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.

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.

Mixture Cure Survival Models with Dependent Censoring

A number of authors have studies the mixture survival model to analyze survival data with nonnegligible cure fractions. A key assumption made by these authors is the independence between the survival time and the censoring time. To our knowledge, no one has studies the mixture cure model in the presence of dependent censoring. To account for such dependence, we propose a more general cure model which allows for dependent censoring. In particular, we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time using a class of Archimedean copula models. Within this framework, we consider the parameter estimation, the cure detection, and the two-sample comparison of latency distribution in the presence of dependent censoring when a proportion of patients is deemed cured. Large sample results using the martingale theory are obtained. We applied the proposed methodologies to the SEER prostate cancer data.

Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.

Analyzing Bivariate Survival Data with Interval Sampling and Application to Cancer Epidemiology

In medical follow-up studies, ordered bivariate survival data are frequently encountered when bivariate failure events are used as the outcomes to identify the progression of a disease. In cancer studies interest could be focused on bivariate failure times, for example, time from birth to cancer onset and time from cancer onset to death. This paper considers a sampling scheme where the first failure event (cancer onset) is identified within a calendar time interval, the time of the initiating event (birth) can be retrospectively confirmed, and the occurrence of the second event (death) is observed sub ject to right censoring. To analyze this type of bivariate failure time data, it is important to recognize the presence of bias arising due to interval sampling. In this paper, nonparametric and semiparametric methods are developed to analyze the bivariate survival data with interval sampling under stationary and semi-stationary conditions. Numerical studies demonstrate the proposed estimating approaches perform well with practical sample sizes in different simulated models. We apply the proposed methods to SEER ovarian cancer registry data for illustration of the methods and theory.

Vascular endothelial growth factors, angiogenesis, and survival in human ileal enterochromaffin cell carcinoids

BACKGROUND AND AIMS: Well-differentiated neuro-endocrine ileal carcinoids are composed of serotonin-producing enterochromaffin (EC) cells. Life expectancy is determined by metastatic spread to the liver because medical treatment options are still very limited. Selective inhibition of angiogenesis or lymphangiogenesis might prevent tumour growth and metastatic spread. We examined the role of the vascular endothelial growth factors (VEGFs) A, B, C, D, and their receptors (VEGFRs) 1, 2, 3 in angiogenesis and lymphangiogenesis of ileal EC cell carcinoids with and without liver metastases. METHODS: The expression of various VEGFs and VEGFRs was determined by quantitative real-time RT-PCR in healthy mucosa, primary tumour, lymph node metastases and liver metastases of 25 patients with ileal EC cell carcinoids. Microvessel density (MVD) was determined by CD-31 staining in primary tumours and lymphatic vessel density (LVD) by LYVE-1 staining. VEGF expression levels, MVD, LVD, and patients' survival time were correlated using logistic regression and Kaplan-Meier survival analysis. RESULTS: VEGF-A was highly expressed with no difference between normal mucosa and tumours. VEGF-B and -D as well as VEGFR-1 and -2 expression levels were significantly increased in the tumours when compared to normal mucosa. Patients with liver metastasis, however, had a significantly lower expression of the factors A, B, and C and the receptors 2 and 3. MVD in primary tumours positively correlated with the expression of VEGF ligands and their receptors, except for VEGF-D. LVD did not correlate with any VEGF ligand or receptor. Interestingly, low expression levels of VEGF-B were associated with poor survival. CONCLUSION: Patients with more aggressive metastatic spreading had relatively decreased expression levels of VEGF ligands and receptors. Thus, anti-angiogenic therapy may not be a suitable target in metastatic ileal EC cell carcinoids.

Survival of bonded lingual retainers with chemical or photo polymerization over a 2-year period: a single-center, randomized controlled clinical trial

