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Man-Lai Tang

Publications and source records attributed to Man-Lai Tang.

15 recordsLinked to original sources
PubMed2006

Sample size determination for matched-pair equivalence trials using rate ratio.

In this article, we compare Wald-type, logarithmic transformation, and Fieller-type statistics for the classical 2-sided equivalence testing of the rate ratio under matched-pair designs with a binary end point. These statistics can be implemented through sample-based, constrained least squares estimation and constrained maximum likelihood (CML) estimation methods. Sample size formulae based on the CML estimation method are developed. We consider formulae that control a prespecified power or confidence width. Our simulation studies show that statistics based on the CML estimation method generally outperform other statistics and methods with respect to actual type I error rate and average width of confidence intervals. Also, the corresponding sample size formulae are valid asymptotically in the sense that the exact power and actual coverage probability for the estimated sample size are generally close to their prespecified values. The methods are illustrated with a real example from a clinical laboratory study.

Biometry↗
PubMed2006

Statistical inference for correlated data in ophthalmologic studies.

In ophthalmologic studies, each subject usually contributes important information for each of two eyes and the values from the two eyes are generally highly correlated. Previous studies showed that test procedures for binary paired data that ignore the presence of intraclass correlation could lead to inflated significance levels. Furthermore, it is possible that asymptotic versions of these procedures that take the intraclass correlation into account could also produce unacceptably high type I error rates when the sample size is small or the data structure is sparse. We propose two alternatives for these situations, namely the exact unconditional and approximate unconditional procedures. According to our simulation results, the exact procedures usually produce extremely conservative empirical type I error rates. That is, the corresponding type I error rates could greatly underestimate the pre-assigned nominal level (e.g. (empirical type I error rate/nominal type I error rate) 0.8). On the other hand, the approximate unconditional procedures usually yield empirical type I error rates close to the pre-chosen nominal level. We illustrate our methodologies with a data set from a retinal detachment study.

Biometry↗
PubMed2006

A test of homogeneity of Hardy-Weinberg disequilibrium across strata.

For genotype data being sampled from several strata with different allele frequencies, it is necessary to verify the assumption of homogeneity of Hardy-Weinberg disequilibrium across strata before testing Hardy-Weinberg law across strata. In practice, disequilibrium can be measured via fixation coefficients (ie, ratios of genotypic frequencies) or disequilibrium coefficients (ie, differences of genotypic frequencies). Test for homogeneity of Hardy-Weinberg disequilibrium using data from several populations has been derived according to fixation coefficients. In this article, using the likelihood score theory extended to nuisance parameters, we derive a homogeneity score test for comparing disequilibrium coefficients across several independent strata. Simulation results demonstrate that the homogeneity score test performs satisfactorily in the sense that its empirical size seldom exceeds the pre-chosen nominal level by more than 10% even for small sample sizes. Corresponding power and sample size formulae are provided as well. We illustrate our test with a real glyoxalase genotype data set.

Gene Frequency↗
PubMed2005

Confidence interval construction for proportion difference in small-sample paired studies.

Paired dichotomous data may arise in clinical trials such as pre-/post-test comparison studies and equivalence trials. Reporting parameter estimates (e.g. odds ratio, rate difference and rate ratio) along with their associated confidence interval estimates becomes a necessity in many medical journals. Various asymptotic confidence interval estimators have long been developed for differences in correlated binary proportions. Nevertheless, the performance of these asymptotic methods may have poor coverage properties in small samples. In this article, we investigate several alternative confidence interval estimators for the difference between binomial proportions based on small-sample paired data. Specifically, we consider exact and approximate unconditional confidence intervals for rate difference via inverting a score test. The exact unconditional confidence interval guarantees the coverage probability, and it is recommended if strict control of coverage probability is required. However, the exact method tends to be overly conservative and computationally demanding. Our empirical results show that the approximate unconditional score confidence interval estimators based on inverting the score test demonstrate reasonably good coverage properties even in small-sample designs, and yet they are relatively easy to implement computationally. We illustrate the methods using real examples from a pain management study and a cancer study.

Biometry↗
PubMed2005

Testing the equality of two Poisson means using the rate ratio.

In this article, we investigate procedures for comparing two independent Poisson variates that are observed over unequal sampling frames (i.e. time intervals, populations, areas or any combination thereof). We consider two statistics (with and without the logarithmic transformation) for testing the equality of two Poisson rates. Two methods for implementing these statistics are reviewed. They are (1) the sample-based method, and (2) the constrained maximum likelihood estimation (CMLE) method. We conduct an empirical study to evaluate the performance of different statistics and methods. Generally, we find that the CMLE method works satisfactorily only for the statistic without the logarithmic transformation (denoted as W(2)) while sample-based method performs better for the statistic using the logarithmic transformation (denoted as W(3)). It is noteworthy that both statistics perform well for moderate to large Poisson rates (e.g. > or =10). For small Poisson rates (e.g. <10), W(2) can be liberal (e.g. actual type I error rate/nominal level > or =1.2) while W(3) can be conservative (e.g. actual type I error rate/nominal level < or =0.8). The corresponding sample size formulae are provided and valid in the sense that the simulated powers associated with the approximate sample size formulae are generally close to the pre-chosen power level. We illustrate our methodologies with a real example from a breast cancer study.

