A flexible model based on piecewise linear approximation for the analysis of left truncated right censored data with covariates, and applications to Worcester Heart Attack Study data and Channing House data.

Left truncated right censored (LTRC) data arise quite commonly from survival studies. In this article, a model based on piecewise linear approximation is proposed for the analysis of LTRC data with covariates. Specifically, the model involves a piecewise linear approximation for the cumulative baseline hazard function of the proportional hazards model. The principal advantage of the proposed model is that it does not depend on restrictive parametric assumptions while being flexible and data-driven. Likelihood inference for the model is developed. Through detailed simulation studies, the robustness property of the model is studied by fitting it to LTRC data generated from different processes covering a wide range of lifetime distributions. A sensitivity analysis is also carried out by fitting the model to LTRC data generated from a process with a piecewise constant baseline hazard. It is observed that the performance of the model is quite satisfactory in all those cases. Analyses of two real LTRC datasets by using the model are provided as illustrative examples. Applications of the model in some practical prediction issues are discussed. In summary, the proposed model provides a comprehensive and flexible approach to model a general structure for LTRC lifetime data.

Two-stage targeted maximum likelihood estimation for mixed aggregate and individual participant data analysis with an application to multidrug resistant tuberculosis.

In this study, we develop a new method for the meta-analysis of mixed aggregate data (AD) and individual participant data (IPD). The method is an adaptation of inverse probability weighted targeted maximum likelihood estimation (IPW-TMLE), which was initially proposed for two-stage sampled data. Our methods are motivated by a systematic review investigating treatment effectiveness for multidrug resistant tuberculosis (MDR-TB) where the available data include IPD from some studies but only AD from others. One complication in this application is that participants with MDR-TB are typically treated with multiple antimicrobial agents where many such medications were not observed in all studies considered in the meta-analysis. We focus here on the estimation of the expected potential outcome while intervening on a specific medication but not intervening on any others. Our method involves the implementation of a TMLE that transports the estimation from studies where the treatment is observed to the full target population. A second weighting component adjusts for the studies with missing (inaccessible) IPD. We demonstrate the properties of the proposed method and contrast it with alternative approaches in a simulation study. We finally apply this method to estimate treatment effectiveness in the MDR-TB case study.

Circulating anti-nuclear autoantibodies in COVID-19 survivors predict long COVID symptoms.

BACKGROUND: Autoimmunity has been reported in patients with severe coronavirus disease 2019 (COVID-19). We investigated whether anti-nuclear/extractable-nuclear antibodies (ANAs/ENAs) were present up to a year after infection, and if they were associated with the development of clinically relevant post-acute sequalae of COVID-19 (PASC) symptoms. METHODS: A rapid-assessment line immunoassay was used to measure circulating levels of ANAs/ENAs in 106 convalescent COVID-19 patients with varying acute phase severities at 3, 6 and 12 months post-recovery. Patient-reported fatigue, cough and dyspnoea were recorded at each time point. Multivariable logistic regression model and receiver operating curves were used to test the association of autoantibodies with patient-reported outcomes and pro-inflammatory cytokines. RESULTS: Compared to age- and sex-matched healthy controls (n=22) and those who had other respiratory infections (n=34), patients with COVID-19 had higher detectable ANAs at 3 months post-recovery (p<0.001). The mean number of ANA autoreactivities per individual decreased between 3 and 12 months (from 3.99 to 1.55) with persistent positive titres associated with fatigue, dyspnoea and cough severity. Antibodies to U1-snRNP and anti-SS-B/La were both positively associated with persistent symptoms of fatigue (p<0.028, area under the curve (AUC) 0.86) and dyspnoea (p<0.003, AUC=0.81). Pro-inflammatory cytokines such as tumour necrosis factor (TNF)-α and C-reactive protein predicted the elevated ANAs at 12 months. TNF-α, D-dimer and interleukin-1ß had the strongest association with symptoms at 12 months. Regression analysis showed that TNF-α predicted fatigue (ß=4.65, p=0.004) and general symptomaticity (ß=2.40, p=0.03) at 12 months. INTERPRETATION: Persistently positive ANAs at 12 months post-COVID are associated with persisting symptoms and inflammation (TNF-α) in a subset of COVID-19 survivors. This finding indicates the need for further investigation into the role of autoimmunity in PASC.

