| Summary: | 碩士 === 淡江大學 === 數學學系 === 93 === In practice such as clinical trials,we often need to compare differences between two treatments groups.If,in addition,there is covariable(s) associated with the response of interest,then we can make use of them to perform an analysis of covariance (ANCOVA) to remove bias and to enhance efficiency.The most common parametric ANCOVA is by linear regression approach with strict model assumptions.For nonparametric ANCOVA,two commonly approaches are ANCOVA by ranking(e.g. Quade,1967) and ANOCOVA by matching(e.g. Quade, 1982).
Extended Rank Analysis of Covariance (ERMP ANCOVA,Chen,2001),which combines the rank ANCOVA and the ANCOVA by matching,uses “rank corrected for mean” and “caliper matching” to adjust for the ranks of the covariates.So that the assumptions are weaker than the rank ANCOVA and does not throw away valuable information.However,tolerance may be conservative,and if the trend between Y and X is inconsistent,the test statistic may not be efficient.
In the thesis,based on the notion of local correlations(Doksum.et al,1994),we divide the support of X into several sections according to variations of correlations between Y and X,then use nonparametric smoothing regression to estimate the conditional mean of Y given X.Given the estimates,we then calculate the corresponding tolerance of each X for their extended ranks of the ERMP test.
We compare the p-values of the ERMP ANCOVA and combinations of ERMP based on separate sections by two examples.We found that the results of the proposed method are slightly better than the ERMP ANCOVA for the examined examples.
|
|---|
