Censored Observations Research Articles

Statistical Issues on Analysis of Censored Data Due to Detection Limit

Measures of substance concentration in urine, serum or other biological matrices often have an assay limit of detection. When concentration levels fall below the limit, the exact measures cannot be obtained, and thus are left censored. Common practice for addressing the censoring issue is to delete or 'fill-in' the censored observations in data analysis, which often results in biased or non-efficient estimates. Assuming the concentration or transformed concentration follows a normal distribution, a Tobit regression model can be applied. When the study population is heterogeneous, for example due to the existence of a latent group of subjects who lack the substance, the problem becomes more challenging. In this paper, we conduct intensive simulation studies to investigate the statistical issues in analyzing censored data and compare different methods in which the data are treated either as a dependent variable or an independent variable. We also analyze triclosan data in the NHANES study and metabolites data in the Bogalusa Heart Study to illustrate the issues. Some guidelines for analyzing such censored data are provided.

On Efficient Monitoring of Weibull Lifetimes Using Censored Median Hybrid DEWMA Chart

A control chart named as the hybrid double exponentially weighted moving average (HDEWMA) to monitor the mean of Weibull distribution in the presence of type-I censored data is proposed in this study. In particular, the focus of this study is to use the conditional median (CM) for the imputation of censored observations. The control chart performance is assessed by the average run length (ARL). A comparison between CM-DEWMA control chart and CM-based HDEWMA control chart is also presented in this article. Assuming different shift sizes and censoring rates, it is observed that the proposed control chart outperforms the CM-DEWMA chart. The effect of estimation, particularly the scale parameter estimation, on ARL is also a part of this study. Finally, a practical example is provided to understand the application and to investigate the performance of the proposal in practical scenarios.

Mixtures of factor analyzers with covariates for modeling multiply censored dependent variables

Censored data arise frequently in diverse applications in which observations to be measured may be subject to some upper and lower detection limits due to the restriction of experimental apparatus such that they are not exactly quantifiable. Mixtures of factor analyzers with censored data (MFAC) have been recently proposed for model-based density estimation and clustering of high-dimensional data in the presence of censored observations. In this paper, we consider an extended version of MFAC by considering regression equations to describe the relationship between covariates and multiply censored dependent variables. Two analytically feasible EM-type algorithms are developed for computing maximum likelihood estimates of model parameters with closed-form expressions. Moreover, we provide an information-based method to compute asymptotic standard errors of mixing proportions and regression coefficients. The utility and performance of our proposed methodology are illustrated through a simulation study and two real data examples.

Inference for Kumaraswamy Distribution Based on Type I Progressive Hybrid Censoring

In this paper, we investigate the estimation problems of unknown parameters of the Kumaraswamy distribution under type I progressive hybrid censoring. This censoring scheme is a combination of progressive type I and hybrid censoring schemes. We derive the maximum likelihood estimates of parameters using an expectation-maximization algorithm. Bayes estimates are obtained under different loss functions using the Lindley method and importance sampling procedure. The highest posterior density intervals of unknown parameters are constructed as well. We also obtain prediction estimates and prediction intervals for censored observations. A Monte Carlo simulation study is performed to compare proposed methods and one real data set is analyzed for illustrative purposes.

