Zhao Yang

Dose-response and finding in phase II clinical studies — MCP-Mod Methodologies

Zhao Yang — Wed, 05 Jun 2013 19:51:00 PDT

This presentation give an overall introduction to the MCP-Mod methodology with detailed step-by-step demonstration.

SAS Macro: Kappa statistic for clustered matched-pair data

Zhao Yang — Wed, 05 Jun 2013 19:17:16 PDT

The SAS macro was developed to calculate the kappa statistic for the clustered matched-pair data.

Generalized McNemar's Test for Homogeneity of the Marginal Distributions

Zhao Yang — Sun, 25 Nov 2012 14:29:11 PST

In the matched-pairs data, McNemar's test (McNemar, 1947) can be applied only to the case in which there are two possible categories for the outcome. In practice, however, it is possible that the outcomes are classified into multiple categories. Under this situation, the test statistic proposed by Stuart (1955) and Maxwell (1970) is useful; it is actually the generalization of the McNemar's test, commonly referred to as generalized McNemar's or Stuart-Maxwell test. There is no public available SAS program to calculate this statistic, the author has developed a SAS macro (the code is detailed in appendix) to perform this test and briefly describes how to use the macro. Examples using the developed SAS macro are also included.

A non-iterative implementation of Tango's score confidence interval for a paired difference of proportions

Zhao Yang — Sun, 25 Nov 2012 14:25:27 PST

For matched-pair binary data, a variety of approaches have been proposed for the construction of a confidence interval (CI) for the difference of marginal probabilities between two procedures. The score-based approximate CI has been shown to outperform other asymptotic CIs. Tango's method provides a score CI by inverting a score test statistic using an iterative procedure. In this paper, we propose an efficient non-iterative method with closed-form expression to calculate Tango's CIs. Examples illustrate the practical application of the new approach.

A note on the tests for clustered matched-pair binary data

Zhao Yang — Sun, 25 Nov 2012 14:23:39 PST

McNemar's test is used to assess the difference between two different procedures (treatments) using independent matched-pair data. For matched-pair data collected in clusters, the tests proposed by Durkalski et al. and Obuchowski are popular and commonly used in practice since these tests do not require distributional assumptions or assumptions on the structure of the within-cluster correlation of the data. Motivated by these tests, this note proposes a modified Obuchowski test and illustrates comparisons of the proposed test with the extant methods. An extensive Monte Carlo simulation study suggests that the proposed test performs well with respect to the nominal size, and has higher power; Obuchowski's test is most conservative, and the performance of the Durkalski's test varies between the modified Obuchowski test and the original Obuchowski's test.

Testing ratio of marginal probabilities in clustered matched-pair binary data

Zhao Yang — Sun, 25 Nov 2012 14:21:33 PST

In diagnostic methods evaluation, analysts commonly focus on the relative size of the treatment difference (ratio of marginal probabilities) between a new and an existing procedures. To assess non-inferiority (a new procedure is, to a pre-specified amount, no worse than an existing procedure) via a ratio of marginal probabilities between two procedures using clustered matched-pair binary data, four ICC-adjusted test statistics are investigated. The calculation of corresponding confidence intervals is also proposed. None of the tests considered require structural within-cluster correlation or distributional assumptions. Results of an extensive Monte Carlo simulation study illustrate that the new approaches effectively maintain the nominal Type I error even for small numbers of clusters. Thus, to design and evaluate non-inferiority via a ratio of marginal probabilities, researchers are suggested to utilize designs that have small cluster-size variability (e.g., nk≤5). Finally, to illustrate the practical application of the tests and recommendations, a real clustered matched-pair collection of data is used to illustrate testing non-inferiority.

Testing non-inferiority for clustered matched-pair binary data in diagnostic medicine

Zhao Yang — Sun, 25 Nov 2012 14:20:18 PST

Testing non-inferiority in active-controlled clinical trials examines whether a new procedure is, to a pre-specified amount, no worse than an existing procedure. To assess non-inferiority between two procedures using clustered matched-pair binary data, two new statistical tests are systematically compared to existing tests. The calculation of corresponding confidence interval is also proposed. None of the tests considered requires structural within-cluster correlation or distributional assumptions. The results of an extensive Monte Carlo simulation study illustrate that the performance of the statistics depends on several factors including the number of clusters, cluster size, probability of success in the test procedure, the homogeneity of the probability of success across clusters, and the intra-cluster correlation coefficient (ICC). In evaluating non-inferiority for a clustered matched-pair study, one should consider all of these issues when choosing an appropriate test statistic. The ICC-adjusted test statistic is generally recommended to effectively control the nominal level when there is constant or small variability of cluster sizes. For a greater number of clusters, the other test statistics maintain the nominal level reasonably well and have higher power. Therefore, with the carefully designed clustered matched-pair study, a combination of the statistics investigated may serve best in data analysis. Finally, to illustrate the practical application of the recommendations, a real clustered matched-pair collection of data is used to illustrate testing non-inferiority.

