| Objective: Sample rate comparison is frequently encountered in medical data processing. In comparison of sample rates between groups, the method ofχ~2 could be adopted. If the hypothesis testing suggests that H0 is rejected and H1 is accepted, the overall rates are not equal or not exactly equal. Multiple comparisons on sample rates are needed for pointing out the specific groups that bear difference. This research aims to explore from the perspective of medical application and is mainly focused on pair-wise comparisons and multiple comparisons with the control group, with the prospect of getting a selection of multiple comparison methods. as well as their scope and application conditions, on sample rates. Also, examples and SAS language are presented for promotion and application.Methods: Monte-Carlo Simulation is adopted. Namely, through duplicate sampling from binomial distributed random number function for 1,000 times and SAS 9.2 software used in programming, the author calculates the proportion of each method's FWER controlledαin multiple comparisons methods by simulation, so as to get the optimum method of multiple comparison on sample rates, and the scope and application conditions of this method by Monte-Carlo Simulation with FWER confined in a standard, and finally, make a contribution to its promotion and application by programming it in SAS and illustrations.Results: The optimum methods the author gets out of the selection of sample rate multiple comparison with FWER confined in a standard are: SNK,Bonferroni,Step-Up Hommel,Step-Up Hochberg,Step-down Holm,Step-down Sidak,Bootstrap and Permutation in pair-wise comparisons;and Dunnett-SNK,Brunden,Bootstrap and Permutation in multiple comparisons with the control group. The application conditions of the optimum method obtained with FWER confined in a standard are: In sample rates'pair-wise comparison, when n≤40 and k≤5, SNK is suggested;and when significant differences existed between each group of samples, Bonferroni is recommended. The stepwise is suggested as it functions more effectively in adjusting test standard than the corresponding single-step. The recommendation order of the stepwise methods are Step-up Hommel> Step-up Hochberg>Step-down Sidak>Step-down Holm;Bootstrap or Permutation, the number in group is large,is preferred when large amount of data is processed, but not applicable in the situation that the sample size difference is great, otherwise wrong conclusion would be reached. In multiple comparisons with the control group, Dunnett-SNK requires no specific application conditions and generates relatively stable results, compared with other methods, and is recommended for universal application. When group number is between 3 and 5, Brunden is recommended. When group number k>5, Brunden's control on FWER is too strong to lead to a too conservative result and hence it is not suggested. Bootstrap or Permutation, the number in group is large,is preferred when large amount of data is processed, but not applicable in the situation that the sample size difference is great.Conclusions: This research explores from the perspective of medical application and through pair-wise comparisons and multiple comparisons with the control group, reach the conclusion that, four methods of gradually-adjusted testing standard are recommend in pair-wise comparisons methods. The recommendation order is that, Step-up Hommel> Step-up Hochberg>Step-down Sidak>Step-down Holm; while,when n≤40 and k≤5, SNK is suggested, but when the sample size difference is great, Bonferroni is recommended. Bootstrap and Permutation are recommended when large amount of data is processed, the number in group is large, and the sample size difference is not great. When comparing sample rates with the control group, Dunnett-SNK is usually the choice, but when group number is between 3 and 5, Brunden is recommended;when group number is large, and when large amount of data is processed and the sample size difference is not great, Bootstrap or Permutation is recommended. |
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