IMPUTATION OF LONGITUDINAL OUTCOMES WHEN MISSINGNESS IS NOT AT RANDOM
Author(s)
Ramsankar Basak1, Michael R. Kosorok, PhD2, Zhang R. Kai, PhD3, Yufeng R. Liu, PhD3;
1UNC Chapel Hill, Research Associate, Chapel Hill, NC, USA, 2UNC Chapel Hill, Biostatistics, Chapel Hill, NC, USA, 3UNC Chapel Hill, STOR, Chapel Hill, NC, USA
1UNC Chapel Hill, Research Associate, Chapel Hill, NC, USA, 2UNC Chapel Hill, Biostatistics, Chapel Hill, NC, USA, 3UNC Chapel Hill, STOR, Chapel Hill, NC, USA
OBJECTIVES: We explore several strategies based on the multiple imputation-based pattern mixture modeling approach for imputing nonignorable missing (i.e., Not Missing At Random or NMAR)) longitudinal outcome.
METHODS: We implement imputing longitudinal outcomes with delta-based marginal sensitivity parameters (ILODMSP). For missing outcomes (i.e., Ys) collected at 3 time points, we assume that Y1 is MAR while subsequent ones are NMAR. We propose to make adjustments to the R package, MICE, as follows. For imputation of 1. Y1, prefill Y2 before it is entered in the imputation model such that the mean difference between missing and nonmissing equals to delta (marginal sensitivity parameter) and a similar method is applied to Y3 using its delta; 2. Y2, prefill Y3 before it is entered in the imputation model similarly, and; 3. Y3, imputed Y2 (with or without adjustment to make up to its delta) is used.
RESULTS: Simulations results show that biases in Y1 remain small across all methods; none of these biases, however, is statistically significant. For Y2 and Y3, both NMAR, biases range from -0.001 to 0.001 (<0.002%) for all NMAR methods; this implies reducing (absolute) bias. We apply the proposed methods to impute quality of life (QoL) or sexual dysfunction outcome - measured at baseline and (approximately) at 3, 12, and 24 months following treatment - in patients newly diagnosed prostate cancer (PCa). All NMAR methods produce less biases in means.
CONCLUSIONS: The proposed methods, which show minimal bias in mean statistics and regression parameter estimates, are transparent and easy to articulate to non-statisticians and practitioners and can easily incorporate clinical assumptions into imputation models. With longitudinal designs being frequently used in outcomes research, out work should help uptake routine sensitivity analysis to deal with different missingness mechanisms. Future research is needed to further refine the method.
METHODS: We implement imputing longitudinal outcomes with delta-based marginal sensitivity parameters (ILODMSP). For missing outcomes (i.e., Ys) collected at 3 time points, we assume that Y1 is MAR while subsequent ones are NMAR. We propose to make adjustments to the R package, MICE, as follows. For imputation of 1. Y1, prefill Y2 before it is entered in the imputation model such that the mean difference between missing and nonmissing equals to delta (marginal sensitivity parameter) and a similar method is applied to Y3 using its delta; 2. Y2, prefill Y3 before it is entered in the imputation model similarly, and; 3. Y3, imputed Y2 (with or without adjustment to make up to its delta) is used.
RESULTS: Simulations results show that biases in Y1 remain small across all methods; none of these biases, however, is statistically significant. For Y2 and Y3, both NMAR, biases range from -0.001 to 0.001 (<0.002%) for all NMAR methods; this implies reducing (absolute) bias. We apply the proposed methods to impute quality of life (QoL) or sexual dysfunction outcome - measured at baseline and (approximately) at 3, 12, and 24 months following treatment - in patients newly diagnosed prostate cancer (PCa). All NMAR methods produce less biases in means.
CONCLUSIONS: The proposed methods, which show minimal bias in mean statistics and regression parameter estimates, are transparent and easy to articulate to non-statisticians and practitioners and can easily incorporate clinical assumptions into imputation models. With longitudinal designs being frequently used in outcomes research, out work should help uptake routine sensitivity analysis to deal with different missingness mechanisms. Future research is needed to further refine the method.
Conference/Value in Health Info
2026-05, ISPOR 2026, Philadelphia, PA, USA
Value in Health, Volume 29, Issue S6
Code
MSR119
Topic
Methodological & Statistical Research
Topic Subcategory
Missing Data, PRO & Related Methods
Disease
SDC: Oncology