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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 and delay 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 40 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.
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A class of generalized linear mixed models adjusted for marginal interpretability
Two popular approaches for relating correlated measurements of a non‐Gaussian response variable to a set of predictors are to fit amarginal modelusing generalized estimating equations and to fit ageneralized linear mixed model(GLMM) by introducing latent random variables. The first approach is effective for parameter estimation, but leaves one without a formal model for the data with which to assess quality of fit or make individual‐level predictions for future observations. The second approach overcomes these deficiencies, but leads to parameter estimates that must be interpreted conditional on the latent variables. To obtain marginal summaries, one needs to evaluate an analytically intractable integral or use attenuation factors as an approximation. Further, we note an unpalatable implication of the standard GLMM. To resolve these issues, we turn to a class of marginally interpretable GLMMs that lead to parameter estimates with a marginal interpretation while maintaining the desirable statistical properties of a conditionally specified model and avoiding problematic implications. We establish the form of these models under the most commonly used link functions and address computational issues. For logistic mixed effects models, we introduce an accurate and efficient method for evaluating the logistic‐normal integral.
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- PAR ID:
- 10453971
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Statistics in Medicine
- Volume:
- 40
- Issue:
- 2
- ISSN:
- 0277-6715
- Format(s):
- Medium: X Size: p. 427-440
- Size(s):
- p. 427-440
- Sponsoring Org:
- National Science Foundation
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