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Efficient ascertainment schemes for maximum likelihood estimation
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
2010 (English)In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 140, no 7, 2078-2088 p.Article in journal (Refereed) Published
Abstract [en]

A well chosen sampling scheme can substantially increase the efficiency of a study. However, it is not always obvious how to sample well. Neyman (1938) presents the possibility of two-stage sampling to increase efficiency in field sampling, and concludes that two-stage sampling sometimes, but not always, reduces the variance of estimates of means. Since then various authors have investigated the effects of two-stage and multistage sampling in different settings, most of which focus on binary outcome variables. In some special cases, such as case-control studies, there are rules of thumb to follow with regards to efficiency, see for example Maydrech and Kupper (1978), but in most other settings more elaborate calculations are necessary to discriminate between different options. Multistage sampling is described in the context of genetic epidemiology by, among others, Whittemore and Halpern (1997): Case-control status of prostate cancer is first ascertained and then more expensive measures such as family history of disease and DNA samples are collected. Asymptotic variances of Horvitz–Thompson estimates are derived. Reilly (1996) investigates optimal allocation of available resources for two-stage data with binary outcomes. Complete information is there available from variables sampled in Stage 1, while Stage 2 variables are sampled more sparsely with probabilities determined by Stage 1 data. Cost is allowed to differ between sampling in Stage 1 and sampling in Stage 2. The author emphasizes the usefulness of pilot studies to obtain information needed to find the optimal allocation. Zhou et al. (2007) investigate outcome dependent sampling where the outcome variable is continuous. Power of tests based on a semi-parametric estimator are compared with the power of an inverse probability weighted estimator and the power of a maximum likelihood estimator based on a simple random sample. 

Place, publisher, year, edition, pages
2010. Vol. 140, no 7, 2078-2088 p.
Keyword [en]
Ascertainment, Cost adjusted efficiency, Fisher information, Efficient design, Outcome dependent sampling, Multistage design, Continuous outcome variables
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-49325DOI: 10.1016/j.jspi.2010.02.003ISI: 000276369000039OAI: oai:DiVA.org:su-49325DiVA: diva2:377169
Funder
Swedish Research Council, 621-2005-2810Swedish Research Council, 621-2008-4946
Available from: 2010-12-13 Created: 2010-12-13 Last updated: 2017-12-11Bibliographically approved
In thesis
1. Design and analysis of response selective samples in observational studies
Open this publication in new window or tab >>Design and analysis of response selective samples in observational studies
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Outcome dependent sampling may increase efficiency in observational studies. It is however not always obvious how to sample efficiently, and how to analyze the resulting data without introducing bias. This thesis describes a general framework for efficiency calculations in multistage sampling, with focus on what is sometimes referred to as ascertainment sampling. A method for correcting for the sampling scheme in analysis of ascertainment samples is also presented. Simulation based methods are used to overcome computational issues in both efficiency calculations and analysis of data.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2011. 68 p.
Keyword
ascertainment, missing data, outcome dependent sampling, response selective samples, sequential design, stochastic EM algorithm
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-49328 (URN)978-91-7447-201-1 (ISBN)
Public defence
2011-02-04, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
At the time of doctoral defense, the following paper was unpublished and had a status as follows: Paper 1: Submitted.Available from: 2011-01-13 Created: 2010-12-13 Last updated: 2011-05-26Bibliographically approved

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