Enhancing SVM for survival data using local invariances and weighting

BackgroundThe necessity to analyze medium-throughput data in epidemiological studies with small sample size, particularly when studying biomedical data may hinder the use of classical statistical methods. Support vector machines (SVM) models can be successfully applied in this setting because they are a powerful tool to analyze data with large number of predictors and limited sample size, especially when handling binary outcomes. However, biomedical research often involves analysis of time-to-event outcomes and has to account for censoring. Methods to handle censored data in the SVM framework can be divided into two classes: those based on support vector regression (SVR) and those based on binary classification. Methods based on SVR seem to be suboptimal to handle sparse data and yield results comparable to Cox proportional hazards model and kernel Cox regression. The limited work dedicated to assess methods based on of SVM for binary classification has been based on SVM learning using privileged information and SVM with uncertain classes.ResultsThis paper proposes alternative methods and extensions within the binary classification framework, specifically, a conditional survival approach for weighting censored observations and a semi-supervised SVM with local invariances. Using simulation studies and some real datasets, we evaluate those two methods and compare them with a weighted SVM model, SVM extensions found in the literature, kernel Cox regression and Cox model.ConclusionsOur proposed methods perform generally better under a wide variety of realistic scenarios about the structure of biomedical data. Specifically, the local invariances method using the conditional survival approach is the most robust method under different scenarios and is a good approach to consider as an alternative to other time-to-event methods. When analysing real data is a method to be considered and recommended since outperforms other methods in proportional and non-proportional scenarios and sparse data, which is something usual in biomedical data and biomarkers analysis.

Coagulation factor activity patterns of venom-induced consumption coagulopathy in naturally occurring tiger snake (Notechis scutatus) envenomed dogs treated with antivenom

BackgroundVenom-induced consumption coagulopathy (VICC) from tiger snake (Notechis scutatus) envenomation results in a dose-dependent coagulopathy that is detectable on coagulometry. However, individual coagulation factor activities in dogs with tiger snake envenomation have not been determined. This study aimed to characterise VICC and the time course of recovery in tiger snake envenomed dogs and to investigate an association between tiger snake venom (TSV) concentrations and factor activity. MethodsThis was a prospective, observational, cohort study. The study cohort was 11 dogs of any age, breed, sex, body weight >10 kg, confirmed serum TSV on ELISA and treated with antivenom. Blood was collected at enrolment before antivenom administration, then at 3, 12 and 24 h after antivenom administration. Tiger snake venom concentrations were detected with a sandwich ELISA. Fibrinogen was measured using a modified Clauss method, and coagulation factors (F) II, V, VII, VIII and X were measured with factor-deficient human plasma using a modified prothrombin (PT) and activated partial thromboplastin (aPTT) method. Linear mixed models, with multiple imputations of censored observations, were used to determine the effect of time and TSV concentration on the coagulation times and factor activity. This cohort was compared to 20 healthy controls. ResultsAt enrolment, there were severe deficiencies in fibrinogen, FV and FVIII, with predicted recovery by 10.86, 11.75 and 13.14 h after antivenom, respectively. There were modest deficiencies in FX and FII, with predicted recovery by 20.57 and 32.49 h after antivenom, respectively. No changes were detected in FVII. Prothrombin time and aPTT were markedly prolonged with predicted recovery of aPTT by 12.58 h. Higher serum TSV concentrations were associated with greater deficiencies in FII, FV and FVIII, and greater prolongations in coagulation times. The median (range) serum TSV concentration was 57 (6–2295) ng/mL. ConclusionsIn tiger snake envenomed dogs, we detected a profound, TSV-concentration-related consumption of select coagulation factors, that rapidly recovered toward normal. These findings allowed further insight into tiger snake VICC in dogs.

Variational Learning of Individual Survival Distributions.

The abundance of modern health data provides many opportunities for the use of machine learning techniques to build better statistical models to improve clinical decision making. Predicting time-to-event distributions, also known as survival analysis, plays a key role in many clinical applications. We introduce a variational time-to-event prediction model, named Variational Survival Inference (VSI), which builds upon recent advances in distribution learning techniques and deep neural networks. VSI addresses the challenges of non-parametric distribution estimation by (i) relaxing the restrictive modeling assumptions made in classical models, and (ii) efficiently handling the censored observations, i.e., events that occur outside the observation window, all within the variational framework. To validate the effectiveness of our approach, an extensive set of experiments on both synthetic and real-world datasets is carried out, showing improved performance relative to competing solutions.

