Bayesian Multiple Imputation Using Fully Conditional Specification for Handling Missing Values in Lung Cancer Data

Abstract

Missing values in medical datasets can reduce statistical efficiency and introduce bias. This study applied Bayesian multiple imputation within the Fully Conditional Specification (FCS) framework and assessed its numerical stability. The data comprised 132 lung cancer patient records collected at Karsa Husada Hospital, Batu, between 2020 and 2025. The variables included age, sex, smoking status, comorbidity, family history, and lung cancer stage. Cancer stage was missing for 42.42% of patients (56/132). Associations between missingness indicators and observed variables were examined using χ² tests for categorical variables and independent t-tests for age. No statistically significant associations were detected (p > 0.05). These findings provided no evidence against MCAR for the variables examined but did not establish MCAR or distinguish MAR from MNAR. Imputation was conducted under an assumed MAR mechanism. All incomplete variables were binary and were imputed using Bayesian logistic regression with posterior parameter draws generated through the Metropolis–Hastings algorithm. The primary analysis generated 20 completed datasets using 20 FCS iterations. Trace plots, acceptance rates, and effective sample sizes showed no clear evidence of systematic non-convergence. Mean bias-reduced logistic regression was fitted to each completed dataset, and estimates were pooled using Rubin's rules. No predictor was significantly associated with Stage IV disease. Precision was limited, particularly for sex (95% CI: 0.012–22.40), smoking status (95% CI: 0.009–5.95), and family history (95% CI: 0.26–12.18). Sensitivity analyses using 50 and 100 completed datasets and a wider slope prior produced similar conclusions. The small sample size and high proportion of missing outcome data limited the precision of the estimates.