Presence Of Censoring Research Articles

An integrated quantitative systems pharmacology virtual population approach for calibration with oncology efficacy endpoints.

In drug development, quantitative systems pharmacology (QSP) models are becoming an increasingly important mathematical tool for understanding response variability and for generating predictions to inform development decisions. Virtual populations are essential for sampling uncertainty and potential variability in QSP model predictions, but many clinical efficacy endpoints can be difficult to capture with QSP models that typically rely on mechanistic biomarkers. In oncology, challenges are particularly significant when connecting tumor size with time-to-event endpoints like progression-free survival while also accounting for censoring due to consent withdrawal, loss in follow-up, or safety criteria. Here, we expand on our prior work and propose an extended virtual population selection algorithm that can jointly match tumor burden dynamics and progression-free survival times in the presence of censoring. We illustrate the core components of our algorithm through simulation and calibration of a signaling pathway model that was fitted to clinical data for a small molecule targeted inhibitor. This methodology provides an approach that can be tailored to other virtual population simulations aiming to match survival endpoints for solid-tumor clinical datasets.

The local to unity dynamic Tobit model

This paper considers highly persistent time series that are subject to nonlinearities in the form of censoring or an occasionally binding constraint, such as are regularly encountered in macroeconomics. A tractable candidate model for such series is the dynamic Tobit with a root local to unity. We show that this model generates a process that converges weakly to a non-standard limiting process, that is constrained (regulated) to be positive. Surprisingly, despite the presence of censoring, the OLS estimators of the model parameters are consistent. We show that this allows OLS-based inferences to be drawn on the overall persistence of the process (as measured by the sum of the autoregressive coefficients), and for the null of a unit root to be tested in the presence of censoring. Our simulations illustrate that the conventional ADF test substantially over-rejects when the data is generated by a dynamic Tobit with a unit root, whereas our proposed test is correctly sized. We provide an application of our methods to testing for a unit root in the Swiss franc/euro exchange rate, during a period when this was subject to an occasionally binding lower bound.

Regression models for average hazard.

Limitations of using the traditional Cox's hazard ratio for summarizing the magnitude of the treatment effect on time-to-event outcomes have been widely discussed, and alternative measures that do not have such limitations are gaining attention. One of the alternative methods recently proposed, in a simple 2-sample comparison setting, uses the average hazard with survival weight (AH), which can be interpreted as the general censoring-free person-time incidence rate on a given time window. In this paper, we propose a new regression analysis approach for the AH with a truncation time τ. We investigate 3 versions of AH regression analysis, assuming (1) independent censoring, (2) group-specific censoring, and (3) covariate-dependent censoring. The proposed AH regression methods are closely related to robust Poisson regression. While the new approach needs to require a truncation time τ explicitly, it can be more robust than Poisson regression in the presence of censoring. With the AH regression approach, one can summarize the between-group treatment difference in both absolute difference and relative terms, adjusting for covariates that are associated with the outcome. This property will increase the likelihood that the treatment effect magnitude is correctly interpreted. The AH regression approach can be a useful alternative to the traditional Cox's hazard ratio approach for estimating and reporting the magnitude of the treatment effect on time-to-event outcomes.

CTIVA: Censored time interval variable analysis.

Traditionally, datasets with multiple censored time-to-events have not been utilized in multivariate analysis because of their high level of complexity. In this paper, we propose the Censored Time Interval Analysis (CTIVA) method to address this issue. It estimates the joint probability distribution of actual event times in the censored dataset by implementing a statistical probability density estimation technique on the dataset. Based on the acquired event time, CTIVA investigates variables correlated with the interval time of events via statistical tests. The proposed method handles both categorical and continuous variables simultaneously-thus, it is suitable for application on real-world censored time-to-event datasets, which include both categorical and continuous variables. CTIVA outperforms traditional censored time-to-event data handling methods by 5% on simulation data. The average area under the curve (AUC) of the proposed method on the simulation dataset exceeds 0.9 under various conditions. Further, CTIVA yields novel results on National Sample Cohort Demo (NSCD) and proteasome inhibitor bortezomib dataset, a real-world censored time-to-event dataset of medical history of beneficiaries provided by the National Health Insurance Sharing Service (NHISS) and National Center for Biotechnology Information (NCBI). We believe that the development of CTIVA is a milestone in the investigation of variables correlated with interval time of events in presence of censoring.

Evaluating Model Specification When Using the Parametric G-Formula in the Presence of Censoring.

