A model to estimate risk of infection with human herpesvirus 8 associated with transfusion from cross-sectional data

In cross-sectional studies of infectious diseases, the data typically consist of: age at the time of study, status (presence or absence) of infection, and a chronology of events possibly associated with the disease. Motivated by a study of how human herpesvirus 8 (HHV-8) is transmitted among children with sickle cell anemia in Uganda, we have developed a flexible parametric approach for combining current-status data with a history of blood transfusions. We model heterogeneity in transfusion-associated risk by a child-specific random effect. We present an extension of the model to accommodate the fact that there is no gold standard for HHV-8 infection and infection status was assessed by a serological assay. The parameters are estimated via maximum likelihood. Finally, we present results from applying various parameterizations of the model to the Ugandan study.     

Meta-analysis for surrogacy: accelerated failure time models and semicompeting risks modeling

There has been great recent interest in the medical and statistical literature in the assessment and validation of surrogate endpoints as proxies for clinical endpoints in medical studies. More recently, authors have focused on using metaanalytical methods for quantification of surrogacy. In this article, we extend existing procedures for analysis based on the accelerated failure time model to this setting. An advantage of this approach relative to proportional hazards model is that it allows for analysis in the semicompeting risks setting, where we model the region where the surrogate endpoint occurs before the true endpoint. Several estimation methods and attendant inferential procedures are presented. In addition, between- and within-trial methods for evaluating surrogacy are developed; a novel principal components procedure is developed for quantifying trial-level surrogacy. The methods are illustrated by application to data from several studies in colorectal cancer.     

Data analytic methods for matched case-control studies

The recent introduction of complex multivariate statistical models in matched case-control studies is a mixed blessing. Their use can lead to a better understanding of the way in which many variables contribute to the risk of disease. On the other hand, these powerful methods can obscure salient features in the data that might have been detected by other, less sophisticated methods. This shortcoming is due to a lack of support methodology for the routine use of these models. Satisfactory computation of estimated relative risks and their standard errors is not sufficient justification for the fitted model. Goodness of fit must be examined if inferences are to be trusted. This paper is concerned with the analysis of matched case-control studies with logistic models. Analogies of these models to linear regression models are emphasized. In particular, basic concepts such as analysis of variance, multiple correlation coefficient, one-degree-of-freedom tests, and residual analysis are discussed. The fairly new field of regression diagnostics is also introduced. All procedures are illustrated on a study of bladder cancer in males.     

Model Diagnostic Plots for Repeated Measures Data

In the analysis of repeated measurements, multivariate regression models that account for the correlations among the observations from the same subject are widely used. Like the usual univariate regression models, these multivariate regression models also need some model diagnostic procedures. Though these models have been widely used, not many studies have been performed in model diagnostic areas. In this paper, we propose simple residual plots to investigate the goodness of model fit for repeated measures data. Here, we mainly focus on the mean model diagnostics. The proposed residual plots are based on the quantile‐quantile(Q–Q) plots of a χ² distribution and a normal distribution. In particular, the proposed model is useful in comparing several models simultaneously. The proposed method is illustrated using two examples. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Joint semiparametric models for case-cohort designs

Two-phase studies such as case-cohort and nested case-control studies are widely used cost-effective sampling strategies. In the first phase, the observed failure/censoring time and inexpensive exposures are collected. In the second phase, a subgroup of subjects is selected for measurements of expensive exposures based on the information from the first phase. One challenging issue is how to utilize all the available information to conduct efficient regression analyses of the two-phase study data. This paper proposes a joint semiparametric modeling of the survival outcome and the expensive exposures. Specifically, we assume a class of semiparametric transformation models and a semiparametric density ratio model for the survival outcome and the expensive exposures, respectively. The class of semiparametric transformation models includes the proportional hazards model and the proportional odds model as special cases. The density ratio model is flexible in modeling multivariate mixed-type data. We develop efficient likelihood-based estimation and inference procedures and establish the large sample properties of the nonparametric maximum likelihood estimators. Extensive numerical studies reveal that the proposed methods perform well under practical settings. The proposed methods also appear to be reasonably robust under various model mis-specifications. An application to the National Wilms Tumor Study is provided.     

Regression analysis of multivariate interval-censored failure time data with application to tumorigenicity experiments

This paper discusses multivariate interval-censored failure time data that occur when there exist several correlated survival times of interest and only interval-censored data are available for each survival time. Such data occur in many fields. One is tumorigenicity experiments, which usually concern different types of tumors, tumors occurring in different locations of animals, or together. For regression analysis of such data, we develop a marginal inference approach using the additive hazards model and apply it to a set of bivariate interval-censored data arising from a tumorigenicity experiment. Simulation studies are conducted for the evaluation of the presented approach and suggest that the approach performs well for practical situations.     

