The Impact of Outliers on Net-Benefit Regression Model in Cost-Effectiveness Analysis

Ordinary least square (OLS) in regression has been widely used to analyze patient-level data in cost-effectiveness analysis (CEA). However, the estimates, inference and decision making in the economic evaluation based on OLS estimation may be biased by the presence of outliers. Instead, robust estimation can remain unaffected and provide result which is resistant to outliers. The objective of this study is to explore the impact of outliers on net-benefit regression (NBR) in CEA using OLS and to propose a potential solution by using robust estimations, i.e. Huber M-estimation, Hampel M-estimation, Tukey''s bisquare M-estimation, MM-estimation and least trimming square estimation. Simulations under different outlier-generating scenarios and an empirical example were used to obtain the regression estimates of NBR by OLS and five robust estimations. Empirical size and empirical power of both OLS and robust estimations were then compared in the context of hypothesis testing.Simulations showed that the five robust approaches compared with OLS estimation led to lower empirical sizes and achieved higher empirical powers in testing cost-effectiveness. Using real example of antiplatelet therapy, the estimated incremental net-benefit by OLS estimation was lower than those by robust approaches because of outliers in cost data. Robust estimations demonstrated higher probability of cost-effectiveness compared to OLS estimation. The presence of outliers can bias the results of NBR and its interpretations. It is recommended that the use of robust estimation in NBR can be an appropriate method to avoid such biased decision making.     

Bayesian semiparametric intensity estimation for inhomogeneous spatial point processes

In this work we propose a fully Bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process. The basic idea is to first convert intensity estimation into a Poisson regression setting via binning data points on a regular grid, and then model the log intensity semiparametrically using an adaptive version of Gaussian Markov random fields to smooth the corresponding counts. The inference is carried by an efficient Markov chain Monte Carlo simulation algorithm. Compared to existing methods for intensity estimation, for example, parametric modeling and kernel smoothing, the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates, but also uses information from the data to adaptively determine the amount of smoothing at the local level. The effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset.     

A General Framework for Longitudinal Data through Marked Point Processes

This paper reviews a general framework for the modelling of longitudinal data with random measurement times based on marked point processes and presents a worked example. We construct a quite general regression models for longitudinal data, which may in particular include censoring that only depend on the past and outside random variation, and dependencies between measurement times and measurements. The modelling also generalises statistical counting process models. We review a non-parametric Nadarya-Watson kernel estimator of the regression function, and a parametric analysis that is based on a conditional least squares (CLS) criterion. The parametric analysis presented, is a conditional version of the generalised estimation equations of LIANG and ZEGER (1986). We conclude that the usual nonparametric and parametric regression modelling can be applied to this general set-up, with some modifications. The presented framework provides an easily implemented and powerful tool for model building for repeated measurements.     

Logistic回归模型及其在昆虫学中的应用

介绍了应用Logistic回归分析对二值反应的试验数据进行分析的方法 ,以及Logistic回归分析模型参数估计及其统计检验的方法 ,并结合 1个实际例子说明了Logistic回归模型的应用。     

Estimating marginal and incremental effects on health outcomes using flexible link and variance function models

We propose an extension to the estimating equations in generalized linear models to estimate parameters in the link function and variance structure simultaneously with regression coefficients. Rather than focusing on the regression coefficients, the purpose of these models is inference about the mean of the outcome as a function of a set of covariates, and various functionals of the mean function used to measure the effects of the covariates. A commonly used functional in econometrics, referred to as the marginal effect, is the partial derivative of the mean function with respect to any covariate, averaged over the empirical distribution of covariates in the model. We define an analogous parameter for discrete covariates. The proposed estimation method not only helps to identify an appropriate link function and to suggest an underlying distribution for a specific application but also serves as a robust estimator when no specific distribution for the outcome measure can be identified. Using Monte Carlo simulations, we show that the resulting parameter estimators are consistent. The method is illustrated with an analysis of inpatient expenditure data from a study of hospitalists.     

Random-effects models for serial observations with binary response

This paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants. Each subject's serial responses are assumed to arise from a logistic model, but with regression coefficients that vary between subjects. The logistic regression parameters are assumed to be normally distributed in the population. Inference is based upon maximum likelihood estimation of fixed effects and variance components, and empirical Bayes estimation of random effects. Exact solutions are analytically and computationally infeasible, but an approximation based on the mode of the posterior distribution of the random parameters is proposed, and is implemented by means of the EM algorithm. This approximate method is compared with a simpler two-step method proposed by Korn and Whittemore (1979, Biometrics 35, 795-804), using data from a panel study of asthmatics originally described in that paper. One advantage of the estimation strategy described here is the ability to use all of the data, including that from subjects with insufficient data to permit fitting of a separate logistic regression model, as required by the Korn and Whittemore method. However, the new method is computationally intensive.     