PD17-09 PROSPECTIVE RANDOMIZED TRIAL OF PARTIAL GLAND ABLATION WITH VASCULAR-TARGETED PHOTOTHERAPY VERSUS ACTIVE SURVEILLANCE FOR LOW RISK PROSTATE CANCER: 5 YEAR RESULTS

You have accessJournal of UrologyProstate Cancer: Localized: Ablative Therapy I (PD17)1 Apr 2020PD17-09 PROSPECTIVE RANDOMIZED TRIAL OF PARTIAL GLAND ABLATION WITH VASCULAR-TARGETED PHOTOTHERAPY VERSUS ACTIVE SURVEILLANCE FOR LOW RISK PROSTATE CANCER: 5 YEAR RESULTS Inderbir Gill*, Peter Scardino, Andre Luis Abreu, and Rahmene Azzouzi Inderbir Gill*Inderbir Gill* More articles by this author , Peter ScardinoPeter Scardino More articles by this author , Andre Luis AbreuAndre Luis Abreu More articles by this author , and Rahmene AzzouziRahmene Azzouzi More articles by this author View All Author Informationhttps://doi.org/10.1097/JU.0000000000000860.09AboutPDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareFacebookLinked InTwitterEmail Abstract INTRODUCTION AND OBJECTIVE: PCM301 randomized 413 men with low risk prostate cancer (PCa) with ≤3 positive cores, 3-5mm max cancer core length (CCL), to partial gland ablation (PGA) with vascular-targeted photodynamic therapy (VTP: n=207) or active surveillance (AS: n=206) and followed them for 2 years. We report 5 year rates of conversion to radical therapy (RT) in each arm and for those with histologic disease progression (DP) prior to RT from PCM301, an extension study. METHODS: PCM301 subjects who did not withdraw consent were eligible for PCM301 5FU, which followed men for an additional 5 years. DP was defined as any of the following: >3 cores positive; any Gleason Grade Group ≥ 2 cancer; any CCL >5 mm; PSA>10 ng/mL on 3 consecutive occasions; any cT3; metastasis; or PCa related death, whichever came first. The absolute risk reductions for VTP vs. AS were computed by Kaplan-Meier analysis and a Cox proportional hazards model with a two-sided, unstratified log-rank test, including treatment effect, was performed to give a hazard ratio (HR) for conversion to RT in the VTP vs AS arms. RESULTS: Data were available for 318 subjects at month (M) 36, 301 at M 48, and 270 at M 60; VTP: 141 (68%) and AS: 129 (62%). The figures show the intent to treat analysis of rates of conversion to RT for (A) all subjects and (B) only those with DP prior to RT. Overall, 142 patients converted to RT: VTP: 50 (24%), AS: 92 (44%). The median time to RT was not reached in either arm due to the high proportion of censored observations. The absolute risk reduction for conversion to RT for VTP vs. AS remained stable from M 24 (25%) through M 36 (27%), M 48 (25%), and M 60 (24%). The HR for RT after VTP vs AS was 0.41 (95% CI, 0.29-0.58; p<0.0001). RT following DP was reported in 105 subjects: VTP: 39 (19%), AS: 66 (32%). The median time to initiation of RT after DP was not reached. The absolute risk reduction remained stable: 19%, 20%, 20% and 19% at M 24, M 36, M 48 and M 60, respectively. The HR for RT following DP for VTP vs. AS was 0.44 (95% CI, 0.30-0.66; p<0.001). CONCLUSIONS: Avoiding RT with its attendant morbidity is the major clinical benefit of VTP PGA for men with low risk PCa. Compared to AS, VTP significantly and durably reduced RT conversion for all subjects and those with objective DP. Source of Funding: Steba Biotech © 2020 by American Urological Association Education and Research, Inc.FiguresReferencesRelatedDetails Volume 203Issue Supplement 4April 2020Page: e372-e373 Advertisement Copyright & Permissions© 2020 by American Urological Association Education and Research, Inc.MetricsAuthor Information Inderbir Gill* More articles by this author Peter Scardino More articles by this author Andre Luis Abreu More articles by this author Rahmene Azzouzi More articles by this author Expand All Advertisement PDF downloadLoading ...

