Robust smoothing of left-censored time series data with a dynamic linear model to infer SARS-CoV-2 RNA concentrations in wastewater

Wastewater sampling for the detection and monitoring of SARS-CoV-2 has been developed and applied at an unprecedented pace, however uncertainty remains when interpreting the measured viral RNA signals and their spatiotemporal variation. The proliferation of measurements that are below a quantifiable threshold, usually during non-endemic periods, poses a further challenge to interpretation and time-series analysis of the data. Inspired by research in the use of a custom Kalman smoother model to estimate the true level of SARS-CoV-2 RNA concentrations in wastewater, we propose an alternative left-censored dynamic linear model. Cross-validation of both models alongside a simple moving average, using data from 286 sewage treatment works across England, allows for a comprehensive validation of the proposed approach. The presented dynamic linear model is more parsimonious, has a faster computational time and is represented by a more flexible modelling framework than the equivalent Kalman smoother. Furthermore we show how the use of wastewater data, transformed by such models, correlates more closely with regional case rate positivity as published by the Office for National Statistics (ONS) Coronavirus (COVID-19) Infection Survey. The modelled output is more robust and is therefore capable of better complementing traditional surveillance than untransformed data or a simple moving average, providing additional confidence and utility for public health decision making. © 2023, American Institute of Mathematical Sciences. All rights reserved.

CORONAVIRUS DISEASE SURVIVAL TIME MODEL FOR FORECASTING

The term "survival analysis" refers to statistical techniques for data analysis where the time until the occurrence of the desired event serves as the outcome variable. Time to event analysis is another name for survival analysis. Applications for survival analysis are fairly broad and include things like calculating a population's survival rate or contrasting the survival of two or more groups. Cox regression analysis is a highly well-liked and frequently applied technique among them. Data on disease states are typically obtained at random epochs or at periodic epochs during follow-up in research looking at biological changes between states of Coronavirus infection and the start of COVID-19 in the human immune system. For instance, after the COVID enters a person's bloodstream by a route of transmission, it progresses through numerous stages that are linked to the depletion of B cells before becoming COVID-19. This study presents the Cox's approach for simulating the link between variables influencing the development of two disease states, namely I= the time epoch of COVID infection and P= the time epoch of COVID-19. Incubation period (IP) or survival time is the precise interval of time between "P and I." It is shown how Cox's model works with several personal infective factors and how well it can estimate the percentage of COVID-19 victims with the same completed length of IP. Such forecast values are then established for a synthetically simulated data set. [ FROM AUTHOR] Copyright of Journal of Pharmaceutical Negative Results is the property of ResearchTrentz and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Censored density forecasts: Production and evaluation

This paper develops methods for the production and evaluation of censored density forecasts. The focus is on censored density forecasts that quantify forecast risks in a middle region of the density covering a specified probability and ignore the magnitude but not the frequency of outlying observations. We propose a fixed-point algorithm that fits a potentially skewed and fat-tailed density to the inner observations, acknowledging that the outlying observations may be drawn from a different but unknown distribution. We also introduce a new test for calibration of censored density forecasts. An application using historical forecast errors from the Federal Reserve Board and the Monetary Policy Committee (MPC) at the Bank of England suggests that the use of censored density functions to represent the pattern of forecast errors results in much greater parameter stability than do uncensored densities. We illustrate the utility of censored density forecasts when quantifying forecast risks after shocks such as the global financial crisis and the COVID-19 pandemic and find that these outperform the official forecasts produced by the MPC. © 2023 John Wiley & Sons, Ltd.

Conformalized survival analysis

In this paper, we develop an inferential method based on conformal prediction, which can wrap around any survival prediction algorithm to produce calibrated, covariate-dependent lower predictive bounds on survival times. In the Type I right-censoring setting, when the censoring times are completely exogenous, the lower predictive bounds have guaranteed coverage in finite samples without any assumptions other than that of operating on independent and identically distributed data points. Under a more general conditionally independent censoring assumption, the bounds satisfy a doubly robust property which states the following: marginal coverage is approximately guaranteed if either the censoring mechanism or the conditional survival function is estimated well. The validity and efficiency of our procedure are demonstrated on synthetic data and real COVID-19 data from the UK Biobank. © 2023 Blackwell Publishing Ltd. All rights reserved.

