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We introduce a robust likelihood approach to inference about marginal distributional characteristics for paired data without modeling correlation/joint probabilities. This method is reproducible in that it is applicable to paired settings with various sizes. The virtue of the new strategy is elucidated via testing marginal homogeneity in paired triplet scenario. We use simulations and real data analysis to demonstrate the merit of our robust likelihood methodology.

Paired data arise naturally in Ophthalmology where pairs of eyes undergo diagnostic tests to predict the presence of certain diseases. The common correlation model is popular for modeling the joint probabilities of responses from fellow eyes for inference about accuracy measures. One of the assumptions underlying the model is exchangeability of fellow eyes that stipulates the accuracy measures such as sensitivities/specificities of fellow eyes be equal. We propose a parametric robust likelihood approach to testing the equality of accuracy measures of fellow eyes without modeling correlation. The robust likelihood procedure is applicable for inference about diagnostic accuracy measures in general paired designs. We provide simulations and analyses of a data set in Ophthalmology to demonstrate the effectiveness of the parametric robust procedure.

We construct a legitimate likelihood function for the agreement kappa coefficient for correlated data without specifically modelling all levels of correlation. This makes available the likelihood ratio test, the score test and other tools without the knowledge of the underlying distributions. This parametric robust likelihood approach applies to general clustered data scenarios. We provide simulations and real data analysis to demonstrate the advantage of the robust procedure.

Pairing serves as a way of lessening heterogeneity but pays the price of introducing more parameters to the model. This complicates the probability structure and makes inference more intricate. We employ the simpler structure of the parallel design to develop a robust score statistic for testing the equality of two multinomial distributions in paired designs. This test incorporates the within-pair correlation in a data-driven manner without a full model specification. In the paired binary data scenario, the robust score statistic turns out to be the McNemar’s test. We provide simulations and real data analysis to demonstrate the advantage of the robust procedure.

Recently Perera et al. introduced two new binocular accuracy measures to evaluate diagnostic tests for paired organs. They adopted the Gaussian copula model to account for correlation between fellow eyes. As the measures are functions of several joint probabilities and due to the nature of the joint models, variations of the estimates for the two new measures were assessed via bootstrapping. We provide a different approach to inference about the two interesting and innovative measures. In our opinion, when patients are independent, the binomial models suffice for inference about the parameters of interest. Inference becomes simple and straightforward. We perform numerical studies and analyse the data set as of Perera et al. for illustration. Also, we investigate thru simulations the issue of robustness of the Gaussian copula and the binomial models under model misspecification.

Supplemental material, SMM880310 Supplemental Material for Inference about binocular sensitivity and specificity of screening tests for paired organs by Tsung-Shan Tsou and Wei-Cheng Hsiao in Statistical Methods in Medical Research

Intuitively, one only needs patients with two positive screening test results for positive predictive values comparison, and those with two negative screening test results for contrasting negative predictive values. Nevertheless, current existing methods rely on the multinomial model that includes superfluous parameters unnecessary for specific comparisons. This practice results in complex statistics formulas. We introduce a novel likelihood approach that fits the intuition by including a minimum number of parameters of interest in paired designs. It is demonstrated that our robust score test statistic is identical to a newly proposed weighted generalized score test statistic. Simulations and real data analysis are used for illustration.

We propose a universal robust likelihood that is able to accommodate correlated binary data without any information about the underlying joint distributions. This likelihood function is asymptotically valid for the regression parameter for any underlying correlation configurations, including varying under- or over-dispersion situations, which undermines one of the regularity conditions ensuring the validity of crucial large sample theories. This robust likelihood procedure can be easily implemented by using any statistical software that provides naive and sandwich covariance matrices for regression parameter estimates. Simulations and real data analyses are used to demonstrate the efficacy of this parametric robust method.

We introduce a universal robust likelihood approach for regression analysis of general count data. The robust likelihood function is able to accommodate a wide range of dispersion and is insensitive to model failures. We use simulations and real data analysis to demonstrate the merit of the robust procedure.

A parametric robust approach for analyzing correlated count data is introduced. This method enables one to construct an asymptotically valid likelihood for the regression parameter when knowledge about the joint distribution for data is scarce or not available. We use simulations and real data analysis to demonstrate the merit of the proposed robust likelihood method.

