Generalized linear mixed model approach to time-to-event data with censored observations

Authors: Yeater, Kathleen; Yocum, George; Rinehart, Joe; Rajamohan, Arun; BOWSHER, JULIA - North Dakota State University; GREENLEE, KENDRA - North Dakota State University

Submitted to: Proceedings of SAS Users Group
Publication Type: Proceedings
Publication Acceptance Date: 7/11/2019
Publication Date: 10/21/2019
Citation: Yeater, K.M., Yocum, G.D., Rinehart, J.P., Rajamohan, A., Bowsher, J., Greenlee, K. 2019. Generalized linear mixed model approach to time-to-event data with censored observations. In: Proceedings of the Southeast SAS Users Group Conference, October 20-22, 2019. Williamsburg, Virginia.

Interpretive Summary: Survival analysis with random effects modeling is an uncommon approach for many agricultural researchers and their statistical collaborators. This proceedings paper provides a working example of an appropriate study design, corresponding analysis, and interpretation of results. Applied statisticians and researchers will be able to refer to this example to update their knowledge on these topics.

Technical Abstract: The time-to-event response is commonly thought of as survival analysis, and typically concerns statistical modeling of expected life span. In the example presented here, alfalfa leafcutting bees, Megachile rotundata, were randomly exposed to one of eight experimental thermoprofiles or two control thermoprofiles, for one to eight weeks. The incorporation of these fluctuating thermoprofiles in the management of the bees increases survival and blocks the development of sub-lethal effects, such as delayed emergence. The data collected here investigates the question of whether any experimental thermoprofile provides better overall survival, with a reduction of sub-lethal effects. The study design incorporates typical aspects of agricultural research; random blocking effects. All M. rotundata prepupae brood cells were randomly placed in individual wells of 24-well culture plates. Plates were randomly assigned to thermoprofile and exposure duration, with three plate replicates per thermoprofile x exposure time. Bees were observed for emergence for 50 days. All bees that were not yet emerged prior to fixed end of study were considered to be censored observations. We fit a generalized linear mixed model (GLMM), using the SAS® GLIMMIX Procedure to the censored data and obtained time-to-emergence function estimates. As opposed to a typical survival analysis approach, such as Kaplan-Meier curve, in the GLMM we were able to include the random model effects from the study design. This is an important inclusion in the model, such that correct standard error and test statistics are generated for mixed models with non-Gaussian data.