Correcting for non-compliance in randomized trials using rank preserving structural failure time models

We propose correcting for non-compliance in randomized trials by estimating the parameters of a class of semi-parametric failure time models, the rank preserving structural failure time models, using a class of rank estimators. These models are the structural or strong version of the “accelerated failure time model with time-dependent covariates” of Cox and Oakes (1984). In this paper we develop a large sample theory for these estimators, derive the optimal estimator within this class, and briefly consider the construction of “partially adaptive” estimators whose efficiency may approach that of the optimal estimator. We show that in the absence of censoring the optimal estimator attains the semiparametric efficiency bound for the model.     

Bayes estimators of the reliability function and parameter of inverted exponential distribution using informative and non-informative priors

In this paper, we propose Bayes estimators of the parameter and reliability function of inverted exponential distribution under the general entropy loss function for complete, type I and type II censored samples. The proposed estimators have been compared with the corresponding maximum-likelihood estimators for their simulated risks (average loss over sample space).     

A method for sample size calculation via E-value in the planning of observational studies

Confounding adjustment plays a key role in designing observational studies such as cross-sectional studies, case-control studies, and cohort studies. In this article, we propose a simple method for sample size calculation in observational research in the presence of confounding. The method is motivated by the notion of E-value, using some bounding factor to quantify the impact of confounders on the effect size. The method can be applied to calculate the needed sample size in observational research when the outcome variable is binary, continuous, or time-to-event. The method can be implemented straightforwardly using existing commercial software such as the PASS software. We demonstrate the performance of the proposed method through numerical examples, simulation studies, and a real application, which show that the proposed method is conservative in providing a slightly bigger sample size than what it needs to achieve a given power.     

Survival analysis using inverse probability of treatment weighted methods based on the generalized propensity score

In survival analysis, treatment effects are commonly evaluated based on survival curves and hazard ratios as causal treatment effects. In observational studies, these estimates may be biased due to confounding factors. The inverse probability of treatment weighted (IPTW) method based on the propensity score is one of the approaches utilized to adjust for confounding factors between binary treatment groups. As a generalization of this methodology, we developed an exact formula for an IPTW log‐rank test based on the generalized propensity score for survival data. This makes it possible to compare the group differences of IPTW Kaplan–Meier estimators of survival curves using an IPTW log‐rank test for multi‐valued treatments. As causal treatment effects, the hazard ratio can be estimated using the IPTW approach. If the treatments correspond to ordered levels of a treatment, the proposed method can be easily extended to the analysis of treatment effect patterns with contrast statistics. In this paper, the proposed method is illustrated with data from the Kyushu Lipid Intervention Study (KLIS), which investigated the primary preventive effects of pravastatin on coronary heart disease (CHD). The results of the proposed method suggested that pravastatin treatment reduces the risk of CHD and that compliance to pravastatin treatment is important for the prevention of CHD. Copyright © 2009 John Wiley & Sons, Ltd.     

Relative efficiency of a censored experiment in terms of fisher information matrix

Fisher information matrix is used to quantify information loss in the randomly right-censored model, A real value approach alternative to the matrix approach of Turrero (1988) is presented for obtaining real valued measures of the relative efficiency of the censored experiment. Properties of the proposed measures are examined. The connection between both approaches and the Bayesian approach to this problem is also studied. Results in the paper are exemplified by considering grouped survival data.     

Estimation of Causal Odds of Concordance using the Aalen Additive Model

A simple summary of a treatment effect is attractive, which is part of the explanation of the success of the Cox model when analysing time‐to‐event data since the relative risk measure is such a convenient summary measure. In practice, however, the Cox model may fail to give a reasonable fit, very often because of time‐changing treatment effect. The Aalen additive hazards model may be a good alternative as time‐changing effects are easily modelled within this model, but results are then evidently more complicated to communicate. In such situations, the odds of concordance measure (OC) is a convenient way of communicating results, and recently Martinussen & Pipper (2012) showed how a variant of the OC measure may be estimated based on the Aalen additive hazards model. In this study, we propose an estimator that should be preferred in observational studies as it always estimates the causal effect on the chosen scale, only assuming that there are no un‐measured confounders. The resulting estimator is shown to be consistent and asymptotically normal, and an estimator of its limiting variance is provided. Two real applications are provided.     

Sensitivity analysis of the unconfoundedness assumption with an application to an evaluation of college choice effects on earnings

We evaluate the effects of college choice on earnings using Swedish register databases. This case study is used to motivate the introduction of a novel procedure to analyse the sensitivity of such an observational study to the assumption made that there are no unobserved confounders – variables affecting both college choice and earnings. This assumption is not testable without further information, and should be considered an approximation of reality. To perform a sensitivity analysis, we measure the departure from the unconfoundedness assumption with the correlation between college choice and earnings when conditioning on observed covariates. The use of a correlation as a measure of dependence allows us to propose a standardised procedure by advocating the use of a fixed value for the correlation, typically 1% or 5%, when checking the sensitivity of an evaluation study. A correlation coefficient is, moreover, intuitive to most empirical scientists, which makes the results of our sensitivity analysis easier to communicate than those of previously proposed methods. In our evaluation of the effects of college choice on earnings, the significantly positive effect obtained could not be questioned by a sensitivity analysis allowing for unobserved confounders inducing at most 5% correlation between college choice and earnings.     