The noniterative conditional expectation (NICE) parametric g-formula can be used to estimate the causal effect of sustained treatment strategies. In addition to identifiability conditions, the validity of the NICE parametric g-formula generally requires the correct specification of models for time-varying outcomes, treatments, and confounders at each follow-up time point. An informal approach for evaluating model specification is to compare the observed distributions of the outcome, treatments, and confounders with their parametric g-formula estimates under the "natural course." In the presence of loss to follow-up, however, the observed and natural-course risks can differ even if the identifiability conditions of the parametric g-formula hold and there is no model misspecification. Here, we describe 2 approaches for evaluating model specification when using the parametric g-formula in the presence of censoring: 1) comparing factual risks estimated by the g-formula with nonparametric Kaplan-Meier estimates and 2) comparing natural-course risks estimated by inverse probability weighting with those estimated by the g-formula. We also describe how to correctly compute natural-course estimates of time-varying covariate means when using a computationally efficient g-formula algorithm. We evaluate the proposed methods via simulation and implement them to estimate the effects of dietary interventions in 2 cohort studies.

On Beta Exponentiated Lomax-Exponential Distribution with applications

This study introduces a new Beta Exponentiated Lomax-Exponential Distribution (BELED) with special reference to its quantile function to enhance closed form solution of its parameters and make its proprietorial effect on data modeling quantifiable with exactness. The obtained BELED which accommodates heavy and light data, either skewed or not, addressed the challenges of intractable parameter estimation in previous related distributions from same family. The BELED properties which includes rth moments, characteristics function, Renyi and Shanon entropy, reliability measures as well as stress-strength model were derived. The estimator (β^) of the exponentiated parameter (β) from an in-built function was obtained in closed form at the modal point in the absence and presence of censoring. Pivot-quantile regression was used to determine the estimate of the scale (σ^) and shape α^ parameters, while the remaining beta generator induced shape parameters (a,b) were derived using maximization techniques via the constrain β^. The quantile function of BELED which averaged out the additive and multiplicative variation in a univariate data set, can be used in modeling the behavioural pattern of both discrete and continuous data.

Estimating distribution of length of stay in a multi-state model conditional on the pathway, with an application to patients hospitalised with Covid-19.

Multi-state models are used to describe how individuals transition through different states over time. The distribution of the time spent in different states, referred to as 'length of stay', is often of interest. Methods for estimating expected length of stay in a given state are well established. The focus of this paper is on the distribution of the time spent in different states conditional on the complete pathway taken through the states, which we call 'conditional length of stay'. This work is motivated by questions about length of stay in hospital wards and intensive care units among patients hospitalised due to Covid-19. Conditional length of stay estimates are useful as a way of summarising individuals' transitions through the multi-state model, and also as inputs to mathematical models used in planning hospital capacity requirements. We describe non-parametric methods for estimating conditional length of stay distributions in a multi-state model in the presence of censoring, including conditional expected length of stay (CELOS). Methods are described for an illness-death model and then for the more complex motivating example. The methods are assessed using a simulation study and shown to give unbiased estimates of CELOS, whereas naive estimates of CELOS based on empirical averages are biased in the presence of censoring. The methods are applied to estimate conditional length of stay distributions for individuals hospitalised due to Covid-19 in the UK, using data on 42,980 individuals hospitalised from March to July 2020 from the COVID19 Clinical Information Network.

Nonparametric bivariate density estimation for censored lifetimes

It is well known that estimation of a bivariate cumulative distribution function of a pair of right censored lifetimes presents challenges unparalleled to the univariate case where a product-limit Kaplan–Meyer’s methodology typically yields optimal estimation, and the literature on optimal estimation of the joint probability density is next to none. The paper, for the first time in the survival analysis literature, develops the theory and methodology of sharp minimax and adaptive nonparametric estimation of the joint density under the mean integrated squared error (MISE) criterion. The theory shows how an underlying joint density, together with the bivariate distribution of censoring variables, affect the estimation, and what and how may or may not be estimated in the presence of censoring. Practical example illustrates the problem.

