General linear models in a missing outcome environment of clinical trials incorporating splines for time-invariant continuous adjustment

Minjeong Park, The University of Texas School of Public Health


Missing outcome is a common occurrence in health research and the problem becomes more severe in longitudinal studies since it requires greater endeavor to collect complete data in subject-follow-up setting. Among many statistical methodologies which have been introduced for managing missing outcomes, commonly used methods are 1) naively ignoring missing data by removing incomplete case (Complete Case (CC) analysis) 2) imputations; last observation carried forward (LOCF), multiple imputations (MI), Expectation-Maximization (EM) algorithm approach and 3) use all available data ; linear mixed models (LMM) and the generalized estimating equations (GEE) approach. Although previous studies have shown the potential usefulness of advanced approaches, e.g. MI, EM algorithm approach, or LMM, their application has been limited in practice due to difficulties in understanding and executing the models, while CC analysis or LOCF imputation method have been popularly used due to its simplicity in execution. Therefore, it is critical to find an alternative as simple and straightforward as CC analysis or LOCF imputation, yet attaining the benefits of advanced methods. We proposed an approach based on the generalized least squares method producing the best linear unbiased estimate, and showed its validity through the comparison of commonly used missing analyses in the simulation study. The simulation was conducted with various missing rates under each missing data mechanism (missing completely at random (MCAR), missing at random (MAR), missing not at random (MNAR)). It showed the validity of the proposed approach under MCAR and MAR, especially showed its superiority where the correlation structure was the first order autoregressive (AR(1)). Under MNAR, the proposed approach yielded the least bias where AR(1), however, it did not show its superiority over others. B-spline was applied to the proposed approach to manage non-linear relationships between an outcome and continuous covariate as a potential confounder. The proposed approach was also applied to Transplantation in Myocardial Infarction Evaluation trial objecting to assess the safety, effect and most efficient timing of bone marrow mononuclear cell (BMMNC) therapy after an acute myocardial infarction (AMI), and compared to the commonly used missing analyses. A total of 120 post-AMI patients from 5 sites were randomized, and the total missing rate was less than 5%. The proposed approach showed similarities to the LMM, yet produced distant results from imputation methods. B-spline function contributed to yield smaller standard deviations. In conclusion, the proposed approach is a powerful alternative of longitudinal data analyses in missing outcome environment, incorporating all available data with less assumptions or restrictions since it is not either likelihood-based or including additional terms such as random effects in the LMM. And it can be the most compatible with AR(1) correlation structure under MAR.

Subject Area

Biostatistics|Public health

Recommended Citation

Park, Minjeong, "General linear models in a missing outcome environment of clinical trials incorporating splines for time-invariant continuous adjustment" (2013). Texas Medical Center Dissertations (via ProQuest). AAI3611289.