Use of Cohort Information in the Design and Analysis of Case-Control Studies

Abstract.  Four case studies are presented to illustrate how information available on cohort members can be used to inform the control selection in epidemiologic case-control studies. The basic framework is the nested case-control paradigm and accompanying analysis methods. Emphasis is on development of intuition for choosing study design candidates, the form of the estimators, and extensions of the basic theory to solve design and analysis problems.     

非实验数据的因果分析——以PSM模型在体育健康回报研究中的应用为例

非实验数据的定量分析因受混杂因素的干扰而失真。倾向值匹配模型(PSM)通过模仿实验设计中的匹配过程,有效地处理了混杂因素的干扰,从而让基于非实验数据的因果效应估计更加真实、可靠。基于CGSS2010数据,运用PSM模型估计了体育行为的健康回报,研究发现,因受选择效应的影响,传统OLS模型低估了体育锻炼的健康回报。体育行为的发生频率与健康回报之间呈现倒U型特征,即随着体育参与频率增加,健康效应先升高,后减小。体育行为在促进健康的同时,健康可能也反向影响着人们的体育锻炼行为。     

Effects of correlated covariates on the asymptotic efficiency of matching and inverse probability weighting estimators for causal inference

In observational studies, the overall aim when fitting a model for the propensity score is to reduce bias for an estimator of the causal effect. To make the assumption of an unconfounded treatment plausible researchers might include many, possibly correlated, covariates in the propensity score model. In this paper, we study how the asymptotic efficiency of matching and inverse probability weighting estimators for average causal effects change when the covariates are correlated. We investigate the case with multivariate normal covariates, a logistic model for the propensity score and linear models for the potential outcomes and show results under different model assumptions. We show that the correlation can both increase and decrease the large sample variances of the estimators, and that the correlation affects the asymptotic efficiency of the estimators differently, both with regard to direction and magnitude. Moreover, the strength of the confounding towards the outcome and the treatment plays an important role.     

The Perpetual Student: Modeling Duration of Undergraduate Studies Based on Lifetime-Type Educational Data

It is important to educational planners to estimate the likelihood and time-scale of graduation of students enrolled on a curriculum. The particular case we are concerned with, emerges when studies are not completed in the prescribed interval of time. Under these circumstances we use a framework of survival analysis applied to lifetime-type educational data to examine the distribution of duration of undergraduate studies for 10,313 students, enrolled in a Greek university during ten consecutive academic years. Non-parametric and parametric survival models have been developed for handling this distribution as well as a modified procedure for testing goodness-of-fit of the models. Data censoring was taken into account in the statistical analysis and the problems of thresholding of graduation and of perpetual students are also addressed. We found that the proposed parametric model adequately describes the empirical distribution provided by non-parametric estimation. We also found significant difference between duration of studies of men and women students. The proposed methodology could be useful to analyse data from any other type and level of education or general lifetime data with similar characteristics.     

Prediction of transplant-free survival in idiopathic pulmonary fibrosis patients using joint models for event times and mixed multivariate longitudinal data

We implement a joint model for mixed multivariate longitudinal measurements, applied to the prediction of time until lung transplant or death in idiopathic pulmonary fibrosis. Specifically, we formulate a unified Bayesian joint model for the mixed longitudinal responses and time-to-event outcomes. For the longitudinal model of continuous and binary responses, we investigate multivariate generalized linear mixed models using shared random effects. Longitudinal and time-to-event data are assumed to be independent conditional on available covariates and shared parameters. A Markov chain Monte Carlo algorithm, implemented in OpenBUGS, is used for parameter estimation. To illustrate practical considerations in choosing a final model, we fit 37 different candidate models using all possible combinations of random effects and employ a deviance information criterion to select a best-fitting model. We demonstrate the prediction of future event probabilities within a fixed time interval for patients utilizing baseline data, post-baseline longitudinal responses, and the time-to-event outcome. The performance of our joint model is also evaluated in simulation studies.     

On Estimation and Tests of Time-Varying Effects in the Proportional Hazards Model

Abstract.  Cox's proportional hazards model is routinely used in many applied fields, some times, however, with too little emphasis on the fit of the model. In this paper, we suggest some new tests for investigating whether or not covariate effects vary with time. These tests are a natural and integrated part of an extended version of the Cox model. An important new feature of the suggested test is that time constancy for a specific covariate is examined in a model, where some effects of other covariates are allowed to vary with time and some are constant; thus making successive testing of time-dependency possible. The proposed techniques are illustrated with the well-known Mayo liver disease data, and a small simulation study investigates the finite sample properties of the tests.     