Testing Marginal Homogeneity in Matched-Pair Polytomous Data

Zhao Yang — Sun, 25 Nov 2012 14:18:46 PST

Statistical tests for assessing marginal homogeneity of matched-pair polytomous data can be classified as a score-type test or a Wald-type test; the Wald-type Bhapkar test is a more powerful alternative to the score-type Stuart–Maxwell test, and the Bhapkar test tends to be liberal. Extending the authors’ earlier work, an additional test of each classification is proposed for testing marginal homogeneity, and the relationships among the available test statistics are established. The results from some limited simulation study suggest that the new proposals are very competitive alternatives to the extant methods. These results are the basis of the authors’ recommendations to practitioners. Information from SAS procedure PROC CATMOD regarding Bhapkar’s test statistic and the relationship among the test statistics make their implementation and calculation convenient and accessible to interested researchers.

Testing marginal homogeneity in clustered matched-pair data

Zhao Yang — Sun, 25 Nov 2012 14:17:24 PST

For general matched-pair data with polytomous responses in biomedical research, the Stuart–Maxwell test and the Bhapkar (1966) test are commonly used for evaluating marginal homogeneity. For data collected in clusters, we propose extensions for statistical inference without structural within-cluster correlation or distributional assumptions. Meanwhile, two extended Obuchowski tests are proposed based on the work of Obuchowski (1998) generally applied to clustered matched-pair binary data. A Monte Carlo simulation study illustrates that our proposed extension to the Stuart–Maxwell test and the two extended Obuchowski tests perform well with respect to the power and the nominal size, though the extended Bhapkar test is asymptotically equivalent to the other three tests, it is not recommended in practice due to its being liberal in the nominal size.

Comments on ‘Non-inferiority tests for clustered matched-pair data’

Zhao Yang — Sun, 25 Nov 2012 14:15:31 PST

A score test for overdispersion in Poisson regression based on the generalized Poisson-2 model

Zhao Yang — Sun, 25 Nov 2012 14:13:10 PST

Overdispersion is a common phenomenon in Poisson modeling. The generalized Poisson (GP) regression model accommodates both overdispersion and underdispersion in count data modeling, and is an increasingly popular platform for modeling overdispersed count data. The Poisson model is one of the special cases in the collection of models which may be specified by GP regression. Thus, we may derive a test of overdispersion which compares the equi-dispersion Poisson model within the context of the more general GP regression model. The score test has an advantage over the likelihood ratio test (LRT) and over the Wald test in that the score test only requires that the parameter of interest be estimated under the null hypothesis (the Poisson model). Herein, we propose a score test for overdispersion based on the GP model (specifically the GP-2 model) and compare the power of the test with the LRT and Wald tests. A simulation study indicates the proposed score test based on asymptotic standard normal distribution is more appropriate in practical applications.

Testing overdispersion in the zero-inflated Poisson model

Zhao Yang — Sun, 25 Nov 2012 14:11:27 PST

The zero-inflated negative binomial (ZINB) model is used to account for commonly occurring overdispersion detected in data that are initially analyzed under the zero-inflated Poisson (ZIP) model. Tests for overdispersion (Wald test, likelihood ratio test [LRT], and score test) based on ZINB model for use in ZIP regression models have been developed. Due to similarity to the ZINB model, we consider the zero-inflated generalized Poisson (ZIGP) model as an alternate model for overdispersed zero-inflated count data. The score test has an advantage over the LRT and the Wald test in that the score test only requires that the parameter of interest be estimated under the null hypothesis. This paper proposes score tests for overdispersion based on the ZIGP model and illustrates that the derived score statistics are exactly the same as the score statistics under the ZINB model. A simulation study indicates the proposed score statistics are preferred to other tests for higher empirical power. In practice, based on the approximate mean–variance relationship in the data, the ZINB or ZIGP model can be considered, and a formal score test based on asymptotic standard normal distribution can be employed for assessing overdispersion in the ZIP model. We provide an example to illustrate the procedures for data analysis.

Some Remarks on Testing Overdispersion in Zero-Inflated Poisson and Binomial Regression Models

Zhao Yang — Sun, 25 Nov 2012 14:09:53 PST

This note extends the score test statistics for overdispersion in Poisson and binomial regression models (Dean, 1992) to the zero-inflated models. Some general results are obtained, and examples illustrate the application of the extended results.

A note on Dean's overdispersion test

Zhao Yang — Sun, 25 Nov 2012 14:08:28 PST

This note discusses an extension to the score test statistics for overdispersion in Poisson and binomial regression models [Dean, C.B., 1992. Testing for overdispersion in Poisson and binomial regression models. J. Amer. Statist. Assoc. 87, 451–457]. Examples illustrate the application of the extended results.

