Exact analysis of dose response for multiple correlated binary outcomes

The neurotoxicity of a substance is often tested using animal bioassays. In the functional observational battery, animals are exposed to a test agent and multiple outcomes are recorded to assess toxicity, using approximately 40 animals measured on up to 30 different items. This design gives rise to a challenging statistical problem: a large number of outcomes for a small sample of subjects. We propose an exact test for multiple binary outcomes, under the assumption that the correlation among these items is equal. This test is based upon an exponential model described by Molenberghs and Ryan (1999, Environmetrics 10, 279-300) and extends the methods developed by Corcoran et al. (2001, Biometrics 57, 941-948) who developed an exact test for exchangeably correlated binary data for groups (clusters) of correlated observations. We present a method that computes an exact p-value testing for a joint dose-response relationship. An estimate of the parameter for dose response is also determined along with its 95% confidence bound. The method is illustrated using data from a neurotoxicity bioassay for the chemical perchlorethylene.     

Exact tests for one sample correlated binary data

In this paper we developed exact tests for one sample correlated binary data whose cluster sizes are at most two. Although significant progress has been made in the development and implementation of the exact tests for uncorrelated data, exact tests for correlated data are rare. Lack of a tractable likelihood function has made it difficult to develop exact tests for correlated binary data. However, when cluster sizes of binary data are at most two, only three parameters are needed to characterize the problem. One parameter is fixed under the null hypothesis, while the other two parameters can be removed by both conditional and unconditional approaches, respectively, to construct exact tests. We compared the exact and asymptotic p-values in several cases. The proposed method is applied to real-life data.     

Testing for linear trends in proportions using correlated otolaryngology or ophthalmology data

This paper is concerned with the issue of testing for trend with correlated binary data. We consider the problem where one has either one or two ears (or eyes) available for analysis at baseline and one wishes to look at changes over time in a dichotomous outcome taking into account the correlation between responses from two ears. A reparameterization of Rosner's (1982, Biometrics 38, 105-114) correlated binary data model is presented and applied to a test for trend where the stratifying variable is age (or any other subject-specific variable). Observed and expected values are calculated for the trend statistic separately for both unilateral and bilateral cases and are then summed to obtain an overall summary statistic. The proposed method is illustrated by a reanalysis of data presented in a published study of the efficacy of antibiotics for the treatment of otitis media.     

Joint regression and association modeling of longitudinal ordinal data

We propose models for longitudinal, or otherwise clustered, ordinal data. The association between subunit responses is characterized by dependence ratios (Ekholm, Smith, and McDonald, 1995, Biometrika 82, 847-854), which are extended from the binary to the multicategory case. The joint probabilities of the subunit responses are expressed as explicit functions of the marginal means and the dependence ratios of all orders, obtaining a computational advantage for likelihood-based inference. Equal emphasis is put on finding regression models for the univariate cumulative probabilities, and on deriving the dependence ratios from meaningful association-generating mechanisms. A data set on the effects of treatment with Fluvoxamine, which has been analyzed in parts before (Molenberghs, Kenward, and Lesaffre, 1997, Biometrika 84, 33-44), is analyzed in its entirety. Selection models are used for studying the sensitivity of the results to drop-out.     

Maximally selected chi-square statistics and binary splits of nominal variables

We address the problem of maximally selected chi-square statistics in the case of a binary Y variable and a nominal X variable with several categories. The distribution of the maximally selected chi-square statistic has already been derived when the best cutpoint is chosen from a continuous or an ordinal X, but not when the best split is chosen from a nominal X. In this paper, we derive the exact distribution of the maximally selected chi-square statistic in this case using a combinatorial approach. Applications of the derived distribution to variable selection and hypothesis testing are discussed based on simulations. As an illustration, our method is applied to a birth data set.     

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.     

