Modeling potential time to event data with competing risks

Patients receiving radical prostatectomy are at risk of metastasis or prostate cancer related death, and often need repeated clinical evaluations to determine whether additional adjuvant or salvage therapies are needed. Since the prostate cancer is a slowly progressing disease, and these additional therapies come with significant side effects, it is important for clinical decision making purposes to estimate a patient’s risk of cancer metastasis, in the presence of a competing risk by death, under the hypothetical condition that the patient does not receive any additional therapy. In observational studies, patients may receive additional therapy by choice; the time to metastasis without any therapy is often a potential outcome and not always observed. We study the competing risks model of Fine and Gray (J Am Stat Assoc, 94:496–509, 1999) with adjustment for treatment choice by inverse probability censoring weighting (IPCW). The model can be fit using standard software for partial likelihood with double IPCW weights. The proposed methodology is used in a prostate cancer study to predict the post-prostatectomy cumulative incidence probability of cancer metastasis without additional adjuvant or salvage therapies.     

Robust logistic regression of family data in the presence of missing genotypes

Large cohort studies are commonly launched to study the risk effect of genetic variants or other risk factors on a chronic disorder. In these studies, family data are often collected to provide additional information for the purpose of improving the inference results. Statistical analysis of the family data can be very challenging due to the missing observations of genotypes, incomplete records of disease occurrences in family members, and the complicated dependence attributed to the shared genetic background and environmental factors. In this article, we investigate a class of logistic models with family-shared random effects to tackle these challenges, and develop a robust regression method based on the conditional logistic technique for statistical inference. An expectation–maximization (EM) algorithm with fast computation speed is developed to handle the missing genotypes. The proposed estimators are shown to be consistent and asymptotically normal. Additionally, a score test based on the proposed method is derived to test the genetic effect. Extensive simulation studies demonstrate that the proposed method performs well in finite samples in terms of estimate accuracy, robustness and computational speed. The proposed procedure is applied to an Alzheimer's disease study.     

A new class of measurement-error models,with applications to dietary data

Measurement-error modelling occurs when one cannot observe a covariate, but instead has possibly replicated surrogate versions of this covariate measured with error. The vast majority of the literature in measurement-error modelling assumes (typically with good reason) that given the value of the true but unobserved (latent) covariate, the replicated surrogates are unbiased for latent covariate and conditionally independent. In the area of nutritional epidemiology, there is some evidence from biomarker studies that this simple conditional independence model may break down due to two causes: (a) systematic biases depending on a person's body mass index, and (b) an additional random component of bias, so that the error structure is the same as a one-way random-effects model. We investigate this problem in the context of (1) estimating distribution of usual nutrient intake, (2) estimating the correlation between a nutrient instrument and usual nutrient intake, and (3) estimating the true relative risk from an estimated relative risk using the error-prone covariate. While systematic bias due to body mass index appears to have little effect, the additional random effect in the variance structure is shown to have a potentially important effect on overall results, both on corrections for relative risk estimates and in estimating the distribution of usual nutrient intake. However, the effect of dietary measurement error on both factors is shown via examples to depend strongly on the data set being used. Indeed, one of our data sets suggests that dietary measurement error may be masking a strong risk of fat on breast cancer, while for a second data set this masking is not so clear. Until further understanding of dietary measurement is available, measurement-error corrections must be done on a study-specific basis, sensitivity analyses should be conducted, and even then results of nutritional epidemiology studies relating diet to disease risk should be interpreted cautiously.     

A decision-theoretic approach to variable selection in discriminant analysis

In discriminant analysis it is often desirable to find a small subset of the variables that were measured on the individuals of known origin, to be used for classifying individuals of unknown origin. In this paper a Bayesian approach to variable selection is used that includes an additional subset of variables for future classification if the additional measurement costs for this subsst are lower than the resulting reduction in expected misclassification costs.     

Small sample sensitivity analysis techniques for computer models.with an application to risk assessment

As modeling efforts expand to a broader spectrum of areas the amount of computer time required to exercise the corresponding computer codes has become quite costly (several hours for a single run is not uncommon). This costly process can be directly tied to the complexity of the modeling and to the large number of input variables (often numbering in the hundreds) Further, the complexity of the modeling (usually involving systems of differential equations) makes the relationships among the input variables not mathematically tractable. In this setting it is desired to perform sensitivity studies of the input-output relationships. Hence, a judicious selection procedure for the choic of values of input variables is required, Latin hypercube sampling has been shown to work well on this type of problem.

