Abstract
We propose a new method to make inference about an eye parameter based on data that contains measurements on both eyes for some subjects, and measurements on only one eye on the others. Subject effects are modeled as additive and random, and correlation between observations on the same subject are taken into account. We derive confidence intervals for the parameter of interest, using unbiased estimators of mean and variance, and yielding explicit formulas. The results are compared to approaches commonly used in the literature, using theoretical considerations and a simulation study. The method works well even for small to moderate sample sizes, for continuous and for discrete data, and it is applicable generally for the situation where data is collected partially in pairs and partially in singles, and inference is to be made about a common location parameter. The conclusions as to how one should best average correlated data may be surprising, and somewhat revising conventional wisdom.
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Acknowledgments
We thank the Department of Ophthalmology, Konventhospital Barmherzige Brueder Linz, for providing anonymized eye- and subject-specific data sets. Furthermore, we would like to thank the editorial team and the reviewers, as well as our colleagues Edgar Brunner, Ludwig Hothorn, and Larry Madden, for helpful comments and excellent suggestions.
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Fuchs, N., Pölz, W. & Bathke, A.C. Confidence intervals for population means of partially paired observations. Stat Papers 58, 35–51 (2017). https://doi.org/10.1007/s00362-015-0686-y
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DOI: https://doi.org/10.1007/s00362-015-0686-y