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On the Inference of Partially Correlated Data with Applications to Public Health Issues

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Innovative Statistical Methods for Public Health Data

Part of the book series: ICSA Book Series in Statistics ((ICSABSS))

Abstract

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.

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References

  • Agresti, A.: Categorical Data Analysis. Wiley, New York (1990)

    MATH  Google Scholar 

  • Akritas, M.G., Kuha, J., Osgood, D.W.: A nonparametric approach to matched pairs with missing data. Sociol. Methods Res. 30, 425–457 (2002)

    Article  MathSciNet  Google Scholar 

  • 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 

  • Dimery, I.W., Nishioka, K., Grossie, B., Ota, D.M., Schantz, S.P., Robbins, K.T., Hong, W.K.: Polyamine metabolism in carcinoma of oral cavity compared with adjacent and normal oral mucosa. Am. J. Surg. 154, 429–433 (1987)

    Article  Google Scholar 

  • Dubnicka, S.R., Blair, R.C., Hettmansperger, T.P.: Rank-based procedures for mixed paired and two-sample designs. J. Mod. Appl. Stat. Methods 1(1), 32–41 (2002)

    MATH  Google Scholar 

  • Efron, B.: Bootstrap methods: another look at the jackknife. Ann. Stat. 7, 1–26 (1979)

    Article  MathSciNet  Google Scholar 

  • Ekbohm, G.: Comparing means in the paired case with missing data on one response. Biometrika 63(1), 169–172 (1976)

    Article  Google Scholar 

  • Fisher, R.A.: Statistical Methods for Research Workers, 4th edn. Oliver & Boyd, London (1932)

    MATH  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 

  • Ibrahim, H.I.: Evaluating the power of the Mann–Whitney test using the bootstrap method. Commun. Stat. Theory Methods 20, 2919–2931 (1991)

    Article  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)

  • Janssen, A.: Resampling Student’s t-type statistics. Ann. Inst. Stat. Math. 57, 507–529 (2005)

    Article  Google Scholar 

  • Janssen, A., Pauls, T.: How do bootstrap and permutation tests work? Ann. Stat. 31, 768–806 (2003)

    Article  MathSciNet  Google Scholar 

  • Konietschke, F., Harrar, S.W., Lange, K., Brunner, E.: Ranking procedures for matched pairs with missing values – asymptotic theory and a small sample approximation. Comput. Stat. Data Anal. 56, 1090–1102 (2012)

    Article  MathSciNet  Google Scholar 

  • Lin, P., Stivers, L.E.: On difference of means with incomplete data. Biometrika 61(2), 325–334 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  • Looney, S.W., Jones, P.W.: A method for comparing two normal means using combined samples of correlated and uncorrelated data. Stat. Med. 22, 1601–1610 (2003)

    Article  Google Scholar 

  • 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 

  • Rempala, G., Looney, S.: Asymptotic properties of a two-sample randomized test for partially dependent data. J. Stat. Plann. Inference 136, 68–89 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Samawi, H.M., Vogel, R.L.: Tests of homogeneity for partially matched-pairs data. Stat. Methodol. 8, 304–313 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Samawi, H.M., Vogel, R.L.: Notes on two sample tests for partially correlated (paired) data. J. Appl. Stat. 41(1), 109–117 (2014)

    Article  MathSciNet  MATH  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., Woodworth, G.G., Lemke, J.: Power estimation for two-sample tests using importance and antithetic resampling. Biom. J. 40(3), 341–354 (1998)

    Article  MATH  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 

  • Steere, A.C., Green, J., Schoen, R.T., Taylor, E., Hutchinson, G.J., Rahn, D.W., Malawista, S.E.: Successful parenteral penicillin therapy of established Lyme arthritis. N. Engl. J. Med. 312(14), 8699–8874 (1985)

    Article  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 

  • Walker, G.A., Saw, J.G.: The distribution of linear combinations of t-variables. J. Am. Stat. Assoc. 73(364), 876–878 (1978)

    MathSciNet  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 

  • Xu, J., Harrar, S.W.: Accurate mean comparisons for paired samples with missing data: an application to a smoking-cessation trial. Biom. J. 54, 281–295 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

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.

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Authors and Affiliations

  1. Department of Biostatistics, Jiann-Ping Hsu College of Public Health, Georgia Southern University, Hendricks Hall, Room 1006, Statesboro, GA, 30460, USA

    Hani M. Samawi

  2. Department of Biostatistics, Jiann-Ping Hsu College of Public Health, Georgia Southern University, Hendricks Hall, Room 1013, Statesboro, GA, 30460, USA

    Robert Vogel

Authors
  1. Hani M. Samawi
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  2. Robert Vogel
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Corresponding authors

Correspondence to Hani M. Samawi or Robert Vogel .

Editor information

Editors and Affiliations

  1. Wallace H. Kuralt Distinguished Professor, Director of Statistical Development and Consultation, School of Social Work, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA

    Ding-Geng (Din) Chen

  2. Arizona State University, Tempe, Arizona, USA

    Jeffrey Wilson

Appendix

Appendix

See Tables 14 and 15.

Table 14 Null distribution to T γ , T c , T γw , and T cw for \( n=2,{n}_1=2,{n}_2=2\ \mathrm{and}\ {\gamma =0.33} \)
Full size table
Table 15 Null distribution to T γ , T c , T γw , and T cw for \( n=3,{n}_1=3,{n}_2=2\ \mathrm{and}\ \gamma =0.375 \)
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Samawi, H.M., Vogel, R. (2015). On the Inference of Partially Correlated Data with Applications to Public Health Issues. In: Chen, DG., Wilson, J. (eds) Innovative Statistical Methods for Public Health Data. ICSA Book Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-18536-1_3

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