However, a variety of situations require that decisions and judgments be made in the face of uncertainty. The source of this uncertainty may be lack ul knowledge about probability distributions associated with input variables, or about different hypothesized future conditions, or may be present as a result of different strategies associated with a decision making process In this paper a generalization of Latin hypercube sampling is given that allows these areas to be investigated without making additional computer runs. In particular it is shown how weights associated with Latin hypercube input vectors may be rhangpd to reflect different probability distribution assumptions on key input variables and yet provide: an unbiased estimate of the cumulative distribution function of the output variable. This allows for different distribution assumptions on input variables to be studied without additional computer runs and without fitting a response surface. In addition these same weights can be used in a modified nonparametric Friedman test to compare treatments, Sample size requirements needed to apply the results of the work are also considered. The procedures presented in this paper are illustrated using a model associated with the risk assessment of geologic disposal of radioactive waste.     

Applying a marginalized frailty model to competing risks

The marginalized frailty model is often used for the analysis of correlated times in survival data. When only two correlated times are analyzed, this model is often referred to as the Clayton–Oakes model [7,22]. With time-to-event data, there may exist multiple end points (competing risks) suggesting that an analysis focusing on all available outcomes is of interest. The purpose of this work is to extend the single risk marginalized frailty model to the multiple risk setting via cause-specific hazards (CSH). The methods herein make use of the marginalized frailty model described by Pipper and Martinussen [24]. As such, this work uses the martingale theory to develop a likelihood based on estimating equations and observed histories. The proposed multivariate CSH model yields marginal regression parameter estimates while accommodating the clustering of outcomes. The multivariate CSH model can be fitted using a data augmentation algorithm described by Lunn and McNeil [21] or by fitting a series of single risk models for each of the competing risks. An example of the application of the multivariate CSH model is provided through the analysis of a family-based follow-up study of breast cancer with death in absence of breast cancer as a competing risk.     

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.     

Disclosure Risk and Disclosure Avoidance for Microdata

Under given concrete exogenous conditions, the fraction of identifiable records in a microdata file without positive identifiers such as name and address is estimated. The effect of possible noise in the data, as well as the sample property of microdata files, is taken into account. Using real microdata files, it is shown that there is no risk of disclosure if the information content of characteristics known to the investigator (additional knowledge) is limited. Files with additional knowledge of large information content yield a high risk of disclosure. This can be eliminated only by massive modifications of the data records, which, however, involve large biases for complex statistical evaluations. In this case, the requirement for privacy protection and high-quality data perhaps may be fulfilled only if the linkage of such files with extensive additional knowledge is prevented by appropriate organizational and legal restrictions.     

Borrowing Information across Populations in Estimating Positive and Negative Predictive Values

A marker's capacity to predict risk of a disease depends on disease prevalence in the target population and its classification accuracy, i.e. its ability to discriminate diseased subjects from non-diseased subjects. The latter is often considered an intrinsic property of the marker; it is independent of disease prevalence and hence more likely to be similar across populations than risk prediction measures. In this paper, we are interested in evaluating the population-specific performance of a risk prediction marker in terms of positive predictive value (PPV) and negative predictive value (NPV) at given thresholds, when samples are available from the target population as well as from another population. A default strategy is to estimate PPV and NPV using samples from the target population only. However, when the marker's classification accuracy as characterized by a specific point on the receiver operating characteristics (ROC) curve is similar across populations, borrowing information across populations allows increased efficiency in estimating PPV and NPV. We develop estimators that optimally combine information across populations. We apply this methodology to a cross-sectional study where we evaluate PCA3 as a risk prediction marker for prostate cancer among subjects with or without previous negative biopsy.     

Pre-test estimation and design in the linear model

As a robust method against model deviation we consider a pre-test estimation function. To optimize a continuous design for this problem we give an asymptotic risk matrix for the quadratic loss. The risk will then be given by an isotonic criterion function of the asymptotic risk matrix. As an optimization criterion we look for a design that minimizes the maximal risk in the deviation model under the restriction that the risk in the original model does not exceed a given bound. This optimization problem will be solved for the polynomial regression, the deviation consisting in one additional regression function and the criterion function being the determinant.     