Testing Approaches for Overdispersion in Poisson Regression versus the Generalized Poisson Model

Zhao Yang — Sun, 25 Nov 2012 14:06:13 PST

Overdispersion is a common phenomenon in Poisson modeling, and the negative binomial (NB) model is frequently used to account for overdispersion. Testing approaches (Wald test, likelihood ratio test (LRT), and score test) for overdispersion in the Poisson regression versus the NB model are available. Because the generalized Poisson (GP) model is similar to the NB model, we consider the former as an alternate model for overdispersed count data. The score test has an advantage over the LRT and the Wald test in that the score test only requires that the parameter of interest be estimated under the null hypothesis. This paper proposes a score test for overdispersion based on the GP model and compares the power of the test with the LRT and Wald tests. A simulation study indicates the score test based on asymptotic standard Normal distribution is more appropriate in practical application for higher empirical power, however, it underestimates the nominal significance level, especially in small sample situations, and examples illustrate the results of comparing the candidate tests between the Poisson and GP models. A bootstrap test is also proposed to adjust the underestimation of nominal level in the score statistic when the sample size is small. The simulation study indicates the bootstrap test has significance level closer to nominal size and has uniformly greater power than the score test based on asymptotic standard Normal distribution. From a practical perspective, we suggest that, if the score test gives even a weak indication that the Poisson model is inappropriate, say at the 0.10 significance level, we advise the more accurate bootstrap procedure as a better test for comparing whether the GP model is more appropriate than Poisson model. Finally, the Vuong test is illustrated to choose between GP and NB2 models for the same dataset.

Score Tests for Zero-Inflation in Overdispersed Count Data

Zhao Yang — Sun, 25 Nov 2012 13:55:23 PST

The negative binomial (NB) model and the generalized Poisson (GP) model are common alternatives to Poisson models when overdispersion is present in the data. Having accounted for initial overdispersion, we may require further investigation as to whether there is evidence for zero-inflation in the data. Two score statistics are derived from the GP model for testing zero-inflation. These statistics, unlike Wald-type test statistics, do not require that we fit the more complex zero-inflated overdispersed models to evaluate zero-inflation. A simulation study illustrates that the developed score statistics reasonably follow a χ2 distribution and maintain the nominal level. Extensive simulation results also indicate the power behavior is different for including a continuous variable than a binary variable in the zero-inflation (ZI) part of the model. These differences are the basis from which suggestions are provided for real data analysis. Two practical examples are presented in this article. Results from these examples along with practical experience lead us to suggest performing the developed score test before fitting a zero-inflated NB model to the data.

Score tests for overdispersion in zero-inflated Poisson mixed models

Zhao Yang — Sun, 25 Nov 2012 13:50:06 PST

This note is motivated by recent works of Xie et al. (2009) and Xiang et al. (2007). Herein, we simplify the score statistic presented by Xie et al. (2009) to test overdispersion in the zero-inflated generalized Poisson (ZIGP) mixed model, and discuss an extension to test overdispersion in zero-inflated Poisson (ZIP) mixed models. Examples highlight the application of the extended results. The extensive simulation study for testing overdispersion in the Poisson mixed model indicates that the proposed score statistics maintain the nominal level reasonably well. In practice, the appropriate model is chosen based on the approximate mean–variance relationship in the data, and a formal score test based on asymptotic standard normal distribution can be employed for testing overdispersion. A case study is provided to illustrate procedures for data analysis.

Confidence intervals for the difference of marginal probabilities in clustered matched-pair binary data

Zhao Yang — Sun, 25 Nov 2012 13:41:24 PST

Although there are several available test statistics to assess the difference of marginal probabilities in clustered matched-pair binary data, associated confidence intervals (CIs) are not readily available. Herein, the construction of corresponding CIs is proposed, and the performance of each CI is investigated. The results from Monte Carlo simulation study indicate that the proposed CIs perform well in maintaining the nominal coverage probability: for small to medium numbers of clusters, the intra-cluster correlation coefficient-adjusted McNemar statistic and its associated Wald or Score CIs are preferred; however, this statistic becomes conservative when the number of clusters is larger so that alternative statistics and their associated CIs are preferred. In practice, a combination of the intra-cluster correlation coefficient-adjusted McNemar statistic with an alternative statistic is recommended. To illustrate the practical application, a real clustered matched-pair collection of data is used to illustrate testing the difference of marginal probabilities and constructing the associated CIs.

R code: A non-iterative implementation of Tango's score confidence interval for a paired difference of proportions

Zhao Yang — Thu, 12 Jul 2012 16:38:26 PDT

For matched-pair binary data, a variety of approaches have been proposed for the construction of a confidence interval (CI) for the difference of marginal probabilities between two procedures. The score-based approximate CI has been shown to outperform other asymptotic CIs. Tango’s method provides a score CI by inverting a score test statistic using an iterative procedure. In the developed R code, we propose an efficient non-iterative method with closed-form expression to calculate Tango’s CIs. Examples illustrate the practical application of the new approach.