A comparative review of methods for comparing means using partially paired data

Area of Science:

• Biostatistics
• Medical Research Methodology
• Statistical Analysis

Background:

• Medical experiments frequently involve partially paired data due to design or missing observations.
• Partially paired data combines both paired and unpaired observations, complicating standard statistical analysis.
• Accurate analysis of partially paired data is crucial for valid medical research findings.

Purpose of the Study:

• To review and compare nine distinct statistical methods for analyzing partially paired data.
• To evaluate the performance of these methods across various simulation scenarios.
• To provide recommendations for appropriate analysis techniques based on data characteristics.

Main Methods:

• Reviewed nine methods: two-sample t-test, paired t-test, corrected z-test, weighted t-test, pooled t-test, optimal pooled t-test, multiple imputation, mixed model, and modified maximum likelihood estimate.
• Conducted extensive simulation studies varying effect sizes, sample sizes, correlations, and data distributions.
• Compared method performance based on type I error rates and statistical power.

Main Results:

• For moderate sample sizes with normally distributed data, the modified maximum likelihood estimator showed superior performance.
• When data were not normally distributed, the optimal pooled t-test demonstrated the best performance with controlled type I error and high power.
• For small sample sizes, the optimal pooled t-test is recommended for data with missing values in both variables, and the paired t-test for data with missing values in only one variable.

Conclusions:

• The choice of statistical method significantly impacts the analysis of partially paired data.
• Modified maximum likelihood and optimal pooled t-test are robust choices under specific conditions (data distribution, sample size, missingness patterns).
• Simulation results guide the selection of appropriate methods for reliable medical data analysis.