Estimation of standard deviations and inverse-variance weights from an observed range.

A variety of methods have been proposed to estimate a standard deviation, when only a sample range has been observed or reported. This problem occurs in the interpretation of individual clinical studies that are incompletely reported, and also in their incorporation into meta-analyses. The methods differ with respect to their focus being either on the standard deviation in the underlying population or on the particular sample in hand, a distinction that has not been widely recognized. In this article, we contrast and compare various estimators of these two quantities with respect to bias and mean squared error, for normally distributed data. We show that unbiased estimators are available for either quantity, and recommend our preferred methods. We also propose a Taylor series method to obtain inverse-variance weights, for samples where only the sample range is available; this method yields very little bias, even for quite small samples. In contrast, the naïve approach of simply taking the inverse of an estimated variance is shown to be substantially biased, and can place unduly large weight on small samples, such as small clinical trials in a meta-analysis. Accordingly, this naïve (but commonly used) method is not recommended.

A Generalized Measure of Cumulative Residual Entropy.

In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy, such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of this generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss a generating function approach, using which we derive different entropy measures. We provide residual and cumulative versions of Sharma-Taneja-Mittal entropy and obtain them as special cases this generalized measure of entropy. Finally, using the newly introduced entropy measures, we establish some relationships between entropy and extropy measures.

Cumulative Residual q-Fisher Information and Jensen-Cumulative Residual χ2 Divergence Measures.

In this work, we define cumulative residual q-Fisher (CRQF) information measures for the survival function (SF) of the underlying random variables as well as for the model parameter. We also propose q-hazard rate (QHR) function via q-logarithmic function as a new extension of hazard rate function. We show that CRQF information measure can be expressed in terms of the QHR function. We define further generalized cumulative residual χ2 divergence measures between two SFs. We then examine the cumulative residual q-Fisher information for two well-known mixture models, and the corresponding results reveal some interesting connections between the cumulative residual q-Fisher information and the generalized cumulative residual χ2 divergence measures. Further, we define Jensen-cumulative residual χ2 (JCR-χ2) measure and a parametric version of the Jensen-cumulative residual Fisher information measure and then discuss their properties and inter-connections. Finally, for illustrative purposes, we examine a real example of image processing and provide some numerical results in terms of the CRQF information measure.

Discrete Versions of Jensen-Fisher, Fisher and Bayes-Fisher Information Measures of Finite Mixture Distributions.

In this work, we first consider the discrete version of Fisher information measure and then propose Jensen-Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes-Fisher information measures for mixing parameter vector of a finite mixture probability mass function and establish some results. We provide some connections between these measures with some known informational measures such as chi-square divergence, Shannon entropy, Kullback-Leibler, Jeffreys and Jensen-Shannon divergences.

Information Generating Function of Ranked Set Samples.

In the present paper, we study the information generating (IG) function and relative information generating (RIG) function measures associated with maximum and minimum ranked set sampling (RSS) schemes with unequal sizes. We also examine the IG measures for simple random sampling (SRS) and provide some comparison results between SRS and RSS procedures in terms of dispersive stochastic ordering. Finally, we discuss the RIG divergence measure between SRS and RSS frameworks.

Meta-analysis of quantile intervals from different studies with an application to a pulmonary tuberculosis data.

After the completion of many studies, experimental results are reported in terms of distribution-free confidence intervals that may involve pairs of order statistics. This article considers a meta-analysis procedure to combine these confidence intervals from independent studies to estimate or construct a confidence interval for the true quantile of the population distribution. Data synthesis is made under both fixed-effect and random-effect meta-analysis models. We show that mean square error (MSE) of the combined quantile estimator is considerably smaller than that of the best individual quantile estimator. We also show that the coverage probability of the meta-analysis confidence interval is quite close to the nominal confidence level. The random-effect meta-analysis model yields a better coverage probability and smaller MSE than the fixed-effect meta-analysis model. The meta-analysis method is then used to synthesize medians of patient delays in pulmonary tuberculosis diagnosis in China to provide an illustration of the proposed methodology.