K-sample omnibus non-proportional hazards tests based on right-censored data.

This work presents novel and powerful tests for comparing non-proportional hazard functions, based on sample-space partitions. Right censoring introduces two major difficulties, which make the existing sample-space partition tests for uncensored data non-applicable: (i) the actual event times of censored observations are unknown and (ii) the standard permutation procedure is invalid in case the censoring distributions of the groups are unequal. We overcome these two obstacles, introduce invariant tests, and prove their consistency. Extensive simulations reveal that under non-proportional alternatives, the proposed tests are often of higher power compared with existing popular tests for non-proportional hazards. Efficient implementation of our tests is available in the R package KONPsurv, which can be freely downloaded from CRAN.

EVALUATION OF UNCONSTRAINING METHODS IN AIRLINES’ REVENUE MANAGEMENT SYSTEMS

Airline revenue management systems are used to calculate booking limits on each fare class to maximize expected revenue for all future flight departures. Their performance depends critically on the forecasting module that uses historical data to project future quantities of demand. Those data are censored or constrained by the imposed booking limits and do not represent true demand since rejected requests are not recorded. Eight unconstraining methods that transform the censored data into more accurate estimates of actual historical demand ranging from naive methods such as discarding all censored observation, to complex, such as Expectation Maximization Algorithm and Projection Detruncation Algorithm, are analyzed and their accuracy is compared. Those methods are evaluated and tested on simulated data sets generated by ICE V2.0 software: first, the data sets that represent true demand were produced, then the aircraft capacity was reduced and EMSRb booking limits for every booking class were calculated. These limits constrained the original demand data at various points of the booking process and the corresponding censored data sets were obtained. The unconstrained methods were applied to the censored observations and the resulting unconstrained data were compared to the actual demand data and their performance was evaluated.

Estimation and Prediction for the Generalized Half Normal Distribution under Hybrid Censoring

Abstract In this article, we make estimation and prediction inferences for the generalized half normal distribution. The maximum likelihood and Bayes estimators of unknown parameters are obtained based on hybrid Type I censored samples. We obtain asymptotic intervals using the observed Fisher information matrix and also construct bootstrap intervals of unknown parameters. Bayes estimators are obtained under the squared error loss function using different approximation methods. We also construct the highest posterior density intervals of unknown parameters. Further one- and two-sample predictors and prediction intervals of censored observations are discussed. A Monte Carlo simulation study is conducted to compare the performance of the proposed methods. We further analyze a real data set for illustrative purposes. Finally, conclusions are presented.

Satisfaction and Tourism Expenditure Behaviour

In the literature, the quantification of the effect of satisfaction on tourists’ expenditure behaviour has not been extensively studied. This research aims to fill in this gap, providing additional information about this crucial relation by analysing it from a microdata perspective. In particular, the Fuzzy Double-Hurdle model, a new model which combines the well-known Double-Hurdle model and the fuzzy set theory, is suggested and presented, both technically and by means of a real case study. The proposed model gathers the advantages of the Double-Hurdle model and the fuzzy set theory together producing a suitable model for the analysis of censored observations in presence of imprecise data. Specifically, the Double-Hurdle model allows to efficiently estimate the average values of a non-negative, non-normally distributed variable characterised by high frequency of zero values, as tourists’ expenditure can be, considering the two-stages nature of the decision process. On the other end, the inclusion of the fuzzy set theory in the regression model allows to cope with the imprecision of both collected information (i.e. levels of satisfaction) and kind of measurement used (i.e. Liker-type scale). The results will help tourism managers to more accurately evaluate the efficacy of their policies and marketing strategies in enhancing tourists’ satisfaction and, consequently, in increasing the level of spending at the destination.

Supervised Dimension Reduction for Large-Scale "Omics" Data With Censored Survival Outcomes Under Possible Non-Proportional Hazards.

