Inference on Survival Data with Covariate Measurement Error - An Imputation-based Approach

We propose a new method for fitting proportional hazards models with error-prone covariates. Regression coefficients are estimated by solving an estimating equation that is the average of the partial likelihood scores based on imputed true covariates. For the purpose of imputation, a linear spline model is assumed on the baseline hazard. We discuss consistency and asymptotic normality of the resulting estimators, and propose a stochastic approximation scheme to obtain the estimates. The algorithm is easy to implement, and reduces to the ordinary Cox partial likelihood approach when the measurement error has a degenerative distribution. Simulations indicate high efficiency and robustness. We consider the special case where error-prone replicates are available on the unobserved true covariates. As expected, increasing the number of replicate for the unobserved covariates increases efficiency and reduces bias. We illustrate the practical utility of the proposed method with an Eastern Cooperative Oncology Group clinical trial where a genetic marker, c-myc expression level, is subject to measurement error.

Survival Analysis with Large Dimensional Covariates: An Application in Microarray Studies

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time (AFT) model. Assessment of the two methods is conducted through simulation studies and through analysis of microarray data obtained from a set of patients with diffuse large B-cell lymphoma where time to survival is of interest. The approaches are shown to match or exceed the predictive performance of a Cox-based and an AFT-based variable selection method. The methods are moreover shown to be much more computationally efficient than their respective Cox- and AFT- based counterparts.

On Causal Mediation Analysis with a Survival Outcome

Suppose that having established a marginal total effect of a point exposure on a time-to-event outcome, an investigator wishes to decompose this effect into its direct and indirect pathways, also know as natural direct and indirect effects, mediated by a variable known to occur after the exposure and prior to the outcome. This paper proposes a theory of estimation of natural direct and indirect effects in two important semiparametric models for a failure time outcome. The underlying survival model for the marginal total effect and thus for the direct and indirect effects, can either be a marginal structural Cox proportional hazards model, or a marginal structural additive hazards model. The proposed theory delivers new estimators for mediation analysis in each of these models, with appealing robustness properties. Specifically, in order to guarantee ignorability with respect to the exposure and mediator variables, the approach, which is multiply robust, allows the investigator to use several flexible working models to adjust for confounding by a large number of pre-exposure variables. Multiple robustness is appealing because it only requires a subset of working models to be correct for consistency; furthermore, the analyst need not know which subset of working models is in fact correct to report valid inferences. Finally, a novel semiparametric sensitivity analysis technique is developed for each of these models, to assess the impact on inference, of a violation of the assumption of ignorability of the mediator.

On the Accelerated Failure Time Model for Current Status and Interval Censored Data

This paper introduces a novel approach to making inference about the regression parameters in the accelerated failure time (AFT) model for current status and interval censored data. The estimator is constructed by inverting a Wald type test for testing a null proportional hazards model. A numerically efficient Markov chain Monte Carlo (MCMC) based resampling method is proposed to simultaneously obtain the point estimator and a consistent estimator of its variance-covariance matrix. We illustrate our approach with interval censored data sets from two clinical studies. Extensive numerical studies are conducted to evaluate the finite sample performance of the new estimators.

Designed Extension of Survival Studies: Application to Clinical Trials with Unrecognized Heterogeneity

It is well known that unrecognized heterogeneity among patients, such as is conferred by genetic subtype, can undermine the power of randomized trial, designed under the assumption of homogeneity, to detect a truly beneficial treatment. We consider the conditional power approach to allow for recovery of power under unexplained heterogeneity. While Proschan and Hunsberger (1995) confined the application of conditional power design to normally distributed observations, we consider more general and difficult settings in which the data are in the framework of continuous time and are subject to censoring. In particular, we derive a procedure appropriate for the analysis of the weighted log rank test under the assumption of a proportional hazards frailty model. The proposed method is illustrated through application to a brain tumor trial.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.

CA15-3 and alkaline phosphatase as predictors for breast cancer recurrence: a combined analysis of seven International Breast Cancer Study Group trials

BACKGROUND: We evaluated the ability of CA15-3 and alkaline phosphatase (ALP) to predict breast cancer recurrence. PATIENTS AND METHODS: Data from seven International Breast Cancer Study Group trials were combined. The primary end point was relapse-free survival (RFS) (time from randomization to first breast cancer recurrence), and analyses included 3953 patients with one or more CA15-3 and ALP measurement during their RFS period. CA15-3 was considered abnormal if >30 U/ml or >50% higher than the first value recorded; ALP was recorded as normal, abnormal, or equivocal. Cox proportional hazards models with a time-varying indicator for abnormal CA15-3 and/or ALP were utilized. RESULTS: Overall, 784 patients (20%) had a recurrence, before which 274 (35%) had one or more abnormal CA15-3 and 35 (4%) had one or more abnormal ALP. Risk of recurrence increased by 30% for patients with abnormal CA15-3 [hazard ratio (HR) = 1.30; P = 0.0005], and by 4% for those with abnormal ALP (HR = 1.04; P = 0.82). Recurrence risk was greatest for patients with either (HR = 2.40; P < 0.0001) and with both (HR = 4.69; P < 0.0001) biomarkers abnormal. ALP better predicted liver recurrence. CONCLUSIONS: CA15-3 was better able to predict breast cancer recurrence than ALP, but use of both biomarkers together provided a better early indicator of recurrence. Whether routine use of these biomarkers improves overall survival remains an open question.

