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Biometrika 1983 70(1):103-110; doi:10.1093/biomet/70.1.103
© 1983 by Biometrika Trust
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Interactive effects of mixtures of stimuli in life table analysis

EDWARD L. KORN and PING-YU LIU

Departrnent of Biomathematics, University of California Los Angeles, California, U.S.A.

An interaction is a response to a mixture of stimuli that, based on the responses to the individual stimuli, seems unexpectedly large or small. The conclusions about the presence of interactions can depend upon the chosen parameterization. For dichotomous outcome variables, a simple probabilistic model of no interaction exists (Finney, 1952). In this model, individuals are at risk from challenges from the background and the separate stimuli, all acting independently. In this paper, this model is extended to survivorship data. To test the hypothesis of no interaction, a likelihood ratio statistic and a statistic based on a standardized interaction are proposed for grouped-time data. A statistic in the spirit of Mantel—Haenszel is constructed for continuous-time data. Asymptotic relative efficiencies of these tests versus the parametric likelihood ratio test are calculated. A limited Monte Carlo study is performed to investigate the small sample properties.

Key Words: Asymptotic relative efficiency • Continuous-time data • Grouped-time data • Interaction • Likelihood ratio test • Mantel—Haenszel test • Survival data • Synergism


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