Multiple imputation to estimate the association between eyes in disease progression with interval-censored data

In many ophthalmologic studies, progression of diseases such as diabetic retinopathy, age-related maculopathy, cataract, and glaucoma is only noted when each eye is examined at intervals that commonly vary between subjects. Such data are often analysed using continuous time survival methods with observed progression assumed to occur at the end of the interval. Tied times of progression can lead to substantial bias in estimation of the association between progression in right and left eyes. We describe a multiple imputation strategy to create multiple data sets without ties, based on drawing interval-censored progression times from a parametric gamma frailty model that accounts for continuous and discrete covariates. We illustrate the method with data from 478 patients with insulin-dependent diabetes mellitus who were followed for progression of diabetic retinopathy in the Sorbinil Retinopathy Trial. Resolution of tied failure times allows for valid estimation of the hazard of progression in one eye given the progression status of the other eye. A simulation study suggests that the method performs well. Results highlight the advantage of multiple imputation that data imputed under one model can be analysed under several alternative models.     

Analysis of clustered failure time data with cure fraction using copula

Clustered survival data in the presence of cure has received increasing attention. In this paper, we consider a semiparametric mixture cure model which incorporates a logistic regression model for the cure fraction and a semiparametric regression model for the failure time. We utilize Archimedean copula (AC) models to assess the strength of association for both susceptibility and failure times between susceptible individuals in the same cluster. Instead of using the full likelihood approach, we consider a composite likelihood function and a two-stage estimation procedure for both marginal and association parameters. A Jackknife procedure that takes out one cluster at a time is proposed for the variance estimation of the estimators. Akaike information criterion is applied to select the best model among ACs. Simulation studies are performed to validate our estimating procedures, and two real data sets are analyzed to demonstrate the practical use of our proposed method.     

Estimating the force of infection for HCV in injecting drug users using interval-censored data

Injecting drug users (IDUs) account for most new HCV infections. The objectives of this study were: to estimate the force of infection for hepatitis C virus in IDUs within the interval-censoring framework and to determine the impact of risk factors such as frequency of injection, drug injected, sharing of syringes and time of first injection on the time to HCV infection. We used data from the Amsterdam Cohort Study collected in The Netherlands and focused on those individuals who were HCV negative upon entry into the study. Based on the results, the force of infection was found to vary with time of first injection. The risk of infection was higher in the first 3 years of an IDU's career, implying estimates based on single cross-sectional studies could be biased. Frequency of injection and type of drug injected were found to be highly significant predictors, whereas sharing syringes was not.     

The analysis of multivariate interval-censored survival data

This paper considers a marginal approach for the analysis of the effect of covariates on multivariate interval-censored survival data.Interval censoring of multivariate events can occur when the events are not directly observable but are detected by periodically performing clinical examinations or laboratory tests. The method assumes the marginal distribution for each event is based on a discrete analogue of the proportional hazards model for interval-censored data. A robust estimator for the covariance matrix is developed that accounts for the correlation between events. A simulation study comparing the performance of this method and a midpoint imputation approach indicates the parameter estimates from the proposed method are less biased. Furthermore, even when the events are only modestly correlated, ignoring the correlation can result in erroneous variance estimators. The method is illustrated using data from an ongoing clinical trial involving subjects with systemic lupus erythematosus.     

Meta-analysis of diagnostic test data: a bivariate Bayesian modeling approach

In the last decades, the amount of published results on clinical diagnostic tests has expanded very rapidly. The counterpart to this development has been the formal evaluation and synthesis of diagnostic results. However, published results present substantial heterogeneity and they can be regarded as so far removed from the classical domain of meta-analysis, that they can provide a rather severe test of classical statistical methods. Recently, bivariate random effects meta-analytic methods, which model the pairs of sensitivities and specificities, have been presented from the classical point of view. In this work a bivariate Bayesian modeling approach is presented. This approach substantially extends the scope of classical bivariate methods by allowing the structural distribution of the random effects to depend on multiple sources of variability. Meta-analysis is summarized by the predictive posterior distributions for sensitivity and specificity. This new approach allows, also, to perform substantial model checking, model diagnostic and model selection. Statistical computations are implemented in the public domain statistical software (WinBUGS and R) and illustrated with real data examples.     