Application of the time-dependent ROC curves for prognostic accuracy with multiple biomarkers

The rapid advancement in molecule technology has led to the discovery of many markers that have potential applications in disease diagnosis and prognosis. In a prospective cohort study, information on a panel of biomarkers as well as the disease status for a patient are routinely collected over time. Such information is useful to predict patients' prognosis and select patients for targeted therapy. In this article, we develop procedures for constructing a composite test with optimal discrimination power when there are multiple markers available to assist in prediction and characterize the accuracy of the resulting test by extending the time-dependent receiver operating characteristic (ROC) curve methodology. We employ a modified logistic regression model to derive optimal linear composite scores such that their corresponding ROC curves are maximized at every false positive rate. We provide theoretical justification for using such a model for prognostic accuracy. The proposed method allows for time-varying marker effects and accommodates censored failure time outcome. When the effects of markers are approximately constant over time, we propose a more efficient estimating procedure under such models. We conduct numerical studies to evaluate the performance of the proposed procedures. Our results indicate the proposed methods are both flexible and efficient. We contrast these methods with an application concerning the prognostic accuracies of expression levels of six genes.     

Diagnostics for joint longitudinal and dropout time modeling

We present a variety of informal graphical procedures for diagnostic assessment of joint models for longitudinal and dropout time data. A random effects approach for Gaussian responses and proportional hazards dropout time is assumed. We consider preliminary assessment of dropout classification categories based on residuals following a standard longitudinal data analysis with no allowance for informative dropout. Residual properties conditional upon dropout information are discussed and case influence is considered. The proposed methods do not require computationally intensive methods over and above those used to fit the proposed model. A longitudinal trial into the treatment of schizophrenia is used to illustrate the suggestions.     

Semiparametric analysis of recurrent events data in the presence of dependent censoring

Dependent censoring occurs in longitudinal studies of recurrent events when the censoring time depends on the potentially unobserved recurrent event times. To perform regression analysis in this setting, we propose a semiparametric joint model that formulates the marginal distributions of the recurrent event process and dependent censoring time through scale-change models, while leaving the distributional form and dependence structure unspecified. We derive consistent and asymptotically normal estimators for the regression parameters. We also develop graphical and numerical methods for assessing the adequacy of the proposed model. The finite-sample behavior of the new inference procedures is evaluated through simulation studies. An application to recurrent hospitalization data taken from a study of intravenous drug users is provided.     

Fitting semiparametric additive hazards models using standard statistical software

The Cox proportional hazards model has become the standard in biomedical studies, particularly for settings in which the estimation covariate effects (as opposed to prediction) is the primary objective. In spite of the obvious flexibility of this approach and its wide applicability, the model is not usually chosen for its fit to the data, but by convention and for reasons of convenience. It is quite possible that the covariates add to, rather than multiply the baseline hazard, making an additive hazards model a more suitable choice. Typically, proportionality is assumed, with the potential for additive covariate effects not evaluated or even seriously considered. Contributing to this phenomenon is the fact that many popular software packages (e.g., SAS, S-PLUS/R) have standard procedures to fit the Cox model (e.g., proc phreg, coxph), but as of yet no analogous procedures to fit its additive analog, the Lin and Ying (1994) semiparametric additive hazards model. In this article, we establish the connections between the Lin and Ying (1994) model and both Cox and least squares regression. We demonstrate how SAS's phreg and reg procedures may be used to fit the additive hazards model, after some straightforward data manipulations. We then apply the additive hazards model to examine the relationship between Model for End-stage Liver Disease (MELD) score and mortality among patients wait-listed for liver transplantation.     

A survey of non-linear optimization techniques

Optimization means the provision of a set of numerical parameter values which will give the best fit of an equation, or series of equations, to a set of data. For simple systems this can be done by differentiating the equations with respect to each parameter in turn, setting the set of partial differential equations to zero, and solving this set of simultaneous equations (as for exwnple in linear regression). In more complicated cases, however, it may be impossible to differentiate the equations, or very difficultly soluble non-linear equations may result. Many numerical optimization techniques to overcome these difficulties have been developed in the least ten years, and this review explains the logical basis of most of them, without going into the detail of computational procedures.The methods fall naturally into two classes - direct search methods, in which only values of the function to be minimized (or maximized) are used - and gradient methods, which also use derivatives of the function. The author considers all the accepted methods in each class, although warning that gradient methods should not be used unless the analytical differentiation of the function to be minimized is possible.If the solution is constrained, that is, certain values of the parameters are regarded as impossible or certain relations between the parameter values must be obeyed, the problem is more difficult. The second part of the review considers methods which have been proposed for the solution of constrained optimization problems.     

