Responder analysis without dichotomization.

In clinical trials, it is common practice to categorize subjects as responders and non-responders on the basis of one or more clinical measurements under pre-specified rules. Such a responder analysis is often criticized for the loss of information in dichotomizing one or more continuous or ordinal variables. It is worth noting that a responder analysis can be performed without dichotomization, because the proportion of responders for each treatment can be derived from a model for the original clinical variables (used to define a responder) and estimated by substituting maximum likelihood estimators of model parameters. This model-based approach can be considerably more efficient and more effective for dealing with missing data than the usual approach based on dichotomization. For parameter estimation, the model-based approach generally requires correct specification of the model for the original variables. However, under the sharp null hypothesis, the model-based approach remains unbiased for estimating the treatment difference even if the model is misspecified. We elaborate on these points and illustrate them with a series of simulation studies mimicking a study of Parkinson's disease, which involves longitudinal continuous data in the definition of a responder.

Testing homogeneity of stratum effects in stratified paired binary data.

For paired binary data, McNemar's test is widely used to test marginal homogeneity or symmetry for a 2 by 2 contingency table. In this article, we extend McNemar's test by considering a series of paired binary data in which the series is defined by a stratification factor. We provide a test for testing homogeneous stratum effects. For illustration, we apply our test to a cancer epidemiology study. Finally, we conduct simulations to show that our test preserves the nominal type I error level and evaluate the power of our test under various scenarios.

Modulatory effect of neoadjuvant chemotherapy on biomarkers expression; assessment by digital image analysis and relationship to residual cancer burden in patients with invasive breast cancer.

The use of digital imaging techniques for biomarker assessment has gained recognition as a valid tool for clinical use. In this study, we used image analysis for evaluation of estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor (HER2), Ki-67 index, and p53 in 172 patients with invasive breast cancer treated with neoadjuvant chemotherapy and compared it with an untreated group (100 cases). We also examined the relationship between biomarker expression and the extent of residual disease using the Web-based MD Anderson residual cancer burden (RCB) calculator. Residual disease was classified as RCB 0/I, II, and III corresponding to complete/near-complete response, moderate, and extensive residual disease, respectively. Overall change in ER, PR, and HER2 status in the treated group was seen in 9.02% (P = .0148), 18.4% (P = .011), and 12.0% (P = .0042), respectively. Change in HER2 status, positive to negative and negative to positive, occurred in 27.2% and 7.0%, respectively. The group with RCB 0/I was frequently younger (P = .0057) and showed higher ER(-) status (P = .0316), lower ER scores (P = .0103), higher Ki-67 index (P = .0008), and p53 (P = .0055) compared with those with RCB II and III. Pathologic tumor stage (P = .0072), lumpectomy versus mastectomy (P = .0048), and p53 expression (P = .0190) were independent predictors of recurrence-free survival. The RCB categories (P = .0003) and tumor grade (P = .0049) were independent predictors of overall survival. This is the first study to conduct a comprehensive analysis of biomarkers in neoadjuvant chemotherapy-treated patients versus an untreated group using the digital image analysis method. We have demonstrated for the first time the relationship between RCB, tumor biomarkers expression, and clinical outcome.

Estimation of the common risk difference in stratified paired binary data with homogeneous stratum effect.

McNemar's test is commonly used to test for the risk difference between two binary variables on matched pairs. For stratified paired binary data, recently a test for the homogeneous stratum effect (HSE) has been developed. If HSE is rejected, then McNemar's test should be applied by stratum; otherwise, in this article we propose a concept of common risk difference (CRD) across the strata and derive point estimators and confidence intervals for CRD. We use a cancer study for illustration and conduct simulations to recommend point estimators and associated confidence intervals with good statistical properties.

Adjusting wheal size measures to correct atopy misclassification.