Predictors of early relapse in postmenopausal women with hormone receptor-positive breast cancer in the BIG 1-98 trial

BACKGROUND: Aromatase inhibitors are considered standard adjuvant endocrine treatment of postmenopausal women with hormone receptor-positive breast cancer, but it remains uncertain whether aromatase inhibitors should be given upfront or sequentially with tamoxifen. Awaiting results from ongoing randomized trials, we examined prognostic factors of an early relapse among patients in the BIG 1-98 trial to aid in treatment choices. PATIENTS AND METHODS: Analyses included all 7707 eligible patients treated on BIG 1-98. The median follow-up was 2 years, and the primary end point was breast cancer relapse. Cox proportional hazards regression was used to identify prognostic factors. RESULTS: Two hundred and eighty-five patients (3.7%) had an early relapse (3.1% on letrozole, 4.4% on tamoxifen). Predictive factors for early relapse were node positivity (P < 0.001), absence of both receptors being positive (P < 0.001), high tumor grade (P < 0.001), HER-2 overexpression/amplification (P < 0.001), large tumor size (P = 0.001), treatment with tamoxifen (P = 0.002), and vascular invasion (P = 0.02). There were no significant interactions between treatment and the covariates, though letrozole appeared to provide a greater than average reduction in the risk of early relapse in patients with many involved lymph nodes, large tumors, and vascular invasion present. CONCLUSION: Upfront letrozole resulted in significantly fewer early relapses than tamoxifen, even after adjusting for significant prognostic factors.

Beneficial effect of recruitable collaterals: a 10-year follow-up study in patients with stable coronary artery disease undergoing quantitative collateral measurements

BACKGROUND: The prognostic relevance of the collateral circulation is still controversial. The goal of this study was to assess the impact on survival of quantitatively obtained, recruitable coronary collateral flow in patients with stable coronary artery disease during 10 years of follow-up. METHODS AND RESULTS: Eight-hundred forty-five individuals (age, 62+/-11 years), 106 patients without coronary artery disease and 739 patients with chronic stable coronary artery disease, underwent a total of 1053 quantitative, coronary pressure-derived collateral measurements between March 1996 and April 2006. All patients were prospectively included in a collateral flow index (CFI) database containing information on recruitable collateral flow parameters obtained during a 1-minute coronary balloon occlusion. CFI was calculated as follows: CFI = (P(occl) - CVP)/(P(ao) - CVP) where P(occl) is mean coronary occlusive pressure, P(ao) is mean aortic pressure, and CVP is central venous pressure. Patients were divided into groups with poorly developed (CFI < 0.25) or well-grown collateral vessels (CFI > or = 0.25). Follow-up information on the occurrence of all-cause mortality and major adverse cardiac events after study inclusion was collected. Cumulative 10-year survival rates in relation to all-cause deaths and cardiac deaths were 71% and 88%, respectively, in patients with low CFI and 89% and 97% in the group with high CFI (P=0.0395, P=0.0109). Through the use of Cox proportional hazards analysis, the following variables independently predicted elevated cardiac mortality: age, low CFI (as a continuous variable), and current smoking. CONCLUSIONS: A well-functioning coronary collateral circulation saves lives in patients with chronic stable coronary artery disease. Depending on the exact amount of collateral flow recruitable during a brief coronary occlusion, long-term cardiac mortality is reduced to one fourth compared with the situation without collateral supply.

Visualization and quantitative analysis of nanoparticles in the respiratory tract by transmission electron microscopy

ABSTRACT: Nanotechnology in its widest sense seeks to exploit the special biophysical and chemical properties of materials at the nanoscale. While the potential technological, diagnostic or therapeutic applications are promising there is a growing body of evidence that the special technological features of nanoparticulate material are associated with biological effects formerly not attributed to the same materials at a larger particle scale. Therefore, studies that address the potential hazards of nanoparticles on biological systems including human health are required. Due to its large surface area the lung is one of the major sites of interaction with inhaled nanoparticles. One of the great challenges of studying particle-lung interactions is the microscopic visualization of nanoparticles within tissues or single cells both in vivo and in vitro. Once a certain type of nanoparticle can be identified unambiguously using microscopic methods it is desirable to quantify the particle distribution within a cell, an organ or the whole organism. Transmission electron microscopy provides an ideal tool to perform qualitative and quantitative analyses of particle-related structural changes of the respiratory tract, to reveal the localization of nanoparticles within tissues and cells and to investigate the 3D nature of nanoparticle-lung interactions.This article provides information on the applicability, advantages and disadvantages of electron microscopic preparation techniques and several advanced transmission electron microscopic methods including conventional, immuno and energy-filtered electron microscopy as well as electron tomography for the visualization of both model nanoparticles (e.g. polystyrene) and technologically relevant nanoparticles (e.g. titanium dioxide). Furthermore, we highlight possibilities to combine light and electron microscopic techniques in a correlative approach. Finally, we demonstrate a formal quantitative, i.e. stereological approach to analyze the distributions of nanoparticles in tissues and cells.This comprehensive article aims to provide a basis for scientists in nanoparticle research to integrate electron microscopic analyses into their study design and to select the appropriate microscopic strategy.