Statistical analysis of HIV infectivity based on partner studies

Partner studies produce data on the infection status of partners of individuals known or assumed to be infected with the human immunodeficiency virus (HIV) after a known or estimated number of contacts. Previous studies have assumed a constant probability of transmission (infectivity) of the virus at each contact. Recently, interest has focused on the possibility of heterogeneity of infectivity across partnerships. This paper develops parametric and nonparametric procedures based on partner data in order to examine the risk of infection after a given number of contacts. Graphical methods and inference techniques are presented that allow the investigator to evaluate the constant infectivity model and consider the impact of heterogeneity of infectivity, error in measurement of the number of contacts, and regression effects of other covariates. The majority of the methods can be computationally implemented easily with use of software to fit generalized linear models. The concepts and techniques are closely related to ideas from discrete survival analysis. A data set on heterosexual transmission is used to illustrate the methods.     

Estimation and Prediction for Cancer Screening Models Using Deconvolution and Smoothing

The model that specifies that cancer incidence, I, is the convolution of the preclinical incidence, g, and the density of time in the preclinical phase, f, has frequently been utilized to model data from cancer screening trials and to estimate such quantities as sojourn time, lead time, and sensitivity. When this model is fit to the above data, the parameters of f as well as the parameter(s) governing screening sensitivity must be estimated. Previously, g was either assumed to be equal to clinical incidence or assumed to be a constant or exponential function that also had to be estimated. Here we assume that the underlying incidence, I, in the study population (in the absence of screening) is known. With I known, g then becomes a function of f, which can be solved for using (numerical) deconvolution, thus eliminating the need to estimate g or make assumptions about it. Since numerical deconvolution procedures may be highly unstable, however, we incorporate a smoothing procedure that produces a realistic g function while still closely reproducing the original incidence function I upon convolution with f. We have also added the concept of competing mortality to the convolution model. This, along with the realistic preclinical incidence function described above, results in more accurate estimates of sojourn time and lead time and allows for estimation of quantities related to overdiagnosis, which we define here.     

Time- and ensemble-averaged direct NOE restraints

Summary NMR data are collected as time- and ensemble-averaged quantities. Yet, in commonly used methods for structure determination of biomolecules, structures are required to satisfy simultaneously a large number of constrainsts. Recently, however, methods have been developed that allow a better fit of the experimental data by the use of time- or ensemble-averaged restraints. Thus far, these methods have been applied to structure refinement using distance and J-coupling restraints. In this paper, time and ensemble averaging is extended to the direct refinement with experimental NOE data. The implementation of time- and ensemble-averaged NOE restraints in DINOSAUR is described and illustrated with experimental NMR data for crambin, a 46-residue protein. Structure refinement with both time- and ensemble-averaged NOE restraints results in lower R-factors, indicating a better fit of the experimental NOE data.     

Statistical inference from single channel records: two-state Markov model with limited time resolution

Though stochastic models are widely used to describe single ion channel behaviour, statistical inference based on them has received little consideration. This paper describes techniques of statistical inference, in particular likelihood methods, suitable for Markov models incorporating limited time resolution by means of a discrete detection limit. To simplify the analysis, attention is restricted to two-state models, although the methods have more general applicability. Non-uniqueness of the mean open-time and mean closed-time estimators obtained by moment methods based on single exponential approximations to the apparent open-time and apparent closed-time distributions has been reported. The present study clarifies and extends this previous work by proving that, for such approximations, the likelihood equations as well as the moment equations (usually) have multiple solutions. Such non-uniqueness corresponds to non-identifiability of the statistical model for the apparent quantities. By contrast, higher-order approximations yield theoretically identifiable models. Likelihood-based estimation procedures are developed for both single exponential and bi-exponential approximations. The methods and results are illustrated by numerical examples based on literature and simulated data, with consideration given to empirical distributions and model control, likelihood plots, and point estimation and confidence regions.     

Model checking for ROC regression analysis

Summary .   The receiver operating characteristic (ROC) curve is a prominent tool for characterizing the accuracy of a continuous diagnostic test. To account for factors that might influence the test accuracy, various ROC regression methods have been proposed. However, as in any regression analysis, when the assumed models do not fit the data well, these methods may render invalid and misleading results. To date, practical model-checking techniques suitable for validating existing ROC regression models are not yet available. In this article, we develop cumulative residual-based procedures to graphically and numerically assess the goodness of fit for some commonly used ROC regression models, and show how specific components of these models can be examined within this framework. We derive asymptotic null distributions for the residual processes and discuss resampling procedures to approximate these distributions in practice. We illustrate our methods with a dataset from the cystic fibrosis registry.     