On a class of non-linear transformation cure rate models.

In this paper, we propose a generalization of the mixture (binary) cure rate model, motivated by the existence of a zero-modified (inflation or deflation) distribution, on the initial number of causes, under a competing cause scenario. This non-linear transformation cure rate model is in the same form of models studied in the past; however, following our approach, we are able to give a realistic interpretation to a specific class of proper transformation functions, for the cure rate modeling. The estimation of the parameters is then carried out using the maximum likelihood method along with a profile approach. A simulation study examines the accuracy of the proposed estimation method and the model discrimination based on the likelihood ratio test. For illustrative purposes, analysis of two real life data-sets, one on recidivism and another on cutaneous melanoma, is also carried out.

Family of bivariate distributions on the unit square: theoretical properties and applications.

We introduce the bivariate unit-log-symmetric model based on the bivariate log-symmetric distribution (BLS) defined in Vila et al. [25] as a flexible family of bivariate distributions over the unit square. We then study its mathematical properties such as stochastic representations, quantiles, conditional distributions, independence of the marginal distributions and marginal moments. Maximum likelihood estimation method is discussed and examined through Monte Carlo simulation. Finally, the proposed model is used to analyze some soccer data sets.

QTc Interval Prolongation and Its Association With Electrolyte Abnormalities and Psychotropic Drug Use Among Patients With Eating Disorders.

Background: Eating disorders (EDs) often develop during adolescence with high mortality rates. Sudden cardiac death in these patients has been associated with corrected QT (QTc) interval prolongation. The significance of extrinsic factors on QTc prolongation in populations with EDs remains controversial. This study assessed the relationship between QTc prolongation in paediatric patients with EDs and extrinsic factors, such as QTc-prolonging medications and electrolyte abnormalities to investigate whether an ED alone is associated with an increased prevalence of QTc prolongation. Methods: Electrocardiograms, electrolytes, and psychopharmaceutical usage were retrospectively analysed from the charts of 264 paediatric patients with EDs. Descriptive statistics were used to assess QTc prolongation and its relationship with electrolyte abnormalities and psychopharmaceuticals. Results: Of 264 patients, 227 had normal QTc intervals (<440 ms), whereas 37 had borderline prolonged (440-460 ms) or prolonged (>460 ms) intervals. The prevalence of QTc intervals exceeding 440 ms in patients with normal electrolytes and not using QTc-prolonging psychotropics mirrored that of the general population (P = 0.59). Of the 23 patients taking psychotropics, 8 had abnormal QTc intervals. The average QTc was greater for patients using QTc-prolonging psychotropics (P = 0.05) with a correlation between interval length and psychotropic usage (P < 0.01). Average potassium (P = 0.08), calcium (P = 0.18), and magnesium (P = 0.08) levels did not significantly differ between those with normal and abnormal QTc intervals. Conclusions: This study suggests that EDs alone may not prolong QTc intervals in paediatric patients with EDs, but psychotropics appear to be a salient external factor in QTc prolongation.

