Mathematical aspects of estimating two treatment effects and a common variance in an assured allocation design. (English) Zbl 1021.62092
Summary: We consider a doubly semi-parametric model for normally distributed random variables which arises in experiments with an assured allocation design. In settling a curious question about estimation of the model’s variance parameter, a certain inequality arises that involves the normal probability density function and its first two integrals. The inequality is of mathematical interest in its own right, and is given a rigorous proof.
MSC:
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62G05 | Nonparametric estimation |
| 62C12 | Empirical decision procedures; empirical Bayes procedures |
Keywords:
assured allocation design; controlled clinical trials; empirical Bayes estimation; inequalities; mixture models; normal distribution; semiparametric models; variance estimationReferences:
| [1] | Finkelstein, M. O.; Levin, B.; Robbins, H., Clinical and prophylactic trials with assured new treatment for those at greater risk. Part I—Introduction, Amer. J. Public Health, 86, 691-695 (1996) |
| [2] | Finkelstein, M. O.; Levin, B.; Robbins, H., Clinical and prophylactic trials with assured new treatment for those at greater risk. Part II—Examples, Amer. J. Public Health, 86, 696-705 (1996) |
| [3] | Robbins, H., Comparing two treatments under biased allocation, La Gaz. Sci. Math. Que., 15, 35-41 (1993) |
| [4] | Robbins, H.; Zhang, C.-H., Estimating a treatment effect under biased sampling, Proc. Nat. Acad. Sci. USA, 85, 3670-3672 (1988) · Zbl 0639.62098 |
| [5] | Robbins, H.; Zhang, C.-H., Estimating the superiority of a drug to a placebo when all and only those patients at risk are treated with the drug, Proc. Nat. Acad. Sci. USA, 86, 3003-3005 (1989) · Zbl 0665.62108 |
| [6] | Robbins, H.; Zhang, C.-H., Estimating a multiplicative treatment effect under biased allocation, Biometrika, 78, 349-354 (1991) · Zbl 0735.62031 |
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