The quantitation of fluorescence by photography.

A method based on theory has been developed for the photographic quantitation of fluorescent substances. DNA stained with ethidium in agarose gels is used as an example of an application of this method. In the course of developing this method we have demonstrated that the empirical methods employed by others authors can give rise to large systematic errors. We have also developed an approximate method based on photographic theory, avoiding the use of digital integration which is required by the rigorous method.     

Statistical power and sample size requirements for three level hierarchical cluster randomized trials

SUMMARY: Cluster randomized clinical trials (cluster-RCT), where the community entities serve as clusters, often yield data with three hierarchy levels. For example, interventions are randomly assigned to the clusters (level three unit). Health care professionals (level two unit) within the same cluster are trained with the randomly assigned intervention to provide care to subjects (level one unit). In this study, we derived a closed form power function and formulae for sample size determination required to detect an intervention effect on outcomes at the subject's level. In doing so, we used a test statistic based on maximum likelihood estimates from a mixed-effects linear regression model for three level data. A simulation study follows and verifies that theoretical power estimates based on the derived formulae are nearly identical to empirical estimates based on simulated data. Recommendations at the design stage of a cluster-RCT are discussed.     

Efficacy of repeated measures in regression models with measurement error.

Ignoring measurement error may cause bias in the estimation of regression parameters. When the true covariates are unobservable, multiple imprecise measurements can be used in the analysis to correct for the associated bias. We suggest a simple estimating procedure that gives consistent estimates of regression parameters by using the repeated measurements with error. The relative Pitman efficiency of our estimator based on models with and without measurement error has been found to be a simple function of the number of replicates and the ratio of intra- to inter-variance of the true covariate. The procedure thus provides a guide for deciding the number of repeated measurements in the design stage. An example from a survey study is presented.     

Empirical regression as a conditional expected value of a special distribution-mixture for a modelfree quantitative recording of stochastical relations

An “empirical” distribution function F?(x, y) is estimated from measured points (xi, yi), i =1(1)n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y). The density function F?(x, y) of F?(x, y) is a mixture of n two-dimensional normal densities. The first order moments of F?(x, y) are the sample means x and y, whilst the second order moments are only proportional to the sample variances and the sample covariance. This “empirical” distribution F?(x, y) is used for evaluation of an empirical regression curve where a free parameter has to be fixed by an optimality criterion. The procedure is demonstrated by an example from morphometrical research.     

Median Regression Model with Interval Censored Data

Quantile regression methods have been used to estimate upper and lower quantile reference curves as the function of several covariates. Especially, in survival analysis, median regression models to the right‐censored data are suggested with several assumptions. In this article, we consider a median regression model for interval‐censored data and construct an estimating equation based on weights derived from interval‐censored data. In a simulation study, the performances of the proposed method are evaluated for both symmetric and right‐skewed distributed failure times. A well‐known breast cancer data are analyzed to illustrate the proposed method.     

Estimating data transformations in nonlinear mixed effects models

A routine practice in the analysis of repeated measurement data is to represent individual responses by a mixed effects model on some transformed scale. For example, for pharmacokinetic, growth, and other data, both the response and the regression model are typically transformed to achieve approximate within-individual normality and constant variance on the new scale; however, the choice of transformation is often made subjectively or by default, with adoption of a standard choice such as the log. We propose a mixed effects framework based on the transform-both-sides model, where the transformation is represented by a monotone parametric function and is estimated from the data. For this model, we describe a practical fitting strategy based on approximation of the marginal likelihood. Inference is complicated by the fact that estimation of the transformation requires modification of the usual standard errors for estimators of fixed effects; however, we show that, under conditions relevant to common applications, this complication is asymptotically negligible, allowing straightforward implementation via standard software.     

Logistic regression for clustered binary data in proband studies with application to familial aggregation of sleep disorders.

Estimation is considered for the class of conditional logistic regression models for clustered binary data proposed by Qu et al. (Communications in Statistics, Series A 16, 3447-3476, 1987) when clusters are sampled on the basis of the outcome for one or more cluster members. The problem is suggested by data from a study designed to investigate familial aggregation of sleep disorders. After appropriate consideration of the mode of ascertainment of "cases" and "controls," it is shown that the model is preserved under this form of sampling, and a method of estimation is presented. The inconsistency of two alternative methods is demonstrated, and an example is provided.     