The past two decades have witnessed significant advances in high-throughput "omics" technologies such as genomics, proteomics, metabolomics, transcriptomics and radiomics. These technologies have enabled simultaneous measurement of the expression levels of tens of thousands of features from individual patient samples and have generated enormous amounts of data that require analysis and interpretation. One specific area of interest has been in studying the relationship between these features and patient outcomes, such as overall and recurrence-free survival, with the goal of developing a predictive "omics" profile. Large-scale studies often suffer from the presence of a large fraction of censored observations and potential time-varying effects of features, and methods for handling them have been lacking. In this paper, we propose supervised methods for feature selection and survival prediction that simultaneously deal with both issues. Our approach utilizes continuum power regression (CPR) - a framework that includes a variety of regression methods - in conjunction with the parametric or semi-parametric accelerated failure time (AFT) model. Both CPR and AFT fall within the linear models framework and, unlike black-box models, the proposed prognostic index has a simple yet useful interpretation. We demonstrate the utility of our methods using simulated and publicly available cancer genomics data.

Forecasting with a Panel Tobit Model

We use a dynamic panel Tobit model with heteroskedasticity to generate point, set, and density forecasts for a large cross-section of short time series of censored observations. Our fully Bayesian approach allows us to flexibly estimate the cross-sectional distribution of heterogeneous coefficients and then implicitly use this distribution as prior to construct Bayes forecasts for the individual time series. We construct set forecasts that explicitly target the average coverage probability for the cross-section. We present a novel application in which we forecast bank-level charge-off rates for credit card and residential real estate loans, comparing various versions of the panel Tobit model.

Combined tail estimation using censored data and expert information

We study tail estimation in Pareto-like settings for datasets with a high percentage of randomly right-censored data, and where some expert information on the tail index is available for the censored observations. This setting arises for instance naturally for liability insurance claims, where actuarial experts build reserves based on the specificity of each open claim, which can be used to improve the estimation based on the already available data points from closed claims. Through an entropy-perturbed likelihood, we derive an explicit estimator and establish a close analogy with Bayesian methods. Embedded in an extreme value approach, asymptotic normality of the estimator is shown, and when the expert is clair-voyant, a simple combination formula can be deduced, bridging the classical statistical approach with the expert information. Following the aforementioned combination formula, a combination of quantile estimators can be naturally defined. In a simulation study, the estimator is shown to often outperform the Hill estimator for censored observations and recent Bayesian solutions, some of which require more information than usually available. Finally we perform a case study on a motor third-party liability insurance claim dataset, where Hill-type and quantile plots incorporate ultimate values into the estimation procedure in an intuitive manner.

Statistical tests for latent class in censored data due to detection limit.

Measures of substance concentration in urine, serum or other biological matrices often have an assay limit of detection. When concentration levels fall below the limit, the exact measures cannot be obtained. Instead, the measures are censored as only partial information that the levels are under the limit is known. Assuming the concentration levels are from a single population with a normal distribution or follow a normal distribution after some transformation, Tobit regression models, or censored normal regression models, are the standard approach for analyzing such data. However, in practice, it is often the case that the data can exhibit more censored observations than what would be expected under the Tobit regression models. One common cause is the heterogeneity of the study population, caused by the existence of a latent group of subjects who lack the substance measured. For such subjects, the measurements will always be under the limit. If a censored normal regression model is appropriate for modeling the subjects with the substance, the whole population follows a mixture of a censored normal regression model and a degenerate distribution of the latent class. While there are some studies on such mixture models, a fundamental question about testing whether such mixture modeling is necessary, i.e. whether such a latent class exists, has not been studied yet. In this paper, three tests including Wald test, likelihood ratio test and score test are developed for testing the existence of such latent class. Simulation studies are conducted to evaluate the performance of the tests, and two real data examples are employed to illustrate the tests.

Time-to-event estimation by re-defining time.