Joint models for mixed categorical outcomes: a study of HIV risk perception and disease status in Mozambique

Two types of bivariate models for categorical response variables are introduced to deal with special categories such as ‘unsure’ or ‘unknown’ in combination with other ordinal categories, while taking additional hierarchical data structures into account. The latter is achieved by the use of different covariance structures for a trivariate random effect. The models are applied to data from the INSIDA survey, where interest goes to the effect of covariates on the association between HIV risk perception (quadrinomial with an ‘unknown risk’ category) and HIV infection status (binary). The final model combines continuation-ratio with cumulative link logits for the risk perception, together with partly correlated and partly shared trivariate random effects for the household level. The results indicate that only age has a significant effect on the association between HIV risk perception and infection status. The proposed models may be useful in various fields of application such as social and biomedical sciences, epidemiology and public health.     

Checking a Semiparametric Additive Risk Model

McKeague and Sasieni [A partly parametric additive risk model. Biometrika 81 (1994) 501] propose a restriction of Aalen’s additive risk model by the additional hypothesis that some of the covariates have time-independent influence on the intensity of the observed counting process. We introduce goodness-of-fit tests for this semiparametric Aalen model. The asymptotic distribution properties of the test statistics are derived by means of martingale techniques. The tests can be adjusted to detect particular alternatives. As one of the most important alternatives we consider Cox’s proportional hazards model. We present simulation studies and an application to a real data set.     

Impact of misspecified residual correlation structure on the parameter estimates in a shared spatial frailty model

In practice, survival data are often collected over geographical regions. Shared spatial frailty models have been used to model spatial variation in survival times, which are often implemented using the Bayesian Markov chain Monte Carlo method. However, this method comes at the price of slow mixing rates and heavy computational cost, which may render it impractical for data-intensive application. Alternatively, a frailty model assuming an independent and identically distributed (iid) random effect can be easily and efficiently implemented. Therefore, we used simulations to assess the bias and efficiency loss in the estimated parameters, if residual spatial correlation is present but using an iid random effect. Our simulations indicate that a shared frailty model with an iid random effect can estimate the regression coefficients reasonably well, even with residual spatial correlation present, when the percentage of censoring is not too high and the number of clusters and cluster size are not too low. Therefore, if the primary goal is to assess the covariate effects, one may choose the frailty model with an iid random effect; whereas if the goal is to predict the hazard, additional care needs to be given due to the efficiency loss in the parameter(s) for the baseline hazard.     

VaR估计中的概率分布设定风险与改进

 在金融风险管理中,金融风险的事先判断具有极其重要的意义,然而金融机构金融决策事前支持技术的缺陷常常被忽略,在金融投资收益率概率分布估计方法尚未建立以前,将样本数据特征纳入风险度量的计算则不失为一种改进风险判断的有效途径。本文选择度量金融风险的主流方法—VaR技术来讨论概率分布设定风险,探讨依据数据特征改进和扩展VaR计算方法,通过对Delta-正态方法与Delta-Gamma-Cornish-Fisher扩展方法估计VaR值的比较,从实证分析角度论证了扩展方法在VaR估计中的有效性与稳健性。     

Bayesian methods for the cross-design synthesis of epidemiological and toxicological evidence

Summary.  Systematic review and synthesis (meta-analysis) methods are now increasingly used in many areas of health care research. We investigate the potential usefulness of these methods for combining human and animal data in human health risk assessment of exposure to environmental chemicals. Currently, risk assessments are often based on narrative review and expert judgment, but systematic review and formal synthesis methods offer a more transparent and rigorous approach. The method is illustrated by using the example of trihalomethane exposure and its possible association with low birth weight. A systematic literature review identified 13 relevant studies (five epidemiological and eight toxicological). Study-specific dose–response slope estimates were obtained for each of the studies and synthesized by using Bayesian meta-analysis models. Sensitivity analyses of the results obtained to the assumptions made suggest that some assumptions are critical. It is concluded that systematic review methods should be used in the synthesis of evidence for environmental standard setting, that meta-analysis will often be a valuable approach in these contexts and that sensitivity analyses are an important component of the approach whether or not formal synthesis methods (such as systematic review and meta-analysis) are used.     