A robust generalized score test for comparing groups of cluster binary data is proposed. This novel test is asymptotically valid for practically any underlying correlation configurations including the situation when correlation coefficients vary within or between clusters. This structure generally undermines the validity of the typical large sample properties of the method of maximum likelihood. Simulations and real data analysis are used to demonstrate the merit of this parametric robust method. Results show that our test is superior to two recently proposed test statistics advocated by other researchers.

Traditionally, analysis of Hydrology employs only one hydrological variable. Recently, Nadarajah [A bivariate distribution with gamma and beta marginals with application to drought data. J Appl Stat. 2009;36:277–301] proposed a bivariate model with gamma and beta as marginal distributions to analyse the drought duration and the proportion of drought events. However, the validity of this method hinges on fulfilment of stringent assumptions. We propose a robust likelihood approach which can be used to make inference for general bivariate continuous and proportion data. Unlike the gamma–beta (GB) model which is sensitive to model misspecification, the new method provides legitimate inference without knowing the true underlying distribution of the bivariate data. Simulations and the analysis of the drought data from the State of Nebraska, USA, are provided to make contrasts between this robust approach and the GB model.

In independent and identically distributed situations, we show that one can properly correct the Poisson and the negative binomial likelihood functions to become asymptotically identical to the profile likelihood function for the mean parameter of nonnegative continuous distributions under mild conditions. We present theoretical justifications and use data analyses to demonstrate the merit of our new robust likelihood method.

This article introduces two parametric robust diagnostic methods for detecting influential observations in the setting of generalized linear models with continuous responses. The legitimacy of the two proposed methods requires no knowledge of the true underlying distributions so long as their second moments exist. The performance of the two proposed influence diagnostic tools is investigated through limited simulation studies and the analyses of an illustration.

Objective Cervicovaginitis is a highly prevalent disease that is a burden on healthcare globally. Immediate and adequate treatment can eradicate the infection and block subsequent complications. The feasibility of achip-based multiplexed immunoassay using liposomal nanovesicles was tested. Materials and Methods A multiplexed immunoassay chip containing five antibodies for five pathogens ( Chlamydia trachomatis , Escherichia coli , Neisseria gonorrhoeae , Streptococcus agalactiae , and Candida albicans ) was established and tested. Four patients with spiking of candidiasis were enrolled. The difference between positive and negative readings was evaluated using the paired Student t test. Results The detection threshold of Candida in this microarray was 100,000 CFU/mL in a vaginal sample, and the time required for the whole procedure was 3 hours. The testing of the four patients showed 100% for both sensitivity and specificity. Conclusion This microarray chip was a rapid, easy, inexpensive and sensitive tool for detecting female lower genital tract Candida infection in a one-time vaginal sampling process, although the data on the four other pathogens were still unavailable. A larger population study is encouraged to test the validity of this multiplexed immunoassay chip.

In this article, the parametric robust regression approaches are proposed for making inferences about regression parameters in the setting of generalized linear models (GLMs). The proposed methods are able to test hypotheses on the regression coefficients in the misspecified GLMs. More specifically, it is demonstrated that with large samples, the normal and gamma regression models can be properly adjusted to become asymptotically valid for inferences about regression parameters under model misspecification. These adjusted regression models can provide the correct type I and II error probabilities and the correct coverage probability for continuous data, as long as the true underlying distributions have finite second moments.

A new means of estimating the correlation coefficient for cluster binary data in the regression settings is introduced. The creation of this method is founded upon the violation of Bartlett's second identity when adopting the binomial distributions to model binary data that are correlated. The new methodology applies to any sensible link functions that connect the success probability and covariates. One can easily implement the procedure by using any statistical software providing the naive and the sandwich covariance matrices for regression parameter estimates. Simulations and real data analyses are used to demonstrate the efficacy of our new procedure.

Multivariate normal, due to its well-established theories, is commonly utilized to analyze correlated data of various types. However, the validity of the resultant inference is, more often than not, erroneous if the model assumption fails. We present a modification for making the multivariate normal likelihood acclimatize itself to general correlated data. The modified likelihood is asymptotically legitimate for any true underlying joint distributions so long as they have finite second moments. One can, hence, acquire full likelihood inference without knowing the true random mechanisms underlying the data. Simulations and real data analysis are provided to demonstrate the merit of our proposed parametric robust method.