Latency function estimation under the mixture cure model when the cure status is available.

This paper addresses the problem of estimating the conditional survival function of the lifetime of the subjects experiencing the event (latency) in the mixture cure model when the cure status information is partially available. The approach of past work relies on the assumption that long-term survivors are unidentifiable because of right censoring. However, in some cases this assumption is invalid since some subjects are known to be cured, e.g., when a medical test ascertains that a disease has entirely disappeared after treatment. We propose a latency estimator that extends the nonparametric estimator studied in López-Cheda et al. (TEST 26(2):353-376, 2017b) to the case when the cure status is partially available. We establish the asymptotic normality distribution of the estimator, and illustrate its performance in a simulation study. Finally, the estimator is applied to a medical dataset to study the length of hospital stay of COVID-19 patients requiring intensive care.

Optimal analysis of adaptive type-II progressive censored for new unit-lindley model

The parameters, reliability, and hazard rate functions of the Unit-Lindley distribution based on adaptive Type-II progressive censored sample are estimated using both non-Bayesian and Bayesian inference methods in this study. The Newton–Raphson method is used to obtain the maximum likelihood and maximum product of spacing estimators of unknown values in point estimation. On the basis of observable Fisher information data, estimated confidence ranges for unknown parameters and reliability characteristics are created using the delta approach and the frequentist estimators' asymptotic normality approximation. To approximate confidence intervals, two bootstrap approaches are utilized. Using an independent gamma density prior, a Bayesian estimator for the squared-error loss is derived. The Metropolis–Hastings algorithm is proposed to approximate the Bayesian estimates and also to create the associated highest posterior density credible intervals. Extensive Monte Carlo simulation tests are carried out to evaluate the performance of the developed approaches. For selecting the optimum progressive censoring scheme, several optimality criteria are offered. A practical case based on COVID-19 data is used to demonstrate the applicability of the presented methodologies in real-life COVID-19 scenarios. © 2022 The Author(s)

An Expectation-Maximization Algorithm for Including Oncological COVID-19 Deaths in Survival Analysis.

We address the problem of how COVID-19 deaths observed in an oncology clinical trial can be consistently taken into account in typical survival estimates. We refer to oncological patients since there is empirical evidence of strong correlation between COVID-19 and cancer deaths, which implies that COVID-19 deaths cannot be treated simply as non-informative censoring, a property usually required by the classical survival estimators. We consider the problem in the framework of the widely used Kaplan-Meier (KM) estimator. Through a counterfactual approach, an algorithmic method is developed allowing to include COVID-19 deaths in the observed data by mean-imputation. The procedure can be seen in the class of the Expectation-Maximization (EM) algorithms and will be referred to as Covid-Death Mean-Imputation (CoDMI) algorithm. We discuss the CoDMI underlying assumptions and the convergence issue. The algorithm provides a completed lifetime data set, where each Covid-death time is replaced by a point estimate of the corresponding virtual lifetime. This complete data set is naturally equipped with the corresponding KM survival function estimate and all available statistical tools can be applied to these data. However, mean-imputation requires an increased variance of the estimates. We then propose a natural extension of the classical Greenwood's formula, thus obtaining expanded confidence intervals for the survival function estimate. To illustrate how the algorithm works, CoDMI is applied to real medical data extended by the addition of artificial Covid-death observations. The results are compared with the estimates provided by the two naïve approaches which count COVID-19 deaths as censoring or as deaths by the disease under study. In order to evaluate the predictive performances of CoDMI an extensive simulation study is carried out. The results indicate that in the simulated scenarios CoDMI is roughly unbiased and outperforms the estimates obtained by the naïve approaches. A user-friendly version of CoDMI programmed in R is freely available.

Comparing and combining data from immune assays based on left-censored multivariate normal model assuming common assay differences across settings.