Statistical Powers of Some Tests for Checking Homogeneity of Survival Distributions with Disjointed Ends in the Presence of Censoring

This paper considered the comparison of some tests for assessing the overall homogeneity of Kaplan-Meier survival curves under low and high censoring rates when the curves are disjointed towards the end. The performances of these tests were measured by their statistical powers. Monte Carlo simulation study was conducted to evaluate and numerically compare the relative performances of Log-rank,Wilcoxon, Tarone-Ware, Peto-Peto, Modified Peto-Peto, the Fleming-Harrington (1,1), and the Babalola-Adeleke tests. The result obtained shows that the Babalola-Adeleke and Fleming-Harrington (1,1) tests have more robust performances than the other five popular tests with relatively high power in detecting differences when the censoring rates in the groups are both low and high. The highest overall average powers under low and high censoring rates were produced by Babalola-Adeleke and Fleming-Harrington (1,1) tests respectively. Hence, these two tests are the most suitable tests for diagnosing homogeneity of survival curves under these conditions.

Estimation of adherence to medication treatment in presence of censoring.

The purpose of this study is to provide a theoretical framework for the analysis of medication adherence based on longitudinal data from electronic medication monitors and to suggest methods for unbiased estimation of the effect of time and covariates on adherence. After defining the statistical summaries involved in adherence analyses and the assumptions necessary for their estimation, we address the issue of bias encountered when adherence is estimated on censored data. We suggest 2 unbiased methods to estimate adherence: (i) indirect combining implementation and persistence; and (ii) based on weights, allowing estimation of the effect of time and covariates on adherence via generalized estimating equations models. We applied the proposed methods to investigate the effect of sex on adherence in a sample of 43 oncology patients followed 1 year. Implementation was higher for men than for women at baseline (98.8 vs. 97.5%, odds ratio [OR] 2.08, 95% confidence interval [CI]: 1.00-4.35), whereas the relationship was reversed at 1 year (94.5 vs. 96.4%, OR 0.65, 95%CI: 0.28-1.52). Adherence declined faster in men, with year-end values of 46.3% for men and 92.2% for women (OR 0.07, 95%CI: 0.02-0.26). Estimation of adherence is a complex statistical issue with longitudinal and duration data, possibly censored, interleaving. This study provides a theoretical framework and suggests methods for unbiased estimation of adherence as a function of time and covariates. This allows the effect of an intervention to be estimated in clinical trials, and helps healthcare providers reframe adherence programmes to address covariates such as sex.

Doubly-robust methods for differences in restricted mean lifetimes using pseudo-observations.

In clinical studies or trials comparing survival times between two treatment groups, the restricted mean lifetime (RML), defined as the expectation of the survival from time 0 to a prespecified time-point, is often the quantity of interest that is readily interpretable to clinicians without any modeling restrictions. It is well known that if the treatments are not randomized (as in observational studies), covariate adjustment is necessary to account for treatment imbalances due to confounding factors. In this article, we propose a simple doubly-robust pseudo-value approach to effectively estimate the difference in the RML between two groups (akin to a metric for estimating average causal effects), while accounting for confounders. The proposed method combines two general approaches: (a) group-specific regression models for the time-to-event and covariate information, and (b) inverse probability of treatment assignment weights, where the RMLs are replaced by the corresponding pseudo-observations for survival outcomes, thereby mitigating the estimation complexities in presence of censoring. The proposed estimator is double-robust, in the sense that it is consistent if at least one of the two working models remains correct. In addition, we explore the potential of available machine learning algorithms in causal inference to reduce possible bias of the causal estimates in presence of a complex association between the survival outcome and covariates. We conduct extensive simulation studies to assess the finite-sample performance of the pseudo-value causal effect estimators. Furthermore, we illustrate our methodology via application to a dataset from a breast cancer cohort study. The proposed method is implementable using the R package drRML, available in GitHub.

Comparison of tree-based methods used in survival data

Abstract Survival trees and forests are popular non-parametric alternatives to parametric and semi-parametric survival models. Conditional inference trees (Ctree) form a non-parametric class of regression trees embedding tree-structured regression models into a well-defined theory of conditional inference procedures. The Ctree is applicable in a varietyof regression-related issues, involving nominal, ordinal, numeric, censored, as well as multivariate response variables and arbitrary measurement scales of covariates. Conditional inference forests (Cforest) consitute a survival forest method which combines a large number of Ctrees. The Cforest provides a unified and flexible framework for ensemble learning in the presence of censoring. The random survival forests (RSF) methodology extends the random forests method enabling the approximation of rich classes of functions while maintaining generalisation errors low. In the present study, the Ctree, Cforest and RSF methods are discussed in detail and the performances of the survival forest methods, namely the Cforest and RSF have been compared with a simulation study. The results of the simulation demonstrate that the RSF method with a log-rank score distinction criteria outperforms the Cforest and the RSF with log-rank distinction criteria.

