Sonnet 5 delegate 1.332
GPT 5.4 mini delegate 1.332
Gemini 3 Flash Preview delegate 1.236

Voting matrix

Constructed Delegation Matrix

To / From Claude Sonnet 5 GPT 5.4 mini Gemini 3 Flash Preview
Claude Sonnet 5 0.0000.1060.182
GPT 5.4 mini 0.1060.0000.182
Gemini 3 Flash Preview 0.1060.1060.000
A 0.0000.0000.000
B 0.0000.7890.637
C 0.7890.0000.000
D 0.0000.0000.000
E 0.0000.0000.000

Embeddings

Sample Embeddings

24 samples
Claude Sonnet 5 sample #0 · C · 1536 dims C Claude Sonnet 5 sample #1 · C · 1536 dims C Claude Sonnet 5 sample #2 · C · 1536 dims C Claude Sonnet 5 sample #3 · C · 1536 dims C Claude Sonnet 5 sample #4 · C · 1536 dims C Claude Sonnet 5 sample #5 · B · 1536 dims B Claude Sonnet 5 sample #6 · C · 1536 dims C Claude Sonnet 5 sample #7 · C · 1536 dims C GPT 5.4 mini sample #0 · B · 1536 dims B GPT 5.4 mini sample #1 · B · 1536 dims B GPT 5.4 mini sample #2 · B · 1536 dims B GPT 5.4 mini sample #3 · C · 1536 dims C GPT 5.4 mini sample #4 · B · 1536 dims B GPT 5.4 mini sample #5 · B · 1536 dims B GPT 5.4 mini sample #6 · B · 1536 dims B GPT 5.4 mini sample #7 · B · 1536 dims B Gemini 3 Flash Preview sample #0 · B · 1536 dims B Gemini 3 Flash Preview sample #1 · C · 1536 dims C Gemini 3 Flash Preview sample #2 · C · 1536 dims C Gemini 3 Flash Preview sample #3 · B · 1536 dims B Gemini 3 Flash Preview sample #4 · B · 1536 dims B Gemini 3 Flash Preview sample #5 · B · 1536 dims B Gemini 3 Flash Preview sample #6 · C · 1536 dims C Gemini 3 Flash Preview sample #7 · C · 1536 dims C
Claude Sonnet 5 GPT 5.4 mini Gemini 3 Flash Preview

Samples

Agent Responses

Claude Sonnet 5 openai_compatible · anthropic/claude-sonnet-5
#0 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

The missingness mechanism described—where higher BMI (which itself may be correlated with lower physical activity) predicts non-syncing—suggests the missingness may depend on the unobserved outcome itself, making a naive MAR assumption risky. A Pattern-Mixture...

#1 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

The missingness depends on BMI, which is related to the likelihood of syncing devices, but since Physical Activity itself (the variable with missing data) directly influences syncing behavior, this suggests the missingness mechanism is tied to the unobserved v...

#2 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

The missingness mechanism described—where higher BMI participants (likely correlated with lower physical activity) are less likely to sync devices—suggests the missingness is tied to the unobserved values themselves, indicating Missing Not At Random (MNAR) rat...

#3 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

The scenario describes missingness linked to BMI, which likely also correlates with the actual physical activity levels themselves—meaning the missingness mechanism is plausibly Non-Ignorable (MNAR) rather than simply MAR. Since assuming MAR (as in MICE, optio...

#4 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

The scenario describes missingness linked to BMI, which is highly correlated with the very variable being measured (Physical Activity), suggesting the missingness mechanism may depend on the unobserved outcome itself rather than being fully explained by observ...

#5 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

The mechanism described—non-syncing linked to BMI, an observed covariate—fits the definition of Missing at Random (MAR), since the missingness can be explained by measured variables rather than the unobserved outcome itself. Multiple Imputation by Chained Equa...

#6 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

The missingness mechanism described (BMI-related non-syncing) suggests the probability of missing data may be linked to the unobserved physical activity values themselves, not just observed covariates, making a strict MAR assumption (as in MICE) risky and pote...

#7 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

The missingness mechanism is plausibly linked to the outcome itself (physical activity) rather than purely to observed covariates like BMI, making a naive MAR assumption risky. Given the explicit ambiguity and the stated goal of transparency/robustness for pub...