Background The aim of this study was to evaluate the effectiveness of a refined theory-based Interactive Postpartum Sexual Health Education Program to enhance postpartum women's effective contraceptive behavior. Study Design Participants (N=250) were randomized to three groups. Experimental Group A received our intervention program via strategies that matched participants' learning preparedness, as determined by the transtheoretical model. Experimental Group B received only a pamphlet. The control group received routine education. Only Group A received health education. Data were collected at baseline, 3 days, 2 months and 3 months postpartum. Results Women who received theory-based postpartum sexual health education program had significantly greater contraceptive self-efficacy and were more likely to choose more effective contraceptive methods at 2 months postpartum than women in the routine teaching and interactive pamphlet-only groups. Conclusion Our theory-based Interactive Postpartum Sexual Health Education Program enhanced postpartum women's contraceptive self-efficacy and effective contraceptive behavior.

In this article, we propose two novel diagnostic measures for the deletion of influential observations for regression parameters in the setting of generalized linear models. The proposed diagnostic methods are capable for detecting the influential observations under model misspecification, as long as the true underlying distributions have finite second moments. More specifically, it is demonstrated that the Poisson likelihood function can be properly adjusted to become asymptotically valid for practically all underlying discrete distributions. The adjusted Poisson regression model that achieves the robustness property is presented. Simulation studies and an illustration are performed to demonstrate the efficacy of the two novel diagnostic procedures.

This article introduces a parametric robust way of determining the mean–variance relationship in the setting of generalized linear models. More specifically, the normal likelihood is properly amended to become asymptotically valid even if normality fails. Consequently, legitimate inference for the parametric relationship between mean and variance could be derived under model misspecification. More details are given to the scenario when the variance is proportional to an unknown power of the mean function. The efficacy of the novel technique is demonstrated via simulations and the analysis of two real data sets.

This article is concerned with inference about link function in generalized linear models. A parametric and yet robust likelihood approach is introduced to accomplish the intended goal. More specifically, it is demonstrated that one can convert normal and gamma likelihoods into robust likelihood functions for the link function. The asymptotic validity of the robust likelihood requires only the existence of the second moments of the underlying distributions. The application of this novel robust likelihood method is demonstrated on the Box–Cox transformation. Simulation studies and real data analysis are provided to demonstrate the efficacy of the new parametric robust procedures.

A parametric robust test is proposed for comparing several coefficients of variation. This test is derived by properly correcting the normal likelihood function according to the technique suggested by Royall and Tsou. The proposed test statistic is asymptotically valid for general random variables, as long as their underlying distributions have finite fourth moments. Simulation studies and real data analyses are provided to demonstrate the effectiveness of the novel robust procedure.

The aim of this article is to provide asymptotically valid likelihood inferences about regression parameters for correlated ordinal response variables. The legitimacy of this novel approach requires no knowledge of the underlying joint distributions so long as their second moments exist. The efficacy of the proposed parametric approach is demonstrated via simulations and the analyses of two real data sets.

We propose two novel diagnostic measures for the detection of influential observations for regression parameters in linear regression. Traditional diagnostic statistics focus on the effect of deletion of data points either on parameter estimates, or on predicted values. A data point is regarded as influential by the new methods if its inclusion determines a significantly different likelihood function for the parameter of interest. The concerned likelihood function is asymptotically valid for practically all underlying distributions whose second moments exist.