Breast Neoplasms↗
PubMed2004

On simultaneous assessment of sensitivity and specificity when combining two diagnostic tests.

Diagnostic tests are seldom adopted in isolation. Few tests have high sensitivity and specificity simultaneously. In these cases, one can increase either the sensitivity or the specificity by combining two component tests under either the 'either positive' rule or the 'both positive' rule. However, there is a tradeoff between sensitivity and specificity when these rules are applied. We propose three statistical procedures to simultaneously assess the sensitivity and specificity when combining two component tests. Measurements of interest include rate difference and rate ratio. Our empirical results demonstrate that (i) the asymptotic test procedures for both measurements and approximate test procedure for rate difference possess inflated type I error rate; (ii) the exact test procedures for both measurements possess deflated type I error rate; and (iii) the approximate (unconditional) test procedure for rate ratio becomes an reliable alternative and nicely controls the actual type I error rate in small to moderate sample sizes. Moreover, the approximate (unconditional) test procedure is computationally less intensive than the exact (unconditional) test procedure. We illustrate our methodologies with a real example from a residual nasopharyngeal carcinoma (RNP) study.

Biometry↗
PubMed2004

Tests of noninferiority via rate difference for three-arm clinical trials with placebo.

In assessing a noninferiority trial, the investigator intends to show efficacy by demonstrating that a new experimental drug/treatment is not worse than a known active control/reference by a small predefined margin. If it is ethically justifiable, it may be advisable to include an additional placebo group for internal validation purpose. This constitutes the well-known three-arm clinical trial with placebo. In this paper, we study two asymptotic statistical methods for testing of noninferiority in three-arm clinical trials with placebo for binary outcomes based on rate difference. They are sample-based estimation method and restricted maximum likelihood estimation method, respectively. We investigate the performance of the proposed test procedures under different sample size allocation settings via a simulation study. Both methods perform satisfactorily under moderate to large sample settings. However, the restricted maximum likelihood estimation method usually possesses slightly smaller actual type I error rates, which are relatively close to the prespecified nominal level, while the sample-based method can be expressed in a simple closed-form format. Real examples from a pharmacological study of patients with functional dyspepsia and a placebo-controlled trial of subjects with acute migraine are used to demonstrate our methodologies.

Humans↗
PubMed2004

Confidence interval for rate ratio in a 2 x 2 table with structural zero: an application in assessing false-negative rate ratio when combining two diagnostic tests.

In this article, we consider problems with correlated data that can be summarized in a 2 x 2 table with structural zero in one of the off-diagonal cells. Data of this kind sometimes appear in infectious disease studies and two-step procedure studies. Lui (1998, Biometrics54, 706-711) considered confidence interval estimation of rate ratio based on Fieller-type, Wald-type, and logarithmic transformation statistics. We reexamine the same problem under the context of confidence interval construction on false-negative rate ratio in diagnostic performance when combining two diagnostic tests. We propose a score statistic for testing the null hypothesis of nonunity false-negative rate ratio. Score test-based confidence interval construction for false-negative rate ratio will also be discussed. Simulation studies are conducted to compare the performance of the new derived score test statistic and existing statistics for small to moderate sample sizes. In terms of confidence interval construction, our asymptotic score test-based confidence interval estimator possesses significantly shorter expected width with coverage probability being close to the anticipated confidence level. In terms of hypothesis testing, our asymptotic score test procedure has actual type I error rate close to the pre-assigned nominal level. We illustrate our methodologies with real examples from a clinical laboratory study and a cancer study.

Biometry↗
PubMed2003

On tests of equivalence via non-unity relative risk for matched-pair design.

Matched-pair design is often used in clinical trials to increase the efficiency of treatment comparison. We consider the problem of equivalence test with a relative risk endpoint in matched-pair studies with binary outcomes, and develop several score and Wald-type statistics for testing a hypothesis of non-unity relative risk. Examples from an assessment of HIV screening test and a cross-over clinical trial of soft contact lenses are used to illustrate the proposed methods. Through simulations we compare the empirical performance of these tests with the test proposed by Lachenbruch and Lynch. We show that a score test based on a reparameterized multinomial model by Tango performs best in the sense that the test satisfactorily controls the type I error rate and its empirical type I error rates are generally much closer to the prespecified nominal significance level than those of the other tests.

AIDS Serodiagnosis↗
PubMed2003

Statistical analysis of noninferiority trials with a rate ratio in small-sample matched-pair designs.