Nonparametric estimation of the survival distribution in censored data

Two nonparametric estimators o f the survival distributionare discussed. The estimators were proposed by Kaplan and Meier (1958) and Breslow (1972) and are applicable when dealing with censored data. It is known that they are asymptotically unbiased and uniformly strongly consistent, and when properly normalized that they converge weakly to the same Gaussian process. In this paper, the properties of the estimators are carefully inspected in small or moderate samples. The Breslow estimator, a shrinkage version of the Kaplan-Meier, nearly always has the smaller mean square error (MSE) whenever the truesurvival probabilityis at least 0.20, but has considerably larger MSE than the Kaplan-Meier estimator when the survivalprobability is near zero.     

The Additive Risk Model for Estimation of Effect of Haplotype Match in BMT Studies

Abstract. In this article we consider a problem from bone marrow transplant (BMT) studies where there is interest on assessing the effect of haplotype match for donor and patient on the overall survival. The BMT study we consider is based on donors and patients that are genotype matched, and this therefore leads to a missing data problem. We show how Aalen's additive risk model can be applied in this setting with the benefit that the time‐varying haplomatch effect can be easily studied. This problem has not been considered before, and the standard approach where one would use the expected‐maximization (EM) algorithm cannot be applied for this model because the likelihood is hard to evaluate without additional assumptions. We suggest an approach based on multivariate estimating equations that are solved using a recursive structure. This approach leads to an estimator where the large sample properties can be developed using product‐integration theory. Small sample properties are investigated using simulations in a setting that mimics the motivating haplomatch problem.     

Effects of nonnormality on the spart for the correlation coefficient: bivariate edgeworth series distribution

The effects of sampling from the bivariate Edgeworth series distribution (BVESD) on the sequential probability ratio test (SPRT) for the correlation coefficient are assessed. The values of the average sample number (ASN) and the operating characteristic (OC) are determined by simulation from such populations. The robustness of the SPRT to this type of nonnormality is demonstrated.     

Estimation of dependence between paired correlated failure times in the presence of covariate measurement error

Summary. In many biomedical studies, covariates are subject to measurement error. Although it is well known that the regression coefficients estimators can be substantially biased if the measurement error is not accommodated, there has been little study of the effect of covariate measurement error on the estimation of the dependence between bivariate failure times. We show that the dependence parameter estimator in the Clayton–Oakes model can be considerably biased if the measurement error in the covariate is not accommodated. In contrast with the typical bias towards the null for marginal regression coefficients, the dependence parameter can be biased in either direction. We introduce a bias reduction technique for the bivariate survival function in copula models while assuming an additive measurement error model and replicated measurement for the covariates, and we study the large and small sample properties of the dependence parameter estimator proposed.     

Modeling categorical covariates for lifetime data in the presence of cure fraction by Bayesian partition structures

In this paper, we propose a Bayesian partition modeling for lifetime data in the presence of a cure fraction by considering a local structure generated by a tessellation which depends on covariates. In this modeling we include information of nominal qualitative variables with more than two categories or ordinal qualitative variables. The proposed modeling is based on a promotion time cure model structure but assuming that the number of competing causes follows a geometric distribution. It is an alternative modeling strategy to the conventional survival regression modeling generally used for modeling lifetime data in the presence of a cure fraction, which models the cure fraction through a (generalized) linear model of the covariates. An advantage of our approach is its ability to capture the effects of covariates in a local structure. The flexibility of having a local structure is crucial to capture local effects and features of the data. The modeling is illustrated on two real melanoma data sets.     

陕西省居民消费、投资与经济增长关系的协整研究

一、引言消费、投资与我国GDP之间的关系一直以来是宏观经济领域讨论的热点,学者们在这方面已经做出了很多有意义的分析和研究,他们普遍都认为消费和投资对我国的经济增长有促进作用,但是在消费、投资对我国GDP作用的大小以及它们之间的相互因果关系上面却存在着不同的观点。在     

A Semiparametrically Efficient Estimator of the Time‐Varying Effects for Survival Data with Time‐Dependent Treatment

The timing of a time‐dependent treatment—for example, when to perform a kidney transplantation—is an important factor for evaluating treatment efficacy. A naïve comparison between the treated and untreated groups, while ignoring the timing of treatment, typically yields biased results that might favour the treated group because only patients who survive long enough will get treated. On the other hand, studying the effect of a time‐dependent treatment is often complex, as it involves modelling treatment history and accounting for the possible time‐varying nature of the treatment effect. We propose a varying‐coefficient Cox model that investigates the efficacy of a time‐dependent treatment by utilizing a global partial likelihood, which renders appealing statistical properties, including consistency, asymptotic normality and semiparametric efficiency. Extensive simulations verify the finite sample performance, and we apply the proposed method to study the efficacy of kidney transplantation for end‐stage renal disease patients in the US Scientific Registry of Transplant Recipients.