Local influence diagnostics for hierarchical count data models with overdispersion and excess zeros

We consider models for hierarchical count data, subject to overdispersion and/or excess zeros. Molenberghs et al. ( 2007 ) and Molenberghs et al. ( 2010 ) extend the Poisson‐normal generalized linear‐mixed model by including gamma random effects to accommodate overdispersion. Excess zeros are handled using either a zero‐inflation or a hurdle component. These models were studied by Kassahun et al. ( 2014 ). While flexible, they are quite elaborate in parametric specification and therefore model assessment is imperative. We derive local influence measures to detect and examine influential subjects, that is subjects who have undue influence on either the fit of the model as a whole, or on specific important sub‐vectors of the parameter vector. The latter include the fixed effects for the Poisson and for the excess‐zeros components, the variance components for the normal random effects, and the parameters describing gamma random effects, included to accommodate overdispersion. Interpretable influence components are derived. The method is applied to data from a longitudinal clinical trial involving patients with epileptic seizures. Even though the data were extensively analyzed in earlier work, the insight gained from the proposed diagnostics, statistically and clinically, is considerable. Possibly, a small but important subgroup of patients has been identified.     

Significance testing for correlated binary outcome data

Multiple logistic regression is a commonly used multivariate technique for analyzing data with a binary outcome. One assumption needed for this method of analysis is the independence of outcome for all sample points in a data set. In ophthalmologic data and other types of correlated binary data, this assumption is often grossly violated and the validity of the technique becomes an issue. A technique has been developed (Rosner, 1984) that utilizes a polychotomous logistic regression model to allow one to look at multiple exposure variables in the context of a correlated binary data structure. This model is an extension of the beta-binomial model, which has been widely used to model correlated binary data when no covariates are present. In this paper, a relationship is developed between the two techniques, whereby it is shown that use of ordinary logistic regression in the presence of correlated binary data can result in true significance levels that are considerably larger than nominal levels in frequently encountered situations. This relationship is explored in detail in the case of a single dichotomous exposure variable. In this case, the appropriate test statistic can be expressed as an adjusted chi-square statistic based on the 2 X 2 contingency table relating exposure to outcome. The test statistic is easily computed as a function of the ordinary chi-square statistic and the correlation between eyes (or more generally between cluster members) for outcome and exposure, respectively. This generalizes some previous results obtained by Koval and Donner (1987, in Festschrift for V. M. Joshi, I. B. MacNeill (ed.), Vol. V, 199-224.(ABSTRACT TRUNCATED AT 250 WORDS)     

Applying the Cox proportional hazards model when the change time of a binary time-varying covariate is interval censored

This paper develops methodology for estimation of the effect of a binary time-varying covariate on failure times when the change time of the covariate is interval censored. The motivating example is a study of cytomegalovirus (CMV) disease in patients with human immunodeficiency virus (HIV) disease. We are interested in determining whether CMV shedding predicts an increased hazard for developing active CMV disease. Since a clinical screening test is needed to detect CMV shedding, the time that shedding begins is only known to lie in an interval bounded by the patient's last negative and first positive tests. In a Cox proportional hazards model with a time-varying covariate for CMV shedding, the partial likelihood depends on the covariate status of every individual in the risk set at each failure time. Due to interval censoring, this is not always known. To solve this problem, we use a Monte Carlo EM algorithm with a Gibbs sampler embedded in the E-step. We generate multiple completed data sets by drawing imputed exact shedding times based on the joint likelihood of the shedding times and event times under the Cox model. The method is evaluated using a simulation study and is applied to the data set described above.     

The ancestral distance test: what relatedness can reveal about correlated evolution in large lineages with missing character data and incomplete phylogenies

The ancestral distance test is introduced to detect correlated evolution between two binary traits in large phylogenies that may lack resolved subclades, branch lengths, and/or comparative data. We define the ancestral distance as the time separating a randomly sampled taxon from its most recent ancestor (MRA) with extant descendants that have an independent trait. The sampled taxon either has (target sample) or lacks (nontarget sample) a dependent trait. Modeled as a Markov process, we show that the distribution of ancestral distances for the target sample is identical to that of the nontarget sample when characters are uncorrelated, whereas ancestral distances are smaller on average for the target sample when characters are correlated. Simulations suggest that the ancestral distance can be estimated using the time, total branch length, taxonomic rank, or number of speciation events between a sampled taxon and the MRA. These results are shown to be robust to deviations from Markov assumptions. A Monte Carlo technique estimates P-values when fully resolved phylogenies with branch lengths are available, and we evaluate the Monte Carlo approach using a data set with known correlation. Measures of relatedness were found to provide a robust means to test hypotheses of correlated character evolution.