Aims and objectives. To examine and compare the effects of acupressure on the perceived health-related quality of life of the participants with bronchiectasis. Background. In an attempt to offer comfort, pain control and symptom management, nursing is becoming increasingly involved in offering complementary-alternative medicine as part of its caring-healing focus in comprehensive patient care. Acupressure is one such modality that is being increasingly used by both medical and nursing professionals. While acupressure has been reported to have beneficial effects in patients with respiratory disease, the benefits to bronchiectasis patients have remained uncertain. Design. A randomized, partially blinded study consisting of three groups. Methods. Thirty-five out-patients of both genders, aged 59·46 SD 11·52 years, who were suffering from bronchiectasis, were randomly split into one of three groups: standard care with supplemental acupressure for eight weeks (11 participants); standard care with supplemental sham acupressure for eight weeks (11 participants); and standard care alone (13 participants). Outcomes were determined by changes in daily sputum amounts, sputum self-assessment, six-minute walking distance, breathing difficulty (measured on the dyspnea visual analogue scale) and health-related quality of life (measured by the Saint George Respiratory Questionnaire). Results. The sputum self-assessment score improved over time for the sham acupressure participants (P = 0·03), when compared with the controls. For acupressure participants, the Saint George respiratory questionnaire activity component scores also improved over time, compared with controls (P = 0·01) after adjustment for covariates (treatment, time, age, sex and baseline values). Other variables did not differ between the standard care alone group and the other two groups. Conclusions. Eight weeks of self-administered acupressure could be useful in reducing the effects of bronchiectasis on a patient's daily activities. Relevance to clinical practice. Acupressure may be regarded as a viable nursing intervention.

This article establishes a robust likelihood function about regression parameters for the correlation coefficients modeled in a generalized linear model fashion. The validity of the proposed likelihood requires no knowledge of the true underlying distributions, so long as they have finite fourth moments. The efficacy of the robust methodology is shown via simulations. The asymptotic variance of the maximum-likelihood estimate and the empirical error probabilities of the resultant robust likelihood ratio test are specifically exhibited.

Count data are very often analyzed under the assumption of a Poisson model [( Agresti, A., 1996 . An Introduction to Categorical Data Analysis. Wiley, New York; Generalized Linear Models, second ed. Chapman & Hall, New York)]. However, the derived inference is generally erroneous if the underlying distribution is not Poisson (Biometrika 70, 269–274). A parametric robust regression approach is proposed for the analysis of count data. More specifically it will be demonstrated that the Poisson regression model could be properly adjusted to become asymptotically valid for inference about regression parameters, even if the Poisson assumption fails. With large samples the novel robust methodology provides legitimate likelihood functions for regression parameters, so long as the true underlying distributions have finite second moments. Adjustments that robustify the Poisson regression will be given, respectively, under log link and identity link functions. Simulation studies will be used to demonstrate the efficacy of the robust Poisson regression model.

This paper introduces an exploratory way to determine how variance relates to the mean in generalized linear models. This novel method employs the robust likelihood technique introduced by Royall and Tsou. A urinary data set collected by Ginsberg et al. and the fabric data set analysed by Lee and Nelder are considered to demonstrate the applicability and simplicity of the proposed technique. Application of the proposed method could easily reveal a mean–variance relationship that would generally be left unnoticed, or that would require more complex modelling to detect. Copyright © 2006 John Wiley & Sons, Ltd.

Tsou (in comm Stat-Theor Math 32: 2013–2019, 2003) proposed a parametric robust procedure for testing the equality of two population variances. With large samples the proposed test remains valid under model misspecification. In this article the robust technique is further extended to the comparison of several population variances. More specifically the score test derived on the basis of normal models is adjusted to become robust. The adjusted robust test provides asymptotically valid inference so long as the true underlying distributions have finite fourth moments. Unlike most robust nonparametric approaches, this novel robust technique too provides legitimate variance estimates for estimators of the interested parameters.

Tsou (2003a) proposed a parametric procedure for making robust inference for mean regression parameters in the context of generalized linear models. This robust procedure is extended to model variance heterogeneity. The normal working model is adjusted to become asymptotically robust for inference about regression parameters of the variance function for practically all continuous response variables. The connection between the novel robust variance regression model and the estimating equations approach is also provided.

This article introduces a parametric robust way of making valid inferences for the correlation coefficient. More specifically, it will be demonstrated that the bivariate normal likelihood function can be made asymptotically valid for practically all underlying bivariate continuous distributions. The adjustment to the bivariate normal model that achieves the robustness property will be presented. Simulation studies will be performed to demonstrate the finite sample performance of the novel robust procedure.

Summary In reality it is more often the case when part of data have been drawn from some distribution other than that we believe they have been drawn from. Traditional nonparametric or parametric statistics are insufficient for such contaminated data. Tsou [Tsou, T.-S. (2003). Parametric robust inferences for regression parameters under generalized linear models. Submitted] proposed parametric robust regression techniques that provide asymptotically valid inference for regression parameters so long as the true distributions that generate the data have finite second moments. It will be demonstrated that the novel robust regression tools fit well for the regression analysis of data generated from unknown and distinct families of distributions.