In vaccine research towards the prevention of infectious diseases, immune response biomarkers serve as an important tool for comparing and ranking vaccine candidates based on their immunogenicity and predicted protective effect. However, analyses of immune response outcomes can be complicated by differences across assays when immune response data are acquired from multiple groups/laboratories. Motivated by a real-world problem to accommodate the use of two different neutralization assays in COVID-19 vaccine trials, we propose methods based on left-censored multivariate normal model assuming common assay differences across settings, to adjust for differences between assays with respect to measurement error and the lower limit of detection. Our proposed methods integrate external paired-sample data with bridging assumptions to achieve two objectives, both using pooled data acquired from different assays: (i) comparing immunogenicity between vaccine regimens, and (ii) evaluating correlates of risk. In simulation studies, for the first objective, our method leads to unbiased calibrated assay mean with good coverage of bootstrap confidence interval, as well as valid test for immunogenicity comparison, while the alternative method assuming constant calibration model between assays leads to biased estimate of assay mean with undercoverage problem and invalid test with inflated type-I error; for the second objective, in the presence of noticeable left-censoring rate, our proposed method can drastically outperform the existing method that ignores left-censoring, in terms of reduced bias and improved precision. We apply the proposed methods to SARS-CoV-2 spike-pseudotyped virus neutralization assay data generated in vaccine and convalescent samples by two different laboratories.

Informative Censoring-A Cause of Bias in Estimating COVID-19 Mortality Using Hospital Data.

(1) Background: Several retrospective observational analyzed treatment outcomes for COVID-19; (2) Methods: Inverse probability of censoring weighting (IPCW) was applied to correct for bias due to informative censoring in database of hospitalized patients who did and did not receive convalescent plasma; (3) Results: When compared with an IPCW analysis, overall mortality was overestimated using an unadjusted Kaplan-Meier curve, and hazard ratios for the older age group compared to the youngest were underestimated using the Cox proportional hazard models and 30-day mortality; (4) Conclusions: An IPCW analysis provided stabilizing weights by hospital admission.

Optimal Analysis of Adaptive Type-II Progressive Censored for New Unit-Lindley Model

The parameters, reliability, and hazard rate functions of the Unit-Lindley distribution based on adaptive Type-II progressive censored sample are estimated using both non-Bayesian and Bayesian inference methods in this study. The Newton-Raphson method is used to obtain the maximum likelihood and maximum product of spacing estimators of unknown values in point estimation. On the basis of observable Fisher information data, estimated confidence ranges for unknown parameters and reliability characteristics are created using the delta approach and the frequentist estimators’ asymptotic normality approximation. To approximate confidence intervals, two bootstrap approaches are utilized. Using an independent gamma density prior, a Bayesian estimator for the squared-error loss is derived. The Metropolis-Hastings algorithm is proposed to approximate the Bayesian estimates and also to create the associated highest posterior density credible intervals. Extensive Monte Carlo simulation tests are carried out to evaluate the performance of the developed approaches. For selecting the optimum progressive censoring scheme, several optimality criteria are offered. A practical case based on COVID-19 data is used to demonstrate the applicability of the presented methodologies in real-life COVID-19 scenarios.

The case against censoring of progression-free survival in cancer clinical trials - A pandemic shutdown as an illustration.

BACKGROUND: Missing data may lead to loss of statistical power and introduce bias in clinical trials. The Covid-19 pandemic has had a profound impact on patient health care and on the conduct of cancer clinical trials. Although several endpoints may be affected, progression-free survival (PFS) is of major concern, given its frequent use as primary endpoint in advanced cancer and the fact that missed radiographic assessments are to be expected. The recent introduction of the estimand framework creates an opportunity to define more precisely the target of estimation and ensure alignment between the scientific question and the statistical analysis. METHODS: We used simulations to investigate the impact of two basic approaches for handling missing tumor scans due to the pandemic: a "treatment policy" strategy, which consisted in ascribing events to the time they are observed, and a "hypothetical" approach of censoring patients with events during the shutdown period at the last assessment prior to that period. We computed the power of the logrank test, estimated hazard ratios (HR) using Cox models, and estimated median PFS times without and with a hypothetical 6-month shutdown period with no patient enrollment or tumor scans being performed, varying the shutdown starting times. RESULTS: Compared with the results in the absence of shutdown, the "treatment policy" strategy slightly overestimated median PFS proportionally to the timing of the shutdown period, but power was not affected. Except for one specific scenario, there was no impact on the estimated HR. In general, the pandemic had a greater impact on the analyses using the "hypothetical" strategy, which led to decreased power and overestimated median PFS times to a greater extent than the "treatment policy" strategy. CONCLUSION: As a rule, we suggest that the treatment policy approach, which conforms with the intent-to-treat principle, should be the primary analysis to avoid unnecessary loss of power and minimize bias in median PFS estimates.