Analysis of interval-censored data from circular migrant and non-migrant sexual partnerships using the EM algorithm

In epidemiological studies where subjects are seen periodically on follow-up visits, interval-censored data occur naturally. The exact time the change of state (such as HIV seroconversion) occurs is not known exactly, only that it occurred sometime within a specific time interval. Methods of estimation for interval-censored data are readily available when data are independent. However, methods for correlated interval-censored data are not well developed. This paper considers an approach for estimating the parameters when data are interval-censored and correlated within sexual partnerships. We consider the exact event times for interval-censored observations as unobserved data, only known to be between two time points. Dependency induced by sexual partnerships is modelled as frailties assuming a gamma distribution for frailties and an exponential distribution on the time to infection. This formulation facilitates application of the expectation-maximization (EM) algorithm. Maximization process maximizes the standard survival frailty model. Results show high degree of heterogeneity between sexual partnerships. Intervention strategies aimed at combating the spread of HIV and other sexually transmitted infections (STI)s should treat sexual partnerships as social units and fully incorporate the effects of migration in their strategies.     

含有区间删失数据时的生存函数估计及其SAS实现

目的 介绍生存分析中区间删失数据的特点及含区间删失数据生存函数估计的非参数方法,并介绍其在SAS9.2中的程序实现.方法 采用非参数极大似然估计法对Beadle等研究2种疗法对早期乳腺癌患者形体美容效果研究的区间删失数据进行生存函数估计,并利用SAS中的宏程序%EMICM实现其计算.结果 非参数极大似然估计法有效的计算出了2组疗法患者每个个体的生存概率、死亡概率、累积生存概率以及生存率的标准误,绘制出了2组疗法患者的生存曲线.结论 区间删失数据是临床实践中较常见的一类数据,区间删失数据生存函数估计的非参数方法 是常用的一种方法,但其计算相对右删失数据过程复杂,缺乏相应的软件实现,本文提供的SAS宏程序可以有效的实现计算,为实际工作提供帮助.     

Estimating incidence rates using exact or interval-censored data with an application to hospital-acquired infections

Health-care providers in the UK and elsewhere are required to maintain records of incidents relating to patient safety, including the date and time of each incident. However, for reporting and analysis, the resulting data are typically grouped into discrete time intervals, for example, weekly or monthly counts. The grouping represents a potential loss of information for estimating variations in incidence over time. We use a Poisson point process model to quantify this loss of information. We also suggest some diagnostic procedures for checking the goodness of fit of the Poisson model. Finally, we apply the model to the data on hospital-acquired methicillin-resistant Staphylococcus aureus infections in two hospitals in the north of England. We find that, in one of the hospitals, the estimated incidence decreased by a factor of approximately 2.3 over a 7-year period from 0.323 to 0.097 cases per day per 1000 beds, whereas in the other, the estimated incidence showed only a small and nonsignificant decrease over the same period from 0.137 to 0.131.     

Mixed models for bivariate response repeated measures data using Gibbs sampling

Repeated measures data are frequently incomplete, unbalanced and correlated. There has been a great deal of recent interest in mixed effects models for analysing such data. In this paper, we develop bivariate response mixed effects models that are a generalization of linear mixed effects models for a single response variable. We describe their estimation procedures using a Markov chain Monte Carlo method, the Gibbs sampler. We illustrate the methods with analyses of intravenous vitamin D₃ administration for secondary hyperparathyroidism in hemodialysis patients. In these data there were two response variables on each individual (PTH and calcium level). This study also suffered from attrition, like many longitudinal studies. While, considering the study design, it was reasonable to assume the drop-out mechanism for the calcium (Ca) level to be ‘missing at random’, the drop-out mechanism for the PTH level was likely to be non-ignorable. We found that the posterior treatment effects for the PTH level by the single response model were underestimated compared with those obtained by the bivariate response model, while there were little differences in the posterior features for the Ca level under both models. © 1997 John Wiley & Sons Ltd.     

