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Power of tests for comparing trend curves with application to national immunization survey (NIS)


  • Zhen Zhao

    Corresponding author
    1. Centers for Disease Control and Prevention, 1600 Clifton Road NE, Mail Stop E62 Atlanta, GA 30333, U.S.A.
    • National Center for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention (CDC), 1600 Clifton Rd NE, MS E62, Atlanta, GA 30333, U.S.A.
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  • The findings and conclusions in this article are those of the author and do not necessarily represent the official position of the Centers for Disease Control and Prevention.


To develop statistical tests for comparing trend curves of study outcomes between two socio-demographic strata across consecutive time points, and compare statistical power of the proposed tests under different trend curves data, three statistical tests were proposed. For large sample size with independent normal assumption among strata and across consecutive time points, the Z and Chi-square test statistics were developed, which are functions of outcome estimates and the standard errors at each of the study time points for the two strata. For small sample size with independent normal assumption, the F-test statistic was generated, which is a function of sample size of the two strata and estimated parameters across study period. If two trend curves are approximately parallel, the power of Z-test is consistently higher than that of both Chi-square and F-test. If two trend curves cross at low interaction, the power of Z-test is higher than or equal to the power of both Chi-square and F-test; however, at high interaction, the powers of Chi-square and F-test are higher than that of Z-test. The measurement of interaction of two trend curves was defined. These tests were applied to the comparison of trend curves of vaccination coverage estimates of standard vaccine series with National Immunization Survey (NIS) 2000–2007 data. Copyright © 2011 John Wiley & Sons, Ltd.