Classical and Bayesian Inference for the Inverse Lomax Distribution Under Adaptive Progressive Type-II Censored Data with COVID-19 Application

In this paper, we consider the classical and the Bayesian inferences for unknown parameters of inverse Lomax distribution and their corresponding survival characteristics under the adaptive progressive type-II censoring scheme. In the classical setup, first we obtain the maximum likelihood estimates for the unknown shape parameter of the distribution and its corresponding survival characteristics. Further, we consider symmetric and asymmetric loss functions for the estimation of shape parameter and its corresponding survival characteristics under the Bayesian paradigm. The performances of various derived estimators were recorded using Markov chain Monte Carlo simulation technique for different sample sizes. Finally,a COVID-19 mortality data set is provided to illustrate the computation of various estimators. © 2022 River Publishers.

Nonparametric kernel estimation of the probability of cure in a mixture cure model when the cure status is partially observed.

Cure models are a class of time-to-event models where a proportion of individuals will never experience the event of interest. The lifetimes of these so-called cured individuals are always censored. It is usually assumed that one never knows which censored observation is cured and which is uncured, so the cure status is unknown for censored times. In this paper, we develop a method to estimate the probability of cure in the mixture cure model when some censored individuals are known to be cured. A cure probability estimator that incorporates the cure status information is introduced. This estimator is shown to be strongly consistent and asymptotically normally distributed. Two alternative estimators are also presented. The first one considers a competing risks approach with two types of competing events, the event of interest and the cure. The second alternative estimator is based on the fact that the probability of cure can be written as the conditional mean of the cure status. Hence, nonparametric regression methods can be applied to estimate this conditional mean. However, the cure status remains unknown for some censored individuals. Consequently, the application of regression methods in this context requires handling missing data in the response variable (cure status). Simulations are performed to evaluate the finite sample performance of the estimators, and we apply them to the analysis of two datasets related to survival of breast cancer patients and length of hospital stay of COVID-19 patients requiring intensive care.

Pedagogy of transformation of a random variable, censoring, and truncation of data

The author has been incorporating data analytics into the probability course for students pursuing baccalaureate programs in engineering through weekly assignments and end-of-the-term projects. Data analytics makes the probability course much more relevant to the current trends in business, industry, and medicine that rely on data. The discussion related to the coronavirus pandemic about missing and incomplete data, the inability to pinpoint the exact start of the disease, and so forth offered an opportunity to expand activities in data analytics by examining "truncation" and "censoring" of data. In simple terms, truncation implies the exclusion of data (either not collected or ignored) in a certain range. Censoring implies redefining the data in a certain range while keeping the rest of the original data. A demo was created to explore the association of the transformation of random variables (mixed and conditional) to censoring and truncation. The demo utilized the theory of random variables, simulation, and computational techniques to examine and establish the link between the mixed transformation of variables and censoring. A similar link of conditional transformation of variables to truncation was also seen. The demo was used as the basis for a weekly assignment to the students. The analysis and results suggest that it is possible to expand the scope of the course in engineering probability to provide training in contemporary topics in data analytics.

Bayesian Inferential Approaches and Bootstrap for the Reliability and Hazard Rate Functions under Progressive First-Failure Censoring for Coronavirus Data from Asymmetric Model

This paper deals with the estimation of the parameters for asymmetric distribution and some lifetime indices such as reliability and hazard rate functions based on progressive first-failure censoring. Maximum likelihood, bootstrap and Bayesian approaches of the distribution parameters and reliability characteristics are investigated. Furthermore, the approximate confidence intervals and highest posterior density credible intervals of the parameters are constructed based on the asymptotic distribution of the maximum likelihood estimators and Markov chain Monte Carlo technique, respectively. In addition, the delta method is implemented to obtain the variances of the reliability and hazard functions. Moreover, we apply two methods of bootstrap to construct the confidence intervals. The Bayes inference based on the squared error and LINEX loss functions is obtained. Extensive simulation studies are conducted to evaluate the behavior of the proposed methods. Finally, a real data set of the COVID-19 mortality rate is analyzed to illustrate the estimation methods developed here. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

Inference on the Beta Type I Generalized Half Logistic Distribution under Right-Censored Observation with Application to COVID-19