Measures of discrimination for latent group-based trajectory models

In clinical research, patient care decisions are often easier to make if patients are classified into a manageable number of groups based on homogeneous risk patterns. Investigators can use latent group-based trajectory modeling to estimate the posterior probabilities that an individual will be classified into a particular group of risk patterns. Although this method is increasingly used in clinical research, there is currently no measure that can be used to determine whether an individual's group assignment has a high level of discrimination. In this study, we propose a discrimination index and provide confidence intervals of the probability of the assigned group for each individual. We also propose a modified form of entropy to measure discrimination. The two proposed measures were applied to assess the group assignments of the longitudinal patterns of conduct disorders among young adolescent girls.     

Sensitivity analysis for unmeasured confounding in a marginal structural Cox proportional hazards model

Sensitivity analysis for unmeasured confounding should be reported more often, especially in observational studies. In the standard Cox proportional hazards model, this requires substantial assumptions and can be computationally difficult. The marginal structural Cox proportional hazards model (Cox proportional hazards MSM) with inverse probability weighting has several advantages compared to the standard Cox model, including situations with only one assessment of exposure (point exposure) and time-independent confounders. We describe how simple computations provide sensitivity for unmeasured confounding in a Cox proportional hazards MSM with point exposure. This is achieved by translating the general framework for sensitivity analysis for MSMs by Robins and colleagues to survival time data. Instead of bias-corrected observations, we correct the hazard rate to adjust for a specified amount of unmeasured confounding. As an additional bonus, the Cox proportional hazards MSM is robust against bias from differential loss to follow-up. As an illustration, the Cox proportional hazards MSM was applied in a reanalysis of the association between smoking and depression in a population-based cohort of Norwegian adults. The association was moderately sensitive for unmeasured confounding.     

The Topology of Central Counterparty Clearing Networks and Network Stability

□ This paper derives a measure of central counterparty (CCP) clearing-network risk that is based on the probability that the maximum exposure (the N-th order statistic) of a CCP to an individual general clearing member is large. Our analytical derivation of this probability uses the theory of Laplace asymptotics, which is related to the large deviations theory of rare events. The theory of Laplace asymptotics is an area of applied probability that studies the exponential decay rate of certain probabilities and is often used in the analysis of the tails of probability distributions. We show that the maximum-exposure probability depends on the topology, or structure, of the clearing network. We also derive a CCP's Maximum-Exposure-at-Risk, which provides a metric for evaluating the adequacy of the CCP's and general clearing members’ loss-absorbing financial resources during rare but plausible market conditions. Based on our analysis, we provide insight into how clearing-network structure can affect the maximum-exposure risk of a CCP and, thereby, network stability. We show that the rate function (the exponential decay rate) of the maximum-exposure probability is informative and can be used to compare the relative maximum-exposure risks across different network configurations.     

Bivariate zero-inflated negative binomial regression model with applications

Count data often display excessive number of zero outcomes than are expected in the Poisson regression model. The zero-inflated Poisson regression model has been suggested to handle zero-inflated data, whereas the zero-inflated negative binomial (ZINB) regression model has been fitted for zero-inflated data with additional overdispersion. For bivariate and zero-inflated cases, several regression models such as the bivariate zero-inflated Poisson (BZIP) and bivariate zero-inflated negative binomial (BZINB) have been considered. This paper introduces several forms of nested BZINB regression model which can be fitted to bivariate and zero-inflated count data. The mean–variance approach is used for comparing the BZIP and our forms of BZINB regression model in this study. A similar approach was also used by past researchers for defining several negative binomial and zero-inflated negative binomial regression models based on the appearance of linear and quadratic terms of the variance function. The nested BZINB regression models proposed in this study have several advantages; the likelihood ratio tests can be performed for choosing the best model, the models have flexible forms of marginal mean–variance relationship, the models can be fitted to bivariate zero-inflated count data with positive or negative correlations, and the models allow additional overdispersion of the two dependent variables.     

The Sensitivity of Detrended Long-Memory Processes

Long-memory tests are often complicated by the presence of deterministic trends. Hence, an additional step of detrending the data is necessary. The typical way to detrend a suspected long-memory series is to use OLS or BSP residuals. Applying the method of sensitivity analysis we address the of question of how robust these residuals are in presence of potential long memory components. Unlike short-memory ARMA process long-memory I(d) processes causes sensitivity to OLS/BSP residuals. Therefore, we develop a finite sample measure of the sensitivity of a detrended series based on the residuals. Based on our sensitivity measure we propose a “rule of thumb” for practitioners to choose between the two methods of detrending, has been provided in this article.