PURPOSE: Skin prick testing (SPT) is fundamental to the practice of clinical allergy identifying relevant allergens and predicting the clinical expression of disease. Wheal sizes on SPT are used to identify atopic cases, and the cut-off value for a positive test is commonly set at 3 mm. However, the measured wheal sizes do not solely reflect the magnitude of skin reaction to allergens, but also skin reactivity (reflected in the size of histamine reaction) and other random or non-random factors. We sought to estimate wheal sizes exclusively due to skin response to allergens and propose gender-specific cutoff points of atopy. METHODS: We developed a Bayesian method to adjust observed wheal sizes by excluding histamine and other factor effects, based on which revised cutoff points are proposed for males and females, respectively. The method is then applied to and intensively evaluated using a study population aged 18, at a location on the Isle of Wight in the United Kingdom. To evaluate the proposed approach, two sample t-tests for population means and proportion tests are applied. RESULTS: Four common aeroallergens, house dust mite (HDM), grass pollen, dog dander, and alternaria are considered in the study. Based on 3 mm cutoff, males tend to be more atopic than females (P-values are between 0.00087 and 0.062). After applying the proposed methods to adjust wheal sizes, our findings suggest that misclassifications of atopy occur more often in males. Revised allergen-specific cutoff values are proposed for each gender. CONCLUSION: To reduce the gender discrepancy, we may have two potentially convenient solutions. One way is to apply allergen-specific and gender-specific cutoff values following the proposed method. Alternatively, we can revise the concentration of allergens in the SPT solutions but keep the cutoff values unchanged, which may be more convenient to clinicians.

Bayesian inference of risk ratio of two proportions using a double sampling scheme.

We consider Bayesian point and interval estimation for a risk ratio of two proportion parameters using two independent samples of binary data subject to misclassification. In order to obtain model identifiability, we apply a double sampling scheme. For the identifiable model, we propose a Bayesian method for statistical inference for a two proportion risk ratio. Specifically, we derive an easy-to-implement closed-form sampling algorithm to draw from the posterior distribution of interest. We demonstrate the efficiency of our algorithm for Bayesian inference via Monte Carlo simulation studies and using a real data example.

Wilcoxon-Mann-Whitney test: stratify or not?

The Wilcoxon-Mann-Whitney (WMW) test is the most commonly used nonparametric method to compare two treatments when the underlying distribution of the outcome variable is not normally distributed. In the presence of stratum effects, the van Elteren (vE) test, a stratified WMW test, can be used to adjust for the stratum effect. We provide guidance on how to choose between the two tests in the design phase of clinical trials and in the analysis of clinical data. We show by simulations that both tests preserve the type I error rate regardless of the presence of the stratum effects. Therefore, the test with greater power is preferred. In comparing powers, we found that the WMW test is better when the stratum effects are small, whereas the vE test is better when the stratum effects are large. Finally, when the stratum effects are moderate, the decision depends on the shape of the distribution and the ratio of the number of strata and the number of subjects. In this case, results presented in this article or from similar simulations may be used to determine which test is better.

Sample size calculation for the van Elteren test adjusting for ties.

In this article we study sample size calculation methods for the asymptotic van Elteren test. Because the existing methods are only applicable to continuous data without ties, in this article we develop a new method that can be used on ordinal data. The new method has a closed form formula and is very easy to calculate. The new sample size formula performs very well because our simulations show that the corresponding actual powers are close to the nominal powers.

Sample size calculation for the Wilcoxon-Mann-Whitney test adjusting for ties.

In this paper we study sample size calculation methods for the asymptotic Wilcoxon-Mann-Whitney test for data with or without ties. The existing methods are applicable either to data with ties or to data without ties but not to both cases. While the existing methods developed for data without ties perform well, the methods developed for data with ties have limitations in that they are either applicable to proportional odds alternatives or have computational difficulties. We propose a new method which has a closed-form formula and therefore is very easy to calculate. In addition, the new method can be applied to both data with or without ties. Simulations have demonstrated that the new sample size formula performs very well as the corresponding actual powers are close to the nominal powers.

Power approximation for the van Elteren test based on location-scale family of distributions.

The van Elteren test, as a type of stratified Wilcoxon-Mann-Whitney test for comparing two treatments accounting for stratum effects, has been used to replace the analysis of variance when the normality assumption was seriously violated. The sample size estimation methods for the van Elteren test have been proposed and evaluated previously. However, in designing an active-comparator trial where a sample of responses from the new treatment is available but the patient response data to the comparator are limited to summary statistics, the existing methods are either inapplicable or poorly behaved. In this paper we develop a new method for active-comparator trials assuming the responses from both treatments are from the same location-scale family. Theories and simulations have shown that the new method performs well when the location-scale assumption holds and works reasonably when the assumption does not hold. Thus, the new method is preferred when computing sample sizes for the van Elteren test in active-comparator trials.