In real-life situations, censoring issues do arise due to the incompleteness of data. This article examined the inferences on right-censored beta type I generalized half logistic distribution. In this work, some statistical properties of the beta type I generalized half logistic distribution were derived. Furthermore, the beta type I generalized half logistic distribution was studied under a censoring situation in the presence and absence of covariates. Estimation of model parameters was conducted using the maximum likelihood estimation method. A simulation study was carried out to assess the performance of the parameters of the model in terms of efficiency and consistency. In a real-life application, the model was applied to COVID-19 data and the necessary inferences were drawn. [ FROM AUTHOR] Copyright of International Journal of Mathematics & Mathematical Sciences is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

BAYESIAN INFERENCE FOR THE PARAMETERS OF EXPONENTIATED CHEN DISTRIBUTION BASED ON HYBRID CENSORING

This article presents classical and Bayesian inferences based on Type-II hybrid censored data when the lifetime of the items follows the exponentiated Chen distribution. Based on the hybrid censored data, the maximum likelihood estimates and the asymptotic confidence intervals of the involved parameters are derived. Bayes estimates, under squared error loss and linear-exponential loss functions, and highest posterior density intervals are also derived. Monte Carlo simulations are performed to see the effectiveness of the proposed estimation methods. The Application of real data from Vaccination of COVID-19 data for different countries of the region of the Americas is discussed. [ FROM AUTHOR] Copyright of Pakistan Journal of Statistics is the property of Pakistan Journal of Statistics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Survival analysis: A primer for the clinician scientists.

Survival analysis is a collection of statistical procedures employed on time-to-event data. The outcome variable of interest is time until an event occurs. Conventionally, it dealt with death as the event, but it can handle any event occurring in an individual like disease, relapse from remission, and recovery. Survival data describe the length of time from a time of origin to an endpoint of interest. By time, we mean years, months, weeks, or days from the beginning of being enrolled in the study. The major limitation of time-to-event data is the possibility of an event not occurring in all the subjects during a specific study period. In addition, some of the study subjects may leave the study prematurely. Such situations lead to what is called censored observations as complete information is not available for these subjects. Life table and Kaplan-Meier techniques are employed to obtain the descriptive measures of survival times. The main objectives of survival analysis include analysis of patterns of time-to-event data, evaluating reasons why data may be censored, comparing the survival curves, and assessing the relationship of explanatory variables to survival time. Survival analysis also offers different regression models that accommodate any number of covariates (categorical or continuous) and produces adjusted hazard ratios for individual factor.

Freedom of Information and Personal Confidentiality in Spatial COVID-19 Data

We draw attention to how, in the name of protecting the confidentiality of personal data, national statistical agencies have limited public access to spatial data on COVID-19. We also draw attention to large disparities in the way that access has been limited. In doing so, we distinguish between absolute confidentiality in which the probability of detection is 1, relative confidentiality where this probability is less than 1, and collective confidentiality, which refers to the probability of detection of at least one person. In spatial data, the probability of personal detection is less than 1, and the probability of collective detection varies directly with this probability and COVID-19 morbidity. Statistical agencies have been concerned with relative and collective confidentiality, which they implement using the techniques of truncation, where spatial data are not made public for zones with small populations, and censoring, where exact data are not made public for zones where morbidity is small. Granular spatial data are essential for epidemiological research into COVID-19. We argue that in their reluctance to make these data available to the public, data security officers (DSO) have unreasonably prioritized data protection over freedom of information. We also argue that by attaching importance to relative and collective confidentiality, they have over-indulged in data truncation and censoring. We highlight the need for legislation concerning relative and collective confidentiality, and regulation of DSO practices regarding data truncation and censoring. [ FROM AUTHOR] Copyright of Journal of Official Statistics (JOS) is the property of Journal of Official Statistics (JOS) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Democracy and COVID-19 outcomes.

More democratic countries are often expected to fail at providing a fast, strong, and effective response when facing a crisis such as COVID-19. This could result in higher infections and more negative health effects, but hard evidence to prove this claim is missing for the new disease. Studying the association with five different democracy measures, this study shows that while the infection rates of the disease do indeed appear to be higher for more democratic countries so far, their observed case fatality rates are lower. There is also a negative association between case fatality rates and government attempts to censor media. However, such censorship relates positively to the infection rate.