The primary goal of a time-to-event estimation model is to accurately infer the occurrence time of a target event. Most existing studies focus on developing new models to effectively utilize the information in the censored observations. In this paper, we propose a model to tackle the time-to-event estimation problem from a completely different perspective. Our model relaxes a fundamental constraint that the target variable, time, is a univariate number which satisfies a partial order. Instead, the proposed model interprets each event occurrence time as a time concept with a vector representation. We hypothesize that the model will be more accurate and interpretable by capturing (1) the relationships between features and time concept vectors and (2) the relationships among time concept vectors. We also propose a scalable framework to simultaneously learn the model parameters and time concept vectors. Rigorous experiments and analysis have been conducted in medical event prediction task on seven gene expression datasets. The results demonstrate the efficiency and effectiveness of the proposed model. Furthermore, similarity information among time concept vectors helped in identifying time regimes, thus leading to a potential knowledge discovery related to the human cancer considered in our experiments.

Human Lumbar Spine Responses from Vertical Loading: Ranking of Forces Via Brier Score Metrics and Injury Risk Curves.

This study was conducted to quantify the human tolerance from inferior to superior impacts to whole lumbar spinal columns excised from 43 post mortem human subjects. The specimens were fixed at the ends, aligned in a consistent seated posture, load cells were attached to the proximal and distal ends of the fixation, and the impact was applied using a custom accelerator device. Pretest X-rays and computed tomography (CT) scans, prepositioned X-rays, and posttest X-rays, CT scans and dissection data were used to identify injuries. Right, left, and interval censoring processes were used for the survival analysis, 16 were right censored, 24 were interval censored, and three were left censored observations. Force-based injury risk curves were developed, and the optimal metric describing the underlying response to injury was identified using the Brier score metric. Material, geometry (disc and body areas), and demographic covariates were included in the analysis. The distal force was found to be optimal metric. The bone mineral density was a significant covariate for distal and proximal forces. Both material and geometrical factors affected the transmitted force in this mode of loading. These quantified data serve as the first set of human lumbar spinal column injury risk curves.

Bayesian estimation of the survival characteristics for Hjorth distribution under progressive type-II censoring

In this paper, the Bayes estimation procedure for the parameters and survival characteristics (survival and hazard functions) of the Hjorth distribution has been proposed with progressively type-II censored data. The Bayes estimators are derived with gamma prior and evaluated under squared error loss function. It is known that the censored observations create the complexity in Bayes estimation procedures. Therefore, two approximation techniques, namely Tierney–Kadane approximation method and Markov Chain Monte Carlo method have been used to compute the approximate Bayes estimators. The proposed estimates are compared with the usual maximum likelihood estimators through Monte Carlo simulations. Lastly, a medical data set has been considered to show the applicability of the proposed model as well study in real life scenario.

Estimating Outcome-Exposure Associations when Exposure Biomarker Detection Limits vary Across Batches.

Limit of detection (LOD) issues are ubiquitous in exposure assessment. Although there is an extensive literature on modeling exposure data under such imperfect measurement processes, including likelihood-based methods and multiple imputation, the standard practice continues to be naïve single imputation by a constant (e.g., (Equation is included in full-text article.)). In this article, we consider the situation where, due to the practical logistics of data accrual, sampling, and resource constraints, exposure data are analyzed in multiple batches where the LOD and the proportion of censored observations differ across batches. Compounding this problem is the potential for nonrandom assignment of samples to each batch, often driven by enrollment patterns and biosample storage. This issue is particularly important for binary outcome data where batches may have different levels of outcome enrichment. We first consider variants of existing methods to address varying LODs across multiple batches. We then propose a likelihood-based multiple imputation strategy to impute observations that are below the LOD while simultaneously accounting for differential batch assignment. Our simulation study shows that our proposed method has superior estimation properties (i.e., bias, coverage, statistical efficiency) compared to standard alternatives, provided that distributional assumptions are satisfied. Additionally, in most batch assignment configurations, complete-case analysis can be made unbiased by including batch indicator terms in the analysis model, although this strategy is less efficient relative to the proposed method. We illustrate our method by analyzing data from a cohort study in Puerto Rico that is investigating the relation between endocrine disruptor exposures and preterm birth.