Contexte: Les troubles des conduites alimentaires (TCA) surviennent surtout au cours de l'adolescence et entraînent un taux de mortalité élevé. Chez ces patients, la mort subite d'origine cardiaque a été associée à un allongement de l'intervalle QT corrigé (QTc). La portée des facteurs extrinsèques sur l'allongement de cet intervalle chez les patients atteints de TCA demeure un sujet controversé. La présente étude visait à évaluer la relation entre l'allongement de l'intervalle QTc chez les enfants atteints de TCA et des facteurs extrinsèques, comme la prise de médicaments causant l'allongement de l'intervalle QTc et les anomalies électrolytiques, pour déterminer si la présence d'un TCA est à elle seule associée à une prévalence élevée d'allongement de l'intervalle QTc. Méthodologie: Nous avons analysé rétrospectivement les électrocardiogrammes, les valeurs d'électrolytes et l'utilisation de médicaments psychotropes dans les dossiers de 264 enfants atteints de TCA. Des techniques de statistique descriptive ont été utilisées pour analyser l'allongement de l'intervalle QTc et les liens avec les anomalies électrolytiques et les médicaments psychotropes. Résultats: Parmi les 264 patients, 227 présentaient un intervalle QTc normal (< 440 ms) et 37 présentaient des résultats limites (440 à 460 ms) ou un allongement de l'intervalle (> 460 ms). La prévalence d'un intervalle QTc de 440 ms ou plus chez les patients présentant des taux d'électrolytes normaux et non traités par des médicaments psychotropes causant l'allongement de l'intervalle QTc était semblable à la prévalence dans la population générale (p = 0,59). Huit des 23 patients traités par des médicaments psychotropes présentaient un intervalle QTc anormal. La moyenne des intervalles QTc était supérieure dans le groupe des patients recevant des médicaments psychotropes causant un allongement de l'intervalle QTc (p = 0,05), et il existait une corrélation entre la durée de l'intervalle et de l'usage de médicaments psychotropes (p < 0,01). Les taux moyens de potassium (p = 0,08), de calcium (p = 0,18) et de magnésium (p = 0,08) ne différaient pas de façon significative entre les groupes présentant des intervalles QTc normaux et anormaux. Conclusions: Les résultats de notre étude donnent à penser que le TCA à lui seul ne provoque pas l'allongement de l'intervalle QTc chez les enfants qui en sont atteints, mais que l'utilisation de médicaments psychotropes constitue un facteur externe important dans l'allongement de l'intervalle QTc.

A method was developed for correcting the bias in the usual study weights in meta-analyses.

OBJECTIVES: Our goal was to evaluate the bias in the usual method of estimating study weights in a meta-analysis and to develop a suitable bias correction. STUDY DESIGN AND SETTING: In meta-analyses, it is standard practice to weight studies by the inverse variance of their treatment effects. Weights are usually calculated by taking reciprocals of the estimated variances, but we show that this approach is biased. We established an exact expression for the bias with continuous data, yielding a correction factor for the study weights that yields improved estimation of the treatment effect. RESULTS: With the usual method, the weight for each study is always overestimated, particularly with small samples; also, the variance of the summary treatment effect is underestimated. Our correction yields an unbiased estimate of the summary treatment effect with minimum variance. We illustrate the bias numerically for various scenarios and show how it can substantially affect actual meta-analyses in practice. CONCLUSION: We recommend that the standard method of obtaining study weights should be modified by our bias correction factor. Our method is simple and straightforward to apply. Elimination of this bias will enhance the validity of conclusions from a meta-analysis, compared with the situation when the standard weights are used.

Unified approach to optimal estimation of mean and standard deviation from sample summaries.

Recently, various methods have been developed to estimate the sample mean and standard deviation when only the sample size, and other selected sample summaries are reported. In this paper, we provide a unified approach to optimal estimation that can be easily adopted when only some summary statistics are reported. We show that the proposed estimators have the lowest variance among linear unbiased estimators. We also show that in the most commonly reported cases, that is, when only a three-number or five-number summary is reported, the newly proposed estimators match the previously developed estimators. Finally, we demonstrate the performance of the estimators numerically.

Novel Protein-Protein Interactions Highlighting the Crosstalk between Hypoplastic Left Heart Syndrome, Ciliopathies and Neurodevelopmental Delays.

