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1 Anesthesia and Critical Care, Massachusetts General Hospital, Boston, MA, USA; Department of Anesthesiology and Pain Medicine, University of California, Davis, Davis, CA, USA
2 Department of Neuroscience, University of Pittsburgh, Pittsburgh, PA, USA
3 Anesthesia and Critical Care, Massachusetts General Hospital, Boston, MA, USA; Division of Health Science and Technology, Harvard Medical School/Massachusetts Institute of Technology, Cambridge, MA, USA
* To whom correspondence should be addressed. E-mail: asmith{at}neurostat.mgh.harvard.edu.
In population learning studies, between subject response differences are an important source of variance that must be characterized to identify accurately the features of the learning process common to the population. Although learning is a dynamic process, current population analyses do not use dynamic estimation methods, do not compute both population and individual learning curves, and use learning criteria that are less than optimal. We develop a state-space random effects (SSRE) model to estimate population and individual learning curves, ideal observer curves, and learning trials, and to make dynamic assessments of learning between two populations and within the same population that avoid multiple hypothesis tests. In an 80-trial study of an NMDA antagonist's effect on the ability of rats to execute a set-shift task, our dynamic assessments of learning demonstrated that both the treatment and control groups learned, yet, by trial 35, the treatment group learning was significantly impaired relative to control. We used our SSRE model in a theoretical study to evaluate the design efficiency of learning experiments in terms of the number of animals per group and number of trials per animal required to characterize learning differences between two populations. Our results demonstrated that a maximum difference in the probability of a correct response between the treatment and control group learning curves of 0.07 (0.20) would require 15 to 20 (5 to 7) animals per group in an 80 (60)-trial experiment. The SSRE model offers a practical approach to dynamic analysis of population learning and a theoretical framework for optimal design of learning experiments.
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