"In section 1, we develop a novel method of confidence interval construction for directly standardized rates. These intervals involve saddlepoint approximations to the intractable distribution of a weighted sum of Poisson random variables and the determination of hypothetical Poisson mean values for each of the age groups. Simulation studies show that, in terms of coverage probability and length, the saddlepoint confidence interval (SP) outperforms four competing confidence intervals obtained from the moment matching (M8), gamma-based (G1,G4) and ABC bootstrap (ABC) methods.
In section 2, we first consider Brillinger's classical model for a vital rate estimate with a random denominator. We derive statistical properties for this rate estimate and investigate difficulties encountered while trying to perform statistical inference about its expected value. Since inference about this expected value is not possible, we consider instead confidence intervals for covariance of the bivariate Poisson distribution which underlies Brillinger's model, on the way to proposing a new model which is a modification of Brillinger's model and which has numerous theoretical and computational advantages over the latter. A simulation study for our new model shows that in terms of coverage probability, our novel two-dimensional mid-P "Clopper-Pearson" type confidence interval (CP2) outperforms the "Clopper-Pearson" type interval with no mid-P correction (CP0) and the "Clopper-Pearson" type interval with a classical one-dimensional mid-P correction (CP1). In addition, CP2 was found to be more or less equivalent, in terms of coverage probabilities, to CDF0, CDF1 and CDF2 which are the CDF pivot methods with no mid-P correction, a one-dimensional mid-P correction and a two-dimensional mid-P correction, respectively. Furthermore, method CP2 performed essentially as well as the saddlepoint approximation (SP0) to the CDF0 method. Finally, all of the above-mentioned methods (CDF0, CDF1, CDF2, CP0, CP1, CP2 and SP0) substantially outperform the large sample (LS) method of confidence interval construction, in terms of coverage probability"--Abstract, page iii.
Samaranayake, V. A.
Wen, Xuerong Meggie
Olbricht, Gayla R.
Mathematics and Statistics
Ph. D. in Mathematics
Missouri University of Science and Technology
ix, 59 pages
© 2015 Pasan Manuranga Edirisinghe, All rights reserved.
Dissertation - Open Access
Electronic OCLC #
Edirisinghe, Pasan Manuranga, "Small sample saddlepoint confidence intervals in epidemiology" (2015). Doctoral Dissertations. 2646.