INTRODUCTION The objective of this trial was to compare the survival rates of mandibular lingual retainers bonded with either chemically cured or light-cured adhesive after orthodontic treatment. METHODS Patients having undergone orthodontic treatment at a private orthodontic office were randomly allocated to fixed retainers placed with chemically cured composite or light-cured composite. Eligibility criteria included no active caries, restorations, or fractures on the mandibular anterior teeth, and adequate oral hygiene. The main outcome was any type of first-time lingual retainer breakage; pattern of failure (adapted adhesive remnant index scores) was a secondary outcome. Randomization was accomplished with random permuted blocks of 20 patients with allocation concealed in sequentially numbered, opaque, sealed envelopes. Blinding was applicable for outcome assessment only. Patients were reviewed at 1, 3, and 6 months and then every 6 months after placement of the retainer until completion of the study. Data were analyzed using survival analysis including Cox regression; sensitivity analysis was carried out after data imputation for subjects lost to follow-up. RESULTS Two hundred twenty patients (median age, 16 years; interquartile range, 2; range, 12-47 years) were randomized in a 1:1 ratio to either chemical or light curing. Baseline characteristics were similar between groups, the median follow-up period was 2.19 years (range, 0.003-3.64 years), and 16 patients were lost to follow-up. At a minimum follow-up of 2 years, 47 of 110 (42.7%) and 55 of 110 (50.0%) retainers had some type of failure with chemically cured and light-cured adhesive, respectively (log-rank test, P = 0.35). Data were analyzed on an intention-to-treat basis, and the hazard ratio (HR) was 1.15 (95% confidence interval [CI], 0.88-1.70; P = 0.47). There was weak evidence that age is a significant predictor for lingual retainer failures (HR, 0.96; 95% CI, 0.93-1.00; P = 0.08). Adhesive remnant index scoring was possible for only 66 of the 102 (64.7%) failures and did not differ between composites (Fisher exact test, P = 0.16). No serious harm was observed other than gingivitis associated with plaque accumulation. CONCLUSIONS The results of this study indicated no evidence that survival of mandibular lingual retainers differs between chemically and light-cured adhesives. The overall failure rate was 46.4%; however, this included any type of failure, which may have exaggerated the overall failure rate.

SURVIVAL PREDICTION FOR BRAIN TUMOR PATIENTS USING GENE EXPRESSION DATA

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. In order to evaluate this hypothesis, the general goal of this research is to build models for survival prediction of glioma patients using DNA molecular profiles (U133 Affymetrix gene expression microarrays) along with clinical information. First, a predictive Random Forest model is built for binary outcomes (i.e. short vs. long-term survival) and a small subset of genes whose expression values can be used to predict survival time is selected. Following, a new statistical methodology is developed for predicting time-to-death outcomes using Bayesian ensemble trees. Due to a large heterogeneity observed within prognostic classes obtained by the Random Forest model, prediction can be improved by relating time-to-death with gene expression profile directly. We propose a Bayesian ensemble model for survival prediction which is appropriate for high-dimensional data such as gene expression data. Our approach is based on the ensemble "sum-of-trees" model which is flexible to incorporate additive and interaction effects between genes. We specify a fully Bayesian hierarchical approach and illustrate our methodology for the CPH, Weibull, and AFT survival models. We overcome the lack of conjugacy using a latent variable formulation to model the covariate effects which decreases computation time for model fitting. Also, our proposed models provides a model-free way to select important predictive prognostic markers based on controlling false discovery rates. We compare the performance of our methods with baseline reference survival methods and apply our methodology to an unpublished data set of brain tumor survival times and gene expression data, selecting genes potentially related to the development of the disease under study. A closing discussion compares results obtained by Random Forest and Bayesian ensemble methods under the biological/clinical perspectives and highlights the statistical advantages and disadvantages of the new methodology in the context of DNA microarray data analysis.

Long-term survival after multidisciplinary management of resected pancreatic adenocarcinoma.

INTRODUCTION: Actual 5-year survival rates of 10-18% have been reported for patients with resected pancreatic adenocarcinoma (PC), but the use of multimodality therapy was uncommon in these series. We evaluated long-term survival and patterns of recurrence in patients treated for PC with contemporary staging and multimodality therapy. METHODS: We analyzed 329 consecutive patients with PC evaluated between 1990 and 2002 who underwent resection. Each received a multidisciplinary evaluation and a standard operative approach. Pre- or postoperative chemotherapy and/or chemoradiation were routine. Surgical specimens of 5-year survivors were re-reviewed. A multivariate model of factors associated with long-term survival was constructed. RESULTS: Patients underwent pancreaticoduodenectomy (n = 302; 92%), distal (n = 20; 6%), or total pancreatectomy (n = 7; 2%). A total of 108 patients (33%) underwent vascular reconstruction, 301 patients (91%) received neoadjuvant or adjuvant therapy, 157 specimens (48%) were node positive, and margins were microscopically positive in 52 patients (16%). Median overall survival and disease-specific survival was 23.9 and 26.5 months. Eighty-eight patients (27%) survived a minimum of 5 years and had a median overall survival of 11 years. Of these, 21 (24%) experienced recurrence, 7 (8%) after 5 years. Late recurrences occurred most frequently in the lungs, the latest at 6.7 years. Multivariate analysis identified disease-negative lymph nodes (P = .02) and no prior attempt at resection (P = 0.01) as associated with 5-year survival. CONCLUSIONS: Our 27% actual 5-year survival rate for patients with resected PC is superior to that previously reported, and it is influenced by our emphasis on detailed staging and patient selection, a standardized operative approach, and routine use of multimodality therapy.