On the Inference of Partially Correlated Data with Applications to Public Health Issues
Correlated or matched data is frequently collected under many study designs in applied sciences such as the social, behavioral, economic, biological, medical, epidemiologic, health, public health, and drug developmental sciences in order to have a more efficient design and to control for potential confounding factors in the study. Challenges with respect to availability and cost commonly occur with matching observational or experimental study subjects. Researchers frequently encounter situations where the observed sample consists of a combination of correlated and uncorrelated data due to missing responses. Ignoring cases with missing responses, when analyzing the data, will introduce bias in the inference and reduce the power of the testing procedure. As such, the importance in developing new statistical inference methods to treat partially correlated data and new approaches to model partially correlated data has grown over the past few decades. These methods attempt to account for the special nature of partially correlated data.
In this chapter, we provide several methods to compare two Gaussian distributed means in the two sample location problem under the assumption of partially dependent observations. For categorical data, tests of homogeneity for partially matched-pair data are investigated. Different methods of combining tests of homogeneity based on Pearson chi-square test and McNemar chi-squared test are investigated. Also, we will introduce several nonparametric testing procedures which combine all cases in the study.
KeywordsMcNemar test Pearson chi-square test Inverse chi-square method Weighted chi-square test Tippett method Partially matched-pair Case–control and matching studies T-test Z-test Power of the test p-Value of the test Efficiency Matched pairs sign test Sign test Wilcoxon signed-rank test Correlated and uncorrelated data
We are grateful to the Center for Child & Adolescent Health for providing us with the 2003 National Survey of Children’s Health. Also, we would like to thank the referees and the associate editor for their valuable comments which improved the manuscript.
- Brunner, E., Puri, M.L.: Nonparametric methods in design and analysis of experiments. In: Ghosh, S., Rao, C.R. (eds.) Handbook of Statistics 13, pp. 631–703. North-Holland/Elsevier, Amsterdam (1996)Google Scholar
- Brunner, E., Domhof, S., Langer, F.: Nonparametric Analysis of Longitudinal Data in Factorial Designs. Wiley, New York (2002)Google Scholar
- Child and Adolescent Health Measurement Initiative: National Survey of Children with Special Health Care Needs: Indicator Dataset 6. Data Resource Center for Child and Adolescent Health website. Retrieved from: www.childhealthdata.org (2003)
- Conover, W.J.: Practical Nonparametric Statistics, 3rd edn. Wiley, New York (1999)Google Scholar
- Hedges, L.V., Oklin, I.: Statistical Methods for Meta-Analysis: Combined Test Procedures. Academic, London (1985)Google Scholar
- Hennekens, C.H., Burning, J.E.: Epidemiology in medicine. Boston: Little, Brown (1987)Google Scholar
- Hettmansperger, T.P.: Statistical Inference Based on Ranks. Wiley, New York (1984)Google Scholar
- Hettmansperger, T.P., McKean, J.W.: Robust Nonparametric Statistical Method, 2nd edn. CRC Press, Taylor & Francis Group, New York (2011)Google Scholar
- Im KyungAh: A modified signed rank test to account for missing in small samples with paired data. M.S. Thesis, Department of Biostatistics, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA. http://www.worldcat.org/title/modified-signed-rank-test-to-account-for-missing-data-in-small-samples-with-paired-data/oclc/52418573 (2002)
- Nason, G.P.: On the sum of t and Gaussian random variables. http://www.maths.bris.ac.uk/~guy/Research/papers/SumTGauss.pdf (2005). Accessed 1 May 2011
- Nurnberger, J., Jimerson, D., Allen, J.R., Simmons, S., Gershon, E.: Red cell ouabain-sensitive Na+-K+-adenosine triphosphatase: a state marker in affective disorder inversely related to plasma cortisol. Biol. Psychiatry 17(9), 981–992 (1982)Google Scholar
- Samawi, H.M., Woodworth, G.G., Al-Saleh, M.F.: Two-sample importance resampling for the bootstrap. Metron. LIV(3–4) (1996)Google Scholar
- Samawi, H.M., Yu, L., Vogel, R.L.: On some nonparametric tests for partially correlated data: proposing a new test. Unpublished manuscript (2014)Google Scholar
- Snedecor, G.W., Cochran, W.G.: Statistical Methods, 7th edn. Iowa State University Press, Ames (1980)Google Scholar
- Tang, X.: New test statistic for comparing medians with incomplete paired data. M.S. Thesis, Department of Biostatistics, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA. http://www.google.com/search?hl=en&rlz=1T4ADRA_enUS357US357&q=Tang+X.+%282007%29New+Test+Statistic+for+Comparing+Medians+with+Incomplete+Paired+Data&btnG=Search&aq=f&aqi=&aql=&oq= (2007)
- Tippett, L.H.C.: The Method of Statistics. Williams & Norgate, London (1931)Google Scholar
- Weidmann, E., Whiteside, T.L., Giorda, R., Herberman, R.B., Trucco, M.: The T-cell receptor V beta gene usage in tumor-infiltrating lymphocytes and blood of patients with hepatocellular carcinoma. Cancer Res. 52(21), 5913–5920 (1992)Google Scholar