Hypoplastic left heart syndrome (HLHS) is a severe congenital heart disease (CHD) affecting 1 in 5000 newborns. We constructed the interactome of 74 HLHS-associated genes identified from a large-scale mouse mutagenesis screen, augmenting it with 408 novel protein-protein interactions (PPIs) using our High-Precision Protein-Protein Interaction Prediction (HiPPIP) model. The interactome is available on a webserver with advanced search capabilities. A total of 364 genes including 73 novel interactors were differentially regulated in tissue/iPSC-derived cardiomyocytes of HLHS patients. Novel PPIs facilitated the identification of TOR signaling and endoplasmic reticulum stress modules. We found that 60.5% of the interactome consisted of housekeeping genes that may harbor large-effect mutations and drive HLHS etiology but show limited transmission. Network proximity of diabetes, Alzheimer's disease, and liver carcinoma-associated genes to HLHS genes suggested a mechanistic basis for their comorbidity with HLHS. Interactome genes showed tissue-specificity for sites of extracardiac anomalies (placenta, liver and brain). The HLHS interactome shared significant overlaps with the interactomes of ciliopathy- and microcephaly-associated genes, with the shared genes enriched for genes involved in intellectual disability and/or developmental delay, and neuronal death pathways, respectively. This supported the increased burden of ciliopathy variants and prevalence of neurological abnormalities observed among HLHS patients with developmental delay and microcephaly, respectively.

Nonparametric optimal designs for degradation tests.

This paper discusses the optimal design of a degradation test within the nonparametric framework by assuming the underlying process to be an empirical Lévy process with heterogeneity. The optimization of the experiment relies on the design variables including the sample size, the measurement frequency and total operation time. It is necessary to investigate the effect of the design variables on the estimation of first passage time (FPT). Subject to total experimental cost not exceeding a pre-specified budget, the values of design variables are determined such that the bootstrap mean square error of the 100 p th percentile of the FPT distribution is minimized.

Accuracy of Electrocardiography and Agreement with Echocardiography in the Diagnosis of Pediatric Left Atrial Enlargement.

Left atrial enlargement (LAE) is a marker for diastolic cardiac dysfunction. Echocardiograms are considered the gold-standard for diagnosis, but given their wider access and lower economic cost, electrocardiograms (ECGs) may be useful in identifying patients who would benefit from further investigation. This study investigates the utility of ECG criteria to diagnose LAE in pediatric patients. A retrospective chart review (n = 492) was conducted in patients whose echocardiograms demonstrated LAE by left atrial indexed diameter z-score ≥2.0 and/or increased left atrial to aortic root ratio at various cutoffs (≥1.4, ≥1.6, ≥1.8). ECG criteria studied included: (1) P wave ≥110 msec, (2) P mitrale ≥40 msec, in LII (3) terminal negative P wave deflection in lead V1 > 40 msec, and (4) P/PR segment >1.6 in lead II. Sensitivity, specificity, Cohen's Kappa coefficient (κ), and ROC curves were calculated. A combination of P mitrale ≥40 msec and terminal negative P wave deflection in lead V1 > 40 msec yielded the greatest agreement (κ = 0.221, 95%CI 0.060-0.382), but all ECG criteria used to diagnose LAE had poor diagnostic value (AUC < 0.60). The present ECG criteria should not be used to diagnose LAE in the absence of an echocardiogram and findings should be considered in the context of clinical symptoms.

Expectation Maximization Algorithm for Box-Cox Transformation Cure Rate Model and Assessment of Model Misspecification Under Weibull Lifetimes.

In this paper, we develop likelihood inference based on the expectation maximization algorithm for the Box-Cox transformation cure rate model assuming the lifetimes to follow a Weibull distribution. A simulation study is carried out to demonstrate the performance of the proposed estimation method. Through Monte Carlo simulations, we also study the effect of model misspecification on the estimate of cure rate. Finally, we analyze a well-known data on melanoma with the model and the inferential method developed here.

Bayesian cure rate models induced by frailty in survival analysis.

Frailty models provide a convenient way of modeling unobserved dependence and heterogeneity in survival data which, if not accounted for duly, would result incorrect inference. Gamma frailty models are commonly used for this purpose, but alternative continuous distributions are possible as well. However, with cure rate being present in survival data, these continuous distributions may not be appropriate since individuals with long-term survival times encompass zero frailty. So, we propose here a flexible probability distribution induced by a discrete frailty, and then present some special discrete probability distributions. We specifically focus on a special hyper-Poisson distribution and then develop the corresponding Bayesian simulation, influence diagnostics and an application to real dataset by means of intensive Markov chain Monte Carlo algorithm. These illustrate the usefulness of the proposed model as well as the inferential results developed here.