SummaryThe strength of statistical evidence is measured by the likelihood ratio. Two key performance properties of this measure are the probability of observing strong misleading evidence and the probability of observing weak evidence. For the likelihood function associated with a parametric statistical model, these probabilities have a simple large sample structure when the model is correct. Here we examine how that structure changes when the model fails. This leads to criteria for determining whether a given likelihood function is robust (continuing to perform satisfactorily when the model fails), and to a simple technique for adjusting both likelihoods and profile likelihoods to make them robust. We prove that the expected information in the robust adjusted likelihood cannot exceed the expected information in the likelihood function from a true model. We note that the robust adjusted likelihood is asymptotically fully efficient when the working model is correct, and we show that in some important examples this efficiency is retained even when the working model fails. In such cases the Bayes posterior probability distribution based on the adjusted likelihood is robust, remaining correct asymptotically even when the model for the observable random variable does not include the true distribution. Finally we note a link to standard frequentist methodology—in large samples the adjusted likelihood functions provide robust likelihood-based confidence intervals.

The purposes of this study were to explore the extent to which the practice of disclosing cancer diagnoses to patients is used in Taiwan, to examine the relation between cancer diagnosis disclosure and levels of hope, and to investigate the relation between length of time since diagnosis and levels of hope. The participants in this study were 124 Taiwanese oncology inpatients and outpatients. Of these patients, 79% were informed of their cancer diagnosis. The informed patients reported significantly higher levels of hope than those who were not informed. Finally, patient levels of hope decreased as the time between cancer diagnosis and disclosure increased. The implications of this study are discussed in terms of cancer disclosure practice and enhancement of levels of hope for Taiwanese patients with cancer.

This article introduces a parametric robust way of comparing two population means and two population variances. With large samples the comparison of two means, under model misspecification, is lesser a problem, for, the validity of inference is protected by the central limit theorem. However, the assumption of normality is generally required, so that the inference for the ratio of two variances can be carried out by the familiar F statistic. A parametric robust approach that is insensitive to the distributional assumption will be proposed here. More specifically, it will be demonstrated that the normal likelihood function can be adjusted for asymptotically valid inferences for all underlying distributions with finite fourth moments. The normal likelihood function, on the other hand, is itself robust for the comparison of two means so that no adjustment is needed.

The purpose of this pilot study was to explore the effectiveness of a pain education program to overcome patient-related barriers in managing cancer pain for Taiwanese home care patients with cancer. The pain education program was developed based on previous studies of Taiwanese patient-related barriers to cancer pain management. The Barriers Questionnaire-Taiwan form, the Brief Pain Inventory, the Medication Adherence Questionnaire, and a demographic questionnaire were used for data collection. The sample consisted of 18 patients in the experimental group and 19 patients in the control group. Descriptive statistics, tests, and paired tests were used to analyze the data. Results of this study revealed that patients who received the pain educational program had significantly greater reduction in Barriers Questionnaire-Taiwan form scores and more improvement in medication adherence compared with patients who did not participate in the program. When compared to pretest scores, patients scores after receiving the pain education intervention showed significant improvement on the Barriers Questionnaire-Taiwan form, medication adherence, pain intensity, and pain interference. The results of this study support the effectiveness of the pain education program on overcoming the barriers to cancer pain management for Taiwanese home care patients with cancer.

This study used simulated data to evaluate the performance of distinct conditional generalized estimating equations (CGEE) for the analysis of exchangeable correlation for binary data. The CGEE differs from the usual generalized estimating equations (GEE) in that, instead of marginal expectations, the conditional expectations of the responses were used in the estimating equations. The major distinction among the CGEEs compared was the sizes of the conditioning events used in the conditional expectations. The results show that, for the estimation of correlation coefficient, the bias decreases, and the variance increases when more members in a cluster are included in the conditioning event. The increase of variance is, however, only moderate for small intracluster correlation coefficient. On the other hand, for the estimation of regression parameters, the bias and variance of the estimates both increase when the size of the conditioning event increases. The increase, however, is also insignificant when the correlation coefficient is small.