Smooth estimation of survival functions and hazard ratios from interval-censored data using Bayesian penalized B-splines

We discuss the use of Bayesian P-spline and of the composite link model to estimate survival functions and hazard ratios from interval-censored data. If one further assumes proportionality of the hazards, the proposed strategy provides a smoothed estimate of the baseline hazard along with estimates of global covariate effects. The frequentist properties of our Bayesian estimators are assessed by an extensive simulation study. We further illustrate the methodology by two examples showing that the proportionality of the hazards might also be found inappropriate from interval-censored data.     

A sensitivity approach to modeling longitudinal bivariate ordered data subject to informative dropouts

Incomplete data abound in epidemiological and clinical studies. When the missing data process is not properly investigated, inferences may be misleading. An increasing number of models that incorporate nonrandom incomplete data have become available. At the same time, however, serious doubts have arisen about the validity of these models, known to rely on strong and unverifiable assumptions. A common conclusion emerging from the current literature is the clear need for a sensitivity analysis. We propose in this paper a detailed sensitivity analysis using graphical and analytical techniques to understand the impact of missing-data assumptions on inferences. Specifically, we explore the influence of perturbing a missing at random model locally in the direction of non-random dropout models. Data from a psychiatric trial are used to illustrate the methodology.     

Evolutionary-based association analysis using haplotype data

Association studies, both family-based and population-based, can be powerful means of detecting disease-liability alleles. To increase the information of the test, various researchers have proposed targeting haplotypes. The larger number of haplotypes, however, relative to alleles at individual loci, could decrease power because of the additional degrees of freedom required for the test. An optimal strategy would focus the test on particular haplotypes or groups of haplotypes, much as is done with cladistic-based association analysis. First suggested by Templeton et al. ([1987] Genetics 117:343-351), such analyses use the evolutionary relationships among haplotypes to produce a limited set of hypothesis tests and to increase the interpretability of these tests. To more fully utilize the information contained in the evolutionary relationships among haplotypes and in the sample, we propose generalized linear models (GLM) for the analysis of data from family-based and population-based studies. These models fully account for haplotype phase ambiguity and allow for covariates. The models are encoded into a software package (the Evolutionary-Based Haplotype Analysis Package, EHAP), which also provides for various kinds of exploratory data analysis. The exploratory analyses, such as error checking, estimation of haplotype frequencies, and tools for building cladograms, should facilitate the implementation of cladistic-based association analysis with haplotypes.     

A mixed effect model for bivariate meta‐analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta‐analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re‐analysing the data of two published meta‐analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R . Copyright © 2015 John Wiley & Sons, Ltd.     

Variance estimation of a survival function for interval-censored survival data

Interval-censored survival data often occur in medical studies, especially in clinical trials. In this case, many authors have considered estimation of a survival function. There is, however, relatively little discussion on estimating the variance of estimated survival functions. For right-censored data, a special case of interval-censored data, the most commonly used method for variance estimation is to use the Greenwood formula. In this paper we propose a generalization of the Greenwood formula for variance estimation of a survival function based on interval-censored data. Also a simple bootstrap approach is presented. The two methods are evaluated and compared using simulation studies and a real data set. The simulation results suggest that the methods work well.     

Cost-effectiveness analysis using data from multinational trials: the use of bivariate hierarchical modeling.

Health care cost-effectiveness analysis (CEA) often uses individual patient data (IPD) from multinational randomized controlled trials. Although designed to account for between-patient sampling variability in the clinical and economic data, standard analytical approaches to CEA ignore the presence of between-location variability in the study results. This is a restrictive limitation given that countries often differ in factors that could affect the results of CEAs, such as the availability of health care resources, their unit costs, clinical practice, and patient case mix. The authors advocate the use of Bayesian bivariate hierarchical modeling to analyze multinational cost-effectiveness data. This analytical framework explicitly recognizes that patient-level costs and outcomes are nested within countries. Using real-life data, the authors illustrate how the proposed methods can be applied to obtain (a) more appropriate estimates of overall cost-effectiveness and associated measure of sampling uncertainty compared to standard CEA and (b) country-specific cost-effectiveness estimates that can be used to assess the between-location variability of the study results while controlling for differences in country-specific and patient-specific characteristics. It is demonstrated that results from standard CEA using IPD from multinational trials display a large degree of variability across the 17 countries included in the analysis, producing potentially misleading results. In contrast, "shrinkage estimates' obtained from the modeling approach proposed here facilitate the appropriate quantification of country-specific cost-effectiveness estimates while weighting the results based on the level of information available within each country. The authors suggest that the methods presented here represent a general framework for the analysis of economic data collected from different locations.     

