The Comparison Study Between Four Similar Statistical Issues Of Two-sample Parallel Design In Clinical Trials

It is called"the statistical issues of two-sample parallel design"when we analyze the index (It usually includes efficacy index and safety index.) of the test group and the reference group in drug or medical appliance trials. The statistical issues are closely related to difference, non-inferiority, equivalence and superiority. There are actually six kinds of conditions including two-side difference test, left-side difference test, right-side difference test, equivalence test, superiority test and non-inferiority test. Therefore the issues discussed should be called"six kinds of comparison types in clinical trials".There are more than 90% of medical literatures which didn't use the method of sample size estimation or didn't use the method of sample size estimation properly in China according to statistics. Consequently, the validity and integrity of clinical studies is questionable. Several reasons lead to the problem. Clinical researchers fail to understand the importance of sample size estimation clearly or master the method of sample size estimation overall. There are not any useful reference books or papers currently. And the formulas are not always the same in many kinds of textbooks and papers. There is not any systematic and convenient software, so sample size and power estimation is still uncertain, unconvenient and low in reliability. It is an urgent problem to offer scientific and reasonable formulas and automatic realization methods of software for sample size estimation and power analysis. The comparison of sample size and power can help us to understand the six kinds of types. And it is very practical and meaningful to seek for proper formulas, make comparison between the six kinds of types from several aspects and achieve sample size and power estimation using statistical software.The study mainly includes five parts:Firstly, the proper formulas for two-side difference test, right-side difference test, left-side difference test, equivalence test, superiority test and non-inferiority test for quantitative and qualitative data of two-sample parallel design are derived by means of confidence interval estimation method.Secondly, the accuracy of formulas is verified by means of Monte Carlo simulation of sampling method.Power is the indicator of evaluating the accuracy of the formulas. It proves that the formula is correct if the power has reached the desired level by means of performing verifications 10000 times. The results demonstrate that the power has reached or even exceeded the desired level, indicating that the formulas are correct.Thirdly, the similarities of difference test, equivalence test, superiority test and non-inferiority test have been introduced. At the same time, the differences have been discussed in detail in the aspects of the destination of research, the problems resolved, the content considered at the planning stage, the choice of reference group, the intensity of argumentation, clinical meaning, factors affecting sample size estimation, hypothesis test, hypothesis statistic, significance level, the rejection range, the deduction principle of confidence interval, power analysis and sample size estimation. The most evident difference between difference test and the three special tests is that the latter have considered a margin. The margin is a clinical meaningful difference denoted asδ.Fourthly, we compare sample size, power and the p-value between the six kinds of clinical trials.The change of sample size along with the change ofα,βandδfor a given study when other conditions are fixed is as follows:The sample size required decreases along with the increase ofαandβfor two-side difference test, right-side difference test and left-side difference test. It decreases along with the increase ofα,βand the absolute value ofδfor equivalence test and non-inferiority test. It decreases along with the increase ofαandβ, but it increases along with the increase ofδfor superiority test.The change of power along with the change ofαandδfor a given study when other conditions are fixed is as follows:The power increases along with the increase ofαfor two-side difference test, right-side difference test and left-side difference test. It increases along with the increase ofαand the absolute value ofδfor equivalence test and non-inferiority test. It increases along with the increase ofα, but it decreases along with the increase ofδfor superiority test.The change of p-value along with the change ofδfor a given study when other conditions are fixed is as follows:The p-value decreases along with the increase of the absolute value ofδfor equivalence test and non-inferiority test. But it increases along with the increase ofδfor superiority test.It cannot be understood as equivalent when there is no statistically significant difference between two sample means or two sample proportions in two-side difference test.It may be equivalent or not equivalent when there is no statistically significant difference in two-side difference test. And it may be equivalent or not equivalent when there is a statistically significant difference in two-side difference test.The efficacy of the test drug is not always non-inferior to that of the reference drug when there is no statistically significant difference between two sample means or two sample proportions in left-side difference test.The efficacy of the test drug may be inferior or non-inferior to that of the reference drug when there is no statistically significant difference in left-side difference test. The efficacy of the test drug may be inferior or non-inferior to that of the reference drug when there is a statistically significant difference in left-side difference test.The efficacy of the test drug is not always superior to that of the reference drug when there is a statistically significant difference between two sample means or two sample proportions in right-side difference test. The sample size required in right-side difference test is smaller than that of superiority test when other conditions are fixed. And it is close to that of right-side difference test along with the decrease ofδ_U. The sample size is equal whenδ_U = 0.The power of right-side difference test is larger than that of superiority test when other conditions are fixed. And it is close to that of right-side difference test along with the decrease ofδ_U. The power is equal whenδ_U = 0.The efficacy of the test drug is not superior to that of the reference drug in superiority test when there is no statistically significant difference in right-side difference test. It is superior or not superior to that of the reference drug in superiority test when there is a statistically significant difference in right-side difference test.The order of the sample size required in the six kinds of comparison types for a given study when other conditions are fixed is as follows:The sample size required in right-side difference test is smaller than that of superiority test. The sample size required in non-inferiority test is smaller than that of right-side difference test. The sample size required in non-inferiority test is smaller than that of equivalence test. The sample size required in superiority test is smaller than that of equivalence test whenμ_T-μR>δ. But the sample size required in equivalence test is smaller than that of superiority test whenμ_T-μR<δ. The sample size required in superiority test is smaller than that of equivalence test when PT- PR>δ. But the sample size required in equivalence test is smaller than that of superiority test when PT- PR<δ. The order of other kinds of tests varies with different data.The order of power of the six kinds of comparison types for a given study when other conditions are fixed is as follows:The power of right-side difference test is larger than that of superiority test. The power of non-inferiority test is larger than that of right-side difference test. The power of non-inferiority test is larger than or equal to that of equivalence test. The order of other kinds of tests varies with different data.The order of p-value of the six kinds of comparison types for a given study when other conditions are fixed is as follows:The p-value of right-side difference test is smaller than that of superiority test. The p-value of non-inferiority test is smaller than that of right-side difference test. The p-value of the left-side of equivalence test is equal to that of non-inferiority test. The p-value of two-side difference test is smaller than that of superiority test. The p-value of two-side difference test is smaller than or equal to that of right-side difference test. The p-value of two-side difference test is smaller than or equal to that of left-side difference test. The p-value of right-side difference test is equal to that of two-side difference test when (x|-)_T-(x|-)_R> 0 . The p-value of left-side difference test is equal to that of two-side difference test when (x|-)_T-(x|-)_R< 0 . The p-value of right-side difference test is equal to that of two-side difference test when PT- PR> 0 . The p-value of left-side difference test is equal to that of two-side difference test when PT- PR< 0 . The order of other kinds of tests varies with different data.Fifthly, we achieve the hypothesis test, sample size estimation and power analysis for two-side difference test, right-side difference test, left-side difference test, equivalence test, superiority test and non-inferiority test using SAS program.