GPT 5.4 mini openai_compatible · openai/gpt-5.4-mini
#0 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

The missingness is related to BMI, which is observed and can be included in the imputation model, so the most appropriate primary approach is one that assumes MAR and uses available predictors to recover the missing values efficiently. MICE is standard here be...

#1 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

Because missingness is related to BMI, the data are not plausibly Missing Completely at Random, so a simple complete-case approach is risky. For a primary imputation strategy, MICE is appropriate if we can justify Missing at Random by including BMI, demographi...

#2 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

Because missingness is related to BMI, it is likely not completely random and may be only plausibly MAR after conditioning on observed covariates like BMI and other clinical factors. Multiple Imputation by Chained Equations (MICE) is a standard primary approac...

#3 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

Because missingness is related to higher BMI, it is likely not completely random and may even be missing not at random, so a conservative strategy should explicitly probe that assumption. The best primary approach among the choices is a pattern-mixture model, ...

#4 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

Because missingness is related to BMI, it is not completely random, but it may still be reasonable to assume it is MAR if BMI and other observed covariates are included in the imputation model. Multiple Imputation by Chained Equations (MICE) preserves statisti...

#5 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

The missingness is related to higher BMI, so it is not completely random and may be plausibly handled under MAR if BMI and related covariates are included in the imputation model. Multiple Imputation by Chained Equations uses available demographic and clinical...

#6 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

The missingness is related to BMI, a measured covariate, so a Missing at Random strategy is reasonable if we condition on observed demographic and clinical variables. Multiple Imputation by Chained Equations uses those predictors to recover power while reducin...

#7 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

Because missingness is related to BMI, it is not completely random, so a simple complete-case approach would likely bias the results. The best primary strategy to maximize power while handling plausible MAR is Multiple Imputation by Chained Equations using ava...

Gemini 3 Flash Preview openai_compatible · google/gemini-3-flash-preview
#0 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

The study exhibits a bias where missingness is correlated with a measured variable (BMI), suggesting a Missing at Random (MAR) mechanism. Multiple Imputation by Chained Equations (MICE) is the standard statistical approach to handle such scenarios by using cor...

#1 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

The data exhibits a non-random pattern where missingness is correlated with BMI, suggesting the missingness may be "Non-Ignorable" (MNAR) if physical activity levels directly influenced the failure to sync devices. A Pattern-Mixture Model allows the researcher...

#2 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

The scenario indicates that missingness is tied to BMI, which is likely correlated with the missing 'Physical Activity' levels, suggesting the data may be Missing Not at Random (MNAR). While MICE (B) and MLE (D) are common for Missing at Random data, a Pattern...

#3 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

The scenario describes a Missing at Random (MAR) or potentially Missing Not at Random (MNAR) situation where missingness is correlated with BMI and device usage. Multiple Imputation by Chained Equations (MICE) is the standard best practice for handling MAR dat...

#4 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

The scenario suggests a "Missing at Random" (MAR) or "Missing Not at Random" (MNAR) mechanism because missingness is correlated with BMI and likely the activity level itself. Multiple Imputation (B) effectively handles MAR by using correlates like BMI to reduc...

#5 B · Apply Multiple Imputation by Chained Equations (MICE) using demographic and clinical correlates to fill gaps, assuming data is Missing at Random (MAR). 1536 dims

The scenario describes a Missing at Random (MAR) or potentially Missing Not at Random (MNAR) situation where missingness is correlated with BMI and device usage behavior. Multiple Imputation by Chained Equations (MICE) is the standard robust approach for MAR d...

#6 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

The data exhibit a non-random pattern where missingness is correlated with BMI, suggesting that if BMI and physical activity are related, the missingness may be Non-Ignorable (MNAR). While Multiple Imputation (B) or IPW (E) address systematic differences, they...

#7 C · Utilize a Pattern-Mixture Model to perform a sensitivity analysis that explicitly accounts for Non-Ignorable Missingness (MNAR), acknowledging that the reason for missingness is tied to the variable itself. 1536 dims

The data demonstrates a clear non-random pattern where missingness is correlated with BMI, suggesting that the missingness mechanism may be related to the unobserved underlying physical activity levels (MNAR). Using a Pattern-Mixture Model allows for a robust ...

Timings

Stages

Sampling10129 ms
Embedding560 ms
Signals6 ms
PPV0 ms

Errors

Agent and Round Errors

No errors recorded.