Estimating local and global measures of association for bivariate interval censored data with a smooth estimate of the density

Measures of association for bivariate interval censored data have not yet been studied extensively. Betensky and Finkelstein (Statist. Med. 1999; 18:3101-3109) proposed to calculate Kendall's coefficient of concordance using a multiple imputation technique, but their method becomes computer intensive for moderate to large data sets. We suggest a different approach consisting of two steps. Firstly, a bivariate smooth estimate of the density of log-event times is determined. The smoothing technique is based on a mixture of Gaussian densities fixed on a grid with weights determined by a penalized likelihood approach. Secondly, given the smooth approximation several local and global measures of association can be estimated readily. The performance of our method is illustrated by an extensive simulation study and is applied to tooth emergence data of permanent teeth measured on 4468 children from the Signal-Tandmobiel study.     

Hierarchical Archimedean copula models for the analysis of binary familial data

Archimedean copulas are commonly used in a wide range of statistical models due to their simplicity, manageable analytical expressions, rich choices of generator functions, and other workable properties. However, the exchangeable dependence structure inherent to Archimedean copulas limits its application to familial data, where the dependence among family members is often different. When response variables are binary, modeling the familial associations becomes more challenging due to the stringent constraints imposed on the dependence parameters. This paper proposes hierarchical Archimedean copulas to account for the natural hierarchical dependence structure in familial data and addresses the details in the modeling of binary familial data and the inference based on maximum likelihood estimate. An example showing the flexibility of this powerful tool is also presented with possible extension to other similar studies.     

基于区间删失数据估计方法的COVID-19潜伏期分布估计

目的 新型冠状病毒肺炎疫情已经成为全球关注的公共卫生问题,其潜伏期等流行病学特征尚不明确,本研究旨在对新型冠状病毒肺炎的潜伏期分布进行估计。方法 收集各省份卫生健康委员会官方发布信息平台的确诊病例暴露与发病信息,利用区间删失数据估计方法,基于Log-normal、Gamma和Weibull分布,对新型冠状病毒肺炎的潜伏期分布进行估计。结果 本研究共收集确诊病例109例,平均年龄为39.825岁。基于Log-normal分布的潜伏期M=4.938（P₂₅～P₇₅：3.451～7.304）d,Gamma分布的潜伏期M=5.064（P₂₅～P₇₅：3.489～7.301）d,Weibull分布的潜伏期M=5.678（P₂₅～P₇₅：3.653～7.666）d。Gamma分布的对数似然函数值最大。结论 COVID-19的潜伏期服从Gamma分布,基于区间删失数据的估计方法可用于传染病潜伏期分布的估计。     

Sample-weighted semiparametric estimation of cause-specific cumulative risk and incidence using left- or interval-censored data from electronic health records

Electronic health records (EHRs) can be a cost-effective data source for forming cohorts and developing risk models in the context of disease screening. However, important issues need to be handled: competing outcomes, left-censoring of prevalent disease, interval-censoring of incident disease, and uncertainty of prevalent disease when accurate disease ascertainment is not conducted at baseline. Furthermore, novel tests that are costly and limited in availability can be conducted on stored biospecimens selected as samples from EHRs by using different sampling fractions. We extend sample-weighted semiparametric marginal mixture models to estimating competing risks. For flexible modeling of relative risks, a general transformation of the subdistribution hazard function and regression parameters is used. We propose a numerical algorithm for nonparametrically calculating the maximum likelihood estimates for subdistribution hazard functions and regression parameters. Methods for calculating the consistent confidence intervals for relative and absolute risk estimates are presented. The proposed algorithm and methods show reliable finite sample performance through simulation studies. We apply our methods to a cohort assembled from EHRs at a health maintenance organization where we estimate cumulative risk of cervical precancer/cancer and incidence of infection-clearance by HPV genotype among human papillomavirus (HPV) positive women. There is no significant difference in 3-year HPV-clearance rates across different HPV types, but 3-year cumulative risk of progression-to-precancer/cancer from HPV-16 is relatively higher than the other HPV genotypes.