New classes of tests for the Weibull distribution using Stein's method in the presence of random right censoring.

We develop two new classes of tests for the Weibull distribution based on Stein’s method. The proposed tests are applied in the full sample case as well as in the presence of random right censoring. We investigate the finite sample performance of the new tests using a comprehensive Monte Carlo study. In both the absence and presence of censoring, it is found that the newly proposed classes of tests outperform competing tests against the majority of the distributions considered. In the cases where censoring is present we consider various censoring distributions. Some remarks on the asymptotic properties of the proposed tests are included. We present another result of independent interest; a test initially proposed for use with full samples is amended to allow for testing for the Weibull distribution in the presence of censoring. The techniques developed in the paper are illustrated using two practical examples.

New approaches to parameter estimation with statistical censoring by means of the CEV algorithm: Characterization of its properties for high-performance normal processes

The process of parameter estimation in order to characterize a population using algorithms is in constant development and perfection. Recent years show that data-based decision-making is complex when there is uncertainty generated by statistical censoring. The purpose of this article is to evaluate the effect of statistical censoring on the normal distribution, which is common in many processes. Parameter estimation properties will be characterized with the conditional expected value algorithm, using different censoring percentages and sample sizes. The estimation properties chosen for the study will focus on the monitoring and decision-making related to industrial processes with the presence of censoring.

Quantifying the feasibility of shortening clinical trial duration using surrogate markers.

The potential benefit of using a surrogate marker in place of a long-term primary outcome is very attractive in terms of the impact on study length and cost. Many available methods for quantifying the effectiveness of a surrogate endpoint either rely on strict parametric modeling assumptions or require that the primary outcome and surrogate marker are fully observed that is, not subject to censoring. Moreover, available methods for quantifying surrogacy typically provide a proportion of treatment effect explained (PTE) measure and do not directly address the important questions of whether and how the trial can be ended earlier using the surrogate marker. In this article, we specifically address these important questions by proposing a PTE measure to quantify the feasibility of ending trials early based on endpoint information collected at an earlier landmark point in a time-to-event outcome setting. We provide a framework for deriving an optimally predicted outcome for individual patients at based on a combination of surrogate marker and event time information in the presence of censoring. We propose a non-parametric estimator for the PTE measure and derive the asymptotic properties of our estimators. Finite sample performance of our estimators are illustrated via extensive simulation studies and a real data application examining the potential of hemoglobin A1c and fasting plasma glucose to predict treatment effects on long term diabetes risk based on the Diabetes Prevention Program study.

Characteristic function and Laplace transform‐based tests for exponentiality in the presence of random right censoring

In this paper, the composite hypothesis that lifetimes follow an exponential distribution is tested based on observed randomly right censored data. Testing this hypothesis is complicated by the presence of this censoring, due to the fact that not all lifetimes are observed. To account for this complication, we propose modifications to tests based on the empirical characteristic function and Laplace transform. In the full sample case, these empirical functions can be expressed as integrals with respect to the empirical distribution function of the lifetimes. We propose replacing this estimate of the distribution function by the Kaplan–Meier estimate. The resulting test statistics can be expressed in easily calculable forms in terms of summations of functionals of the observed data. Additionally, a general framework for goodness‐of‐fit testing, in the presence of random right censoring, is outlined. A Monte Carlo study is performed, the results of which indicate that the newly modified tests generally outperform the existing tests. A practical application, concerning initial remission times of leukaemia patients, is discussed along with some concluding remarks and avenues for future research.

Optimal and ethical designs for hypothesis testing in multi-arm exponential trials.

Multi-arm clinical trials are complex experiments which involve several objectives. The demand for unequal allocations in a multi-treatment context is growing and adaptive designs are being increasingly used in several areas of medical research. For uncensored and censored exponential responses, we propose a constrained optimization approach in order to derive the design maximizing the power of the multivariate test of homogeneity, under a suitable ethical constraint. In the absence of censoring, we obtain a very simple closed-form solution that dominates the balanced design in terms of power and ethics. Our suggestion can also accommodate delayed responses and staggered entries, and can be implemented via response adaptive rules. While other targets proposed in the literature could present an unethical behavior, the suggested optimal allocation is frequently unbalanced by assigning more patients to the best treatment, both in the absence and presence of censoring. We evaluate the operating characteristics of our proposal theoretically and by simulations, also redesigning a real lung cancer trial, showing that the constrained optimal target guarantees very good performances in terms of ethical demands, power and estimation precision. Therefore, it is a valid and useful tool in designing clinical trials, especially oncological trials and clinical experiments for grave and novel infectious diseases, where the ethical concern is of primary importance.

