| Independence test of contingency table is common in categorical data analysis.Independence test of contingency tables with complete data have been researched comprehensively and a variety of test methods and practical statistics,such as likelihood ratio statistics,Wald statistics have been constructed.However the previous studies of contingency tables with missing data are fewer.The existence of missing data makes it more difficult to construct effective statistics or estimates.Moreover,the derivation and proof are more complex.The fair use of bootstrap can reduce the influence of incorrect asymptotic distribution because specific distribution is not required.In this paper,undirected graph is used to describe the missing mechanism of contingency table data.Then the constrained EM algorithm is used to obtain the maximum likelihood estimation of parameters and construct a new likelihood ratio statistics.Next we use the traditional likelihood ratio statistics,the newly constructed likelihood ratio statistics,Score statistics,Wald statistics to test independence of 22?contingency table with missing data,and calculate the type I error levels and power of each statistic through simulation study.After that the bootstrap p-value corresponding to each statistic is calculated by the bootstrap.The features of each statistic under the bootstrap are analyzed.Meanwhile the differences of the test effect of each statistic under different missing rate and sample size are explored.Finally,the effectiveness of each statistic under the bootstrap is illustrated by a medical example.The results show that the Wald statistic is better when the sample size is larger and the missing rate is higher while the test results of these four statistics are similar in other cases.Under bootstrap,the likelihood ratio statistics constructed by constrained EM algorithm is recommended when the sample size is small while the test effect of these four statistics are similar when the sample size is large. |
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