Biometrical journal. Biometrische Zeitschrift
-
This is a discussion of the paper' Sample size recalculation in internal pilot study designs' by Tim Friede and Meinhard Kieser, appearing in this special issue on adaptive designs.
-
We examine stochastic inequality probabilities of the form P (X > Y) and P (X > max (Y, Z)) where X, Y, and Z are random variables with beta, gamma, or inverse gamma distributions. We discuss the applications of such inequality probabilities to adaptively randomized clinical trials as well as methods for calculating their values.
-
Comparative Study
Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution.
We prove that the generalized Poisson distribution GP(theta, eta) (eta > or = 0) is a mixture of Poisson distributions; this is a new property for a distribution which is the topic of the book by Consul (1989). Because we find that the fits to count data of the generalized Poisson and negative binomial distributions are often similar, to understand their differences, we compare the probability mass functions and skewnesses of the generalized Poisson and negative binomial distributions with the first two moments fixed. ⋯ These probabilistic comparisons are helpful in selecting a better fitting distribution for modelling count data with long right tails. Through a real example of count data with large zero fraction, we illustrate how the generalized Poisson and negative binomial distributions as well as their zero-inflated distributions can be discriminated.
-
Overdispersion or extra-Poisson variation is very common for count data. This phenomenon arises when the variability of the counts greatly exceeds the mean under the Poisson assumption, resulting in substantial bias for the parameter estimates. ⋯ In this paper, diagnostic measures are proposed for assessing the sensitivity of Dean's score test for overdispersion in Poisson regression. Applications to the well-known fabric faults and Ames salmonella assay data sets illustrate the usefulness of the diagnostics in analyzing overdispersed count data.
-
Without a placebo arm, any non-inferiority inference involving assessment of the placebo effect under the active control trial setting is difficult. The statistical risk for falsely concluding non-inferiority cannot be evaluated unless the constancy assumption approximately holds that the effect of the active control under the historical trial setting where the control effect can be assessed carries to the noninferiority trial setting. The constancy assumption cannot be checked because of missing the placebo arm in the non-inferiority trial. ⋯ Determination of the non-inferiority margin depends on what objective the non-inferiority analysis is intended to achieve. The margin can be a fixed margin or a margin functionally defined. Between-trial differences always exist and need to be properly considered.