Deep Survival Machines: Fully Parametric Survival Regression and Representation Learning for Censored Data With Competing Risks.

We describe a new approach to estimating relative risks in time-to-event prediction problems with censored data in a fully parametric manner. Our approach does not require making strong assumptions of constant proportional hazards of the underlying survival distribution, as required by the Cox-proportional hazard model. By jointly learning deep nonlinear representations of the input covariates, we demonstrate the benefits of our approach when used to estimate survival risks through extensive experimentation on multiple real world datasets with different levels of censoring. We further demonstrate advantages of our model in the competing risks scenario. To the best of our knowledge, this is the first work involving fully parametric estimation of survival times with competing risks in the presence of censoring.

Selection of Appropriate Model for Quality of Life Data of Strabismus Patients Despite Censorship

Introduction: Previous studies on the quality of life of strabismus patients have not examined the existence of censoring to express the relation between the response variable and its predictors. Methods & Materials: The information used in this study is a conducted cross-sectional study in 2012. The sample size is 90 children in the age range (4-18) years and with congenital strabismus. We used the RAND Health Insurance Study questionnaire with ten subscales to evaluate the quality of life, which was increased to 11 dimensions by adding some items related to eye alignment concerns introduced by Archer et al. The demographic profile is also recorded by 13 other questions. We have expressed the relationship between the independent and response variables in each of the 11 dimensions of the questionnaire and the overall quality of life score by fitting the multiple linear regression model. Then we fitted the two models of classic Tobit and CLAD, which are for censoring, to all dimensions of the questionnaire. Results: We showed that in fitting the models to the overall quality of life scale variable, the best model is the multiple linear regression. Because the response variable was normal, and there was no censoring (ceiling and floor effect). However, in the depression subscale, due to the high censoring (28.89% of the ceiling effect) and the almost normal distribution of the response variable (p-value of skewness< 0.05), the appropriate model according to the criteria is the classic Tobit (AIC = 546.33). That is, the classic Tobit model is the best alternative to the multiple linear regression model in the presence of censoring. But these conditions did not exist in all variables. In the subscale, there was a severe censoring performance constraint (67.78% of the ceiling effect). When censoring is high, the distribution of the response variable becomes very skewed, and the distribution of response variables deviates drastically from normal. The distribution of the performance constraint variable was very skewed (p-value <0.001). Here the RMSE standard scale for the classic Tobit model was 28.74, which is much higher than the standard scale for the multiple linear regression model (14.23). The best model for the high censoring was CLAD. Conclusion: To use the appropriate statistical method in the analysis, one must look at how the response variable is distributed. The multiple linear regression model is very widely used, but in the presence of censoring, the use of this model gives skewed results. In this case, the classic Tobit model and its derived model, CLAD, are replaced. The nonparametric CLAD model calculates accurate estimates with minimum defaults and censoring.

Network estimation for censored time-to-event data for multiple events based on multivariate survival analysis.

In general survival analysis, multiple studies have considered a single failure time corresponding to the time to the event of interest or to the occurrence of multiple events under the assumption that each event is independent. However, in real-world events, one event may impact others. Essentially, the potential structure of the occurrence of multiple events can be observed in several survival datasets. The interrelations between the times to the occurrences of events are immensely challenging to analyze because of the presence of censoring. Censoring commonly arises in longitudinal studies in which some events are often not observed for some of the subjects within the duration of research. Although this problem presents the obstacle of distortion caused by censoring, the advanced multivariate survival analysis methods that handle multiple events with censoring make it possible to measure a bivariate probability density function for a pair of events. Considering this improvement, this paper proposes a method called censored network estimation to discover partially correlated relationships and construct the corresponding network composed of edges representing non-zero partial correlations on multiple censored events. To demonstrate its superior performance compared to conventional methods, the selecting power for the partially correlated events was evaluated in two types of networks with iterative simulation experiments. Additionally, the correlation structure was investigated on the electronic health records dataset of the times to the first diagnosis for newborn babies in South Korea. The results show significantly improved performance as compared to edge measurement with competitive methods and reliability in terms of the interrelations of real-life diseases.