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A bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials

Stéphane Laurent, Catherine Legrand (2012)

ESAIM: Probability and Statistics

In many applications, we assume that two random observations x and yare generated according to independent Poisson distributions ( λ S ) x1d4ab;(λS) and ( μ T ) x1d4ab;(μT) and we are interested in performing statistical inference on the ratio φ = λ / μ of the two incidence rates. In vaccine efficacy trials, x and y are typically the numbers of cases in the vaccine and the control groups respectively, φ is called the relative risk and the statistical model is called ‘partial immunity model’. In this paper we...

A Bayesian framework for the ratio of two Poisson rates in the context of vaccine efficacy trials∗

Stéphane Laurent, Catherine Legrand (2012)

ESAIM: Probability and Statistics

In many applications, we assume that two random observations x and y are generated according to independent Poisson distributions ( λ S ) 𝒫(λS) and ( μ T ) 𝒫(μT) and we are interested in performing statistical inference on the ratio φ = λ / μ of the two incidence rates. In vaccine efficacy trials, x and y are typically the numbers of cases in the vaccine and the control groups respectively, φ is called the relative risk...

A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models

Barbora Arendacká (2007)

Kybernetika

We consider a construction of approximate confidence intervals on the variance component σ 1 2 in mixed linear models with two variance components with non-zero degrees of freedom for error. An approximate interval that seems to perform well in such a case, except that it is rather conservative for large σ 1 2 / σ 2 , was considered by Hartung and Knapp in [hk]. The expression for its asymptotic coverage when σ 1 2 / σ 2 → ∞ suggests a modification of this interval that preserves some nice properties of the original and that...

A note on interval estimation for the mean of inverse Gaussian distribution.

M. Arefi, G. R. Mohtashami Borzadaran, Y. Vaghei (2008)

SORT

In this paper, we study the interval estimation for the mean from inverse Gaussian distribution. This distribution is a member of the natural exponential families with cubic variance function. Also, we simulate the coverage probabilities for the confidence intervals considered. The results show that the likelihood ratio interval is the best interval and Wald interval has the poorest performance.

Asymptotic analysis of minimum volume confidence regions for location-scale families

M. Alama-Bućko, A. Zaigraev (2006)

Applicationes Mathematicae

An asymptotic analysis, when the sample size n tends to infinity, of the optimal confidence region established in Czarnowska and Nagaev (2001) is considered. As a result, two confidence regions, both close to the optimal one when n is sufficiently large, are suggested with a mild assumption on the distribution of a location-scale family.

Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model

Wiktor Oktaba (1995)

Applications of Mathematics

By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant | σ 2 ∑ | in the MGM model ( U , X B , σ 2 ∑ ⊗ V ) , ∑ > 0 , scalar σ 2 > 0 , with a matrix V ≥ 0 . A known n × p random matrix U has the expected value E ( U ) = X B , where the n × d matrix X is a known matrix of an experimental design, B is an unknown d × p matrix of parameters and σ 2 ∑ ⊗ V is the covariance matrix of U , ⊗ being the symbol of the Kronecker...

Bolshev's method of confidence limit construction.

Vacys Bagdonavicius, Valentina Nikoulina, Mikhail Nikulin (1997)

Qüestiió

Confidence intervals and regions for the parameters of a distribution are constructed, following the method due to L. N. Bolshev. This construction method is illustrated with Poisson, exponential, Bernouilli, geometric, normal and other distributions depending on parameters.

Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution

Mahdi, Smail (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 62F25, 62F03.A two-sided conditional confidence interval for the scale parameter θ of a Weibull distribution is constructed. The construction follows the rejection of a preliminary test for the null hypothesis: θ = θ0 where θ0 is a given value. The confidence bounds are derived according to the method set forth by Meeks and D’Agostino (1983) and subsequently used by Arabatzis et al. (1989) in Gaussian models and more recently by Chiou and Han (1994, 1995)...

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