| Background:In epidemiology studies, stratification analysis was often used in order to control the confoundings between diseases and exposures. The data was arranged by K×2×2tables when the independent variable and dependent variable are all binary and the confounding variable has K levels. The homogeneity of the odds ratio should be tested before testing whether there is association between disease and exposure and estimating the common odds ratio.There are11test methods about homogeneity test of the odds ratio in K×2×2tables according to the publications. In the study, they are classified into six categories according to how to estimate the common odds raio and data structure.①Mantel-Haenszel methods (M-H):The common odds ratio is estimated by Mantel and Haenszel (1959). The test methods include Breslow-Day test and Breslow-Day-Tarone test, and the Breslow-Day-Tarone test is a correction of Breslow-Day test.②Zelen exact test (exact):It is an extension of Fisher exact test and dose not need to estimate the common odds ratio.③Asymptotic unconditional maximum likelihood methods (AU):The common odds ratio is estimated by asymptotic unconditional maximum likelihood method, the test methods include Wald test、Score test and likelihood ratio test.④Weighted least square method (WLS):The test method is based on which the common odds ratio is estimated by weighted least square method.⑤Asymptotic conditional maximum likelihood methods (AC):The common odds ratio is estimated by asymptotic conditional maximum likelihood method which is based on hypergeometric distribution, the test methods include Zelen test and Score test.⑥Sparse data test method (SD):The test methods are based on which the common odds ratio is estimated by asymptotic conditional maximum likelihood method, and combined with Central Limit theory or Linear Mixture Model, including T4and T5which were proposed by Liang and Self (1985)The author expect to do some special own simulations and give more rational interpretations of homogeneity tests in K×2×2tables based on the six categories.Objective:The study compare the power and type one error of the different homogeneity test methods by Monte Carlo method and to answer the several questions below:1. Which method is most suitable for the sparse data and which method is most suitable for the non sparse data.2. What are the advantages and disadvantages of Zelen exact test and whether is it better than the other test methods?3. If the test methods which common odds ratio are estimated based on hypergeometric distribution are better than the other ones?4. What about the power and type one error of the WLS method which is widely used in heterogeneity test in meta-analysis when the significant level is set to0.05compared to the other test methods? 5. As in heterogeneity test in meta-analysis we often set significant level to0.10, so when the significant is0.10, what about the power and type one error of the11test method and if they change too much?Methods:In the simulation study,4parameters were considered:Ni、ORi、πOi in the ith stratum and stratification number K. Every combination of the4parameters was calculated repeatedly by1000times. The exposure number of control in the ith stratum is generated by using ranbin function in SAS9.2(?). The exposure probability of case is calculated by the formula π1i,=ORiπ0i/ORiπ0i+(1-π0i), the exposure number of case in the ith stratum is generated in the same way. When comparing type one error, all ORis are equal. First, generate the random numbers of logORi of which mean is log OR and variance is0by using rannor function, then calculate the exponentiate of log ORis. When comparing power, not all ORis are equal. First, generate the random numbers of log ORi of which mean is log OR and variance is1by using rannor function, then calculate the exponentiate of log ORis. The π0is are constant or generated by using ranuni function when comparing type one error and power. Because heterogeneity test is necessarily and the significant level is often set to0.10in meta-analysis, the significant levels are set to0.05and0.10separately in the simulation study.Result:In the side of controlling type one error:(1) The asymptotic unconditional Wald test is most suitable for sparse data, the Breslow-Day tes、Breslow-Day-Tarone test、 asymptotic unconditional Score test and asymptotic unconditional likelihood ratio test are better than other test methods for non sparse data.(2) Zelen exact test is too conservative, the amount and time of computation increase too much as the sample size and K increase.(3) The methods that the common odds ratio are estimated based on hypergeometric distribution are worser than the others.(4) The WLS method is more conservative than M-H methods and AU methods.(5) In most situation, the comparisons among the11test methods dose not change much as the significant level changes. In some certain situation, the significant level should be set to0.10.In the side of power:(1) None of the11test methods should be considered in sparse data, as the sample size and K increasing, M-H methods、AU methods and AC methods become more sutiable.(2)Zelen exact test should be discarded because of its low power and computation complexity.(3) AC methods and SD methods are the test methods whose common odds ratio are estimated based on hypergeometric distribution, the power of AC is just so so, but the power of SD is not good.(4) When the sample size and K are not too small, the WLS method worths to be used.(5) The comparisons among the11test methods dose not change much as the significant level changes to be0.10.Conclusion:(1) There are no suitable methods when the sample size is small.(2) SD methods should be discarded.(3) Zelen exact test should not be advocated to be used in practice because it is too conservative.(4) The asymptotic unconditional Score test and asymptotic unconditional likelihood ratio test perform best, and the next is M-H methods.(5) M-H methods should be viewed as the best choice as the sample size and K increase because of its facility in computation. In the study Breslow-Day test should not be corrected because Breslow-Day-Tarone test is more conservative than Breslow-Day test.(6) The AU methods perform better than the AC methods in terms of type one error and power.(7) Although WLS method is more conservative than M-H methods and AU methods, it is widely used in meta-analysis because of its facility in computation when the sample size is large.(8) The result of comparison among the11methods is consistent when the significant level is0.10with that when the significant level is0.05. The author suggest that the significant level should be set to0.10because the power becomes larger as the significant level increases and this simulation study pointed out when the sample size is small the level of0.10was more appropriate. |
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