Modelling Heart Rate Kinetics

The objective of the present study was to formulate a simple and at the same time effective mathematical model of heart rate kinetics in response to movement (exercise). Based on an existing model, a system of two coupled differential equations which give the rate of change of heart rate and the rate of change of exercise intensity is used. The modifications introduced to the existing model are justified and discussed in detail, while models of blood lactate accumulation in respect to time and exercise intensity are also presented. The main modification is that the proposed model has now only one parameter which reflects the overall cardiovascular condition of the individual. The time elapsed after the beginning of the exercise, the intensity of the exercise, as well as blood lactate are also taken into account. Application of the model provides information regarding the individual’s cardiovascular condition and is able to detect possible changes in it, across the data recording periods. To demonstrate examples of successful numerical fit of the model, constant intensity experimental heart rate data sets of two individuals have been selected and numerical optimization was implemented. In addition, numerical simulations provided predictions for various exercise intensities and various cardiovascular condition levels. The proposed model can serve as a powerful tool for a complete means of heart rate analysis, not only in exercise physiology (for efficiently designing training sessions for healthy subjects) but also in the areas of cardiovascular health and rehabilitation (including application in population groups for which direct heart rate recordings at intense exercises are not possible or not allowed, such as elderly or pregnant women).     

Assessing the quality of molecular divergence time estimates by fossil calibrations and fossil-based model selection

Estimates of species divergence times using DNA sequence data are playing an increasingly important role in studies of evolution, ecology and biogeography. Most work has centred on obtaining appropriate kinds of data and developing optimal estimation procedures, whereas somewhat less attention has focused on the calibration of divergences using fossils. Case studies with multiple fossil calibration points provide important opportunities to examine the divergence time estimation problem in new ways. We discuss two cross-validation procedures that address different aspects of inference in divergence time estimation. 'Fossil cross-validation' is a procedure used to identify the impact of different individual calibrations on overall estimation. This can identify fossils that have an exceptionally large error effect and may warrant further scrutiny. 'Fossil-based model cross-validation' is an entirely different procedure that uses fossils to identify the optimal model of molecular evolution in the context of rate smoothing or other inference methods. Both procedures were applied to two recent studies: an analysis of monocot angiosperms with eight fossil calibrations and an analysis of placental mammals with nine fossil calibrations. In each case, fossil calibrations could be ranked from most to least influential, and in one of the two studies, the fossils provided decisive evidence about the optimal molecular evolutionary model.     

Semiparametric estimation in copula models for bivariate sequential survival times

Sequentially observed survival times are of interest in many studies but there are difficulties in analyzing such data using nonparametric or semiparametric methods. First, when the duration of followup is limited and the times for a given individual are not independent, induced dependent censoring arises for the second and subsequent survival times. Non-identifiability of the marginal survival distributions for second and later times is another issue, since they are observable only if preceding survival times for an individual are uncensored. In addition, in some studies a significant proportion of individuals may never have the first event. Fully parametric models can deal with these features, but robustness is a concern. We introduce a new approach to address these issues. We model the joint distribution of the successive survival times by using copula functions, and provide semiparametric estimation procedures in which copula parameters are estimated without parametric assumptions on the marginal distributions. This provides more robust estimates and checks on the fit of parametric models. The methodology is applied to a motivating example involving relapse and survival following colon cancer treatment.     

Confidence intervals for the difference in the success rates of two treatments in the analysis of correlated binary responses

In clinical studies, we often compare the success rates of two treatment groups where post‐treatment responses of subjects within clusters are usually correlated. To estimate the difference between the success rates, interval estimation procedures that do not account for this intraclass correlation are likely inappropriate. To address this issue, we propose three interval procedures by direct extensions of recently proposed methods for independent binary data based on the concepts of design effect and effective sample size used in sample surveys. Each of them is then evaluated with four competing variance estimates. We also extend three existing methods recommended for complex survey data using different weighting schemes required for those three existing methods. An extensive simulation study is conducted for the purposes of evaluating and comparing the performance of the proposed methods in terms of coverage and expected width. The interval estimation procedures are illustrated using three examples in clinical and social science studies. Our analytic arguments and numerical studies suggest that the methods proposed in this work may be useful in clustered data analyses.