Spline Optimum Regression Method and Its Application

IIntroductionUsuallyinersareseveralIntervalsIngrowingcurvesInorganisms,suchas,thecurvesofre－productlvltyandactivity．ThereareessentialdifferencesIntheInternaldevelopinglawsonthedlf－ferentIntervals,therefore,ItIsnotacceptabletotlsesingleelementaryfunctiontofitthecurves．TofitcurvesonalltheIntervalswithsmoothnessorcontinuancebetweenIntervals,asplinefunct;onIsrequired（Robinson1983;Yangetal,1992ah）．Splineregresslonandmethodsforflitinganoptimumsplinefunctionhavelongbeenstudied（…     

Influence functions and robust Bayes and empirical Bayes small area estimation

We introduce new robust small area estimation procedures basedon area-level models. We first find influence functions correspondingto each individual area-level observation by measuring the divergencebetween the posterior density functions of regression coefficientswith and without that observation. Next, based on these influencefunctions, properly standardized, we propose some new robustBayes and empirical Bayes small area estimators. The mean squarederrors and estimated mean squared errors of these estimatorsare also found. A small simulation study compares the performanceof the robust and the regular empirical Bayes estimators. Whenthe model variance is larger than the sample variance, the proposedrobust empirical Bayes estimators are superior.     

Regularized estimation in the accelerated failure time model with high-dimensional covariates

We consider two regularization approaches, the LASSO and the threshold-gradient-directed regularization, for estimation and variable selection in the accelerated failure time model with multiple covariates based on Stute's weighted least squares method. The Stute estimator uses Kaplan-Meier weights to account for censoring in the least squares criterion. The weighted least squares objective function makes the adaptation of this approach to multiple covariate settings computationally feasible. We use V-fold cross-validation and a modified Akaike's Information Criterion for tuning parameter selection, and a bootstrap approach for variance estimation. The proposed method is evaluated using simulations and demonstrated on a real data example.     

Standard errors for EM estimates in generalized linear models with random effects

A procedure is derived for computing standard errors of EM estimates in generalized linear models with random effects. Quadrature formulas are used to approximate the integrals in the EM algorithm, where two different approaches are pursued, i.e., Gauss-Hermite quadrature in the case of Gaussian random effects and nonparametric maximum likelihood estimation for an unspecified random effect distribution. An approximation of the expected Fisher information matrix is derived from an expansion of the EM estimating equations. This allows for inferential arguments based on EM estimates, as demonstrated by an example and simulations.     

Combining predictors for classification using the area under the receiver operating characteristic curve

No single biomarker for cancer is considered adequately sensitive and specific for cancer screening. It is expected that the results of multiple markers will need to be combined in order to yield adequately accurate classification. Typically, the objective function that is optimized for combining markers is the likelihood function. In this article, we consider an alternative objective function-the area under the empirical receiver operating characteristic curve (AUC). We note that it yields consistent estimates of parameters in a generalized linear model for the risk score but does not require specifying the link function. Like logistic regression, it yields consistent estimation with case-control or cohort data. Simulation studies suggest that AUC-based classification scores have performance comparable with logistic likelihood-based scores when the logistic regression model holds. Analysis of data from a proteomics biomarker study shows that performance can be far superior to logistic regression derived scores when the logistic regression model does not hold. Model fitting by maximizing the AUC rather than the likelihood should be considered when the goal is to derive a marker combination score for classification or prediction.     

Asymmetric regression models with limited responses with an application to antibody response to vaccine

We develop regression models for limited and censored data based on the mixture between the log‐power‐normal and Bernoulli‐type distributions. A likelihood‐based approach is implemented for parameter estimation and a small‐scale simulation study is conducted to evaluate parameter recovery, with emphasis on bias estimation. The main conclusion is that the approach is very much satisfactory for moderate and large sample sizes. A real data example, the safety and immunogenecity study of measles vaccine in Haiti, is presented to illustrate how different models can be used to fit this type of data. As shown, the asymmetric models considered seem to present the best fit for the data set under study, revealing significance of the explanatory variable sex, which is not found significant with the log‐normal model.     

On the estimation of average treatment effects with right-censored time to event outcome and competing risks

We are interested in the estimation of average treatment effects based on right-censored data of an observational study. We focus on causal inference of differences between t-year absolute event risks in a situation with competing risks. We derive doubly robust estimation equations and implement estimators for the nuisance parameters based on working regression models for the outcome, censoring, and treatment distribution conditional on auxiliary baseline covariates. We use the functional delta method to show that these estimators are regular asymptotically linear estimators and estimate their variances based on estimates of their influence functions. In empirical studies, we assess the robustness of the estimators and the coverage of confidence intervals. The methods are further illustrated using data from a Danish registry study.