Testing of noninferiority has become increasingly important in modern medicine as a means of comparing a new test procedure to a currently available test procedure. Asymptotic methods have recently been developed for analyzing noninferiority trials using rate ratios under the matched-pair design. In small samples, however, the performance of these asymptotic methods may not be reliable, and they are not recommended. In this article, we investigate alternative methods that are desirable for assessing noninferiority trials, using the rate ratio measure under small-sample matched-pair designs. In particular, we propose an exact and an approximate exact unconditional test, along with the corresponding confidence intervals based on the score statistic. The exact unconditional method guarantees the type I error rate will not exceed the nominal level. It is recommended for when strict control of type I error (protection against any inflated risk of accepting inferior treatments) is required. However, the exact method tends to be overly conservative (thus, less powerful) and computationally demanding. Via empirical studies, we demonstrate that the approximate exact score method, which is computationally simple to implement, controls the type I error rate reasonably well and has high power for hypothesis testing. On balance, the approximate exact method offers a very good alternative for analyzing correlated binary data from matched-pair designs with small sample sizes. We illustrate these methods using two real examples taken from a crossover study of soft lenses and a Pneumocystis carinii pneumonia study. We contrast the methods with a hypothetical example.

Biometry↗
PubMed2002

Simple polynomial multiplication algorithms for exact conditional tests of linearity in a logistic model.

The linear logistic model is often employed in the analysis of binary response data. The well-known asymptotic chi-square and likelihood ratio tests are usually used to detect the assumption of linearity in such a model. For small, sparse, or skewed data, the asymptotic theory is however dubious and exact conditional chi-square and likelihood ratio tests may provide reliable alternatives. In this article, we propose efficient polynomial multiplication algorithms to compute exact significance levels as well as exact powers of these tests. Two options, namely the cell- and stage-wise approaches, in implementing these algorithms will be discussed. When sample sizes are large, we propose an efficient Monte Carlo method for estimating the exact significance levels and exact powers. Real data are used to demonstrate the performance with an application of the proposed algorithms.

Algorithms↗
PubMed2002

On the use of historical control information for trend test in carcinogenesis.

In this article a new non-model-based significance test for detecting dose-response relationship with the incorporation of historical control data is proposed. This non-model-based test is considered simpler from a regulatory perspective because it does not require validating any modeling assumptions. Moreover, our test is especially appropriate to those studies in which the intravenous doses for the investigational chemical are labeled as, e.g., low, medium and high or the dose labels do not suggest any obvious choices of dose scores. This test can be easily adopted for detecting general dose-response shape, such as an umbrella pattern. Simple adjustments will be proposed for better control of the actual Type I error. Data sets from two carcinogenesis studies will be used to illustrate our method. We also evaluate the performance of the proposed test and the famous model-based Tarone's trend test with respect to size and power.

Animals↗
PubMed2002

Sample size determination for establishing equivalence/noninferiority via ratio of two proportions in matched-pair design.

In this article, we propose approximate sample size formulas for establishing equivalence or noninferiority of two treatments in match-pairs design. Using the ratio of two proportions as the equivalence measure, we derive sample size formulas based on a score statistic for two types of analyses: hypothesis testing and confidence interval estimation. Depending on the purpose of a study, these formulas can be used to provide a sample size estimate that guarantees a prespecified power of a hypothesis test at a certain significance level or controls the width of a confidence interval with a certain confidence level. Our empirical results confirm that these score methods are reliable in terms of true size, coverage probability, and skewness. A liver scan detection study is used to illustrate the proposed methods.

Biopsy↗
PubMed2002

Exact unconditional inference for risk ratio in a correlated 2 x 2 table with structural zero.

In this article, we consider small-sample statistical inference for rate ratio (RR) in a correlated 2 x 2 table with a structural zero in one of the off-diagonal cells. Existing Wald's test statistic and logarithmic transformation test statistic will be adopted for this purpose. Hypothesis testing and confidence interval construction based on large-sample theory will be reviewed first. We then propose reliable small-sample exact unconditional procedures for hypothesis testing and confidence interval construction. We present empirical results to evince the better confidence interval performance of our proposed exact unconditional procedures over the traditional large-sample procedures in small-sample designs. Unlike the findings given in Lui (1998, Biometrics 54, 706-711), our empirical studies show that the existing asymptotic procedures may not attain a prespecified confidence level even in moderate sample-size designs (e.g., n = 50). Our exact unconditional procedures on the other hand do not suffer from this problem. Hence, the asymptotic procedures should be applied with caution. We propose two approximate unconditional confidence interval construction methods that outperform the existing asymptotic ones in terms of coverage probability and expected interval width. Also, we empirically demonstrate that the approximate unconditional tests are more powerful than their associated exact unconditional tests. A real data set from a two-step tuberculosis testing study is used to illustrate the methodologies.

Confidence Intervals↗