Isolated left ventricular apical hypoplasia:Systematic review and analysis of the 37 cases reported so far

BACKGROUND Isolated left ventricular apical hypoplasia(ILVAH),also known as truncated left ventricle(LV),is a very unusual cardiomyopathy.It is characterised by a truncated,spherical,and non-apex forming LV.The true apex is occupied by the right ventricle.Due to the rarity of the disease,just a few case reports and limited case series have been published in the field.AIM To analysing the so far 37 reported ILVAH cases worldwide.METHODS The electronic databases PubMed and Scopus were investigated from their establishment up to December 13,2022.RESULTS The majority of cases reported occurred in males(52.7%).Mean age at diagnosis was 26.1±19.6 years.More than a third of the patients were asymptomatic(35.1%).The most usual clinical presentation was breathlessness(40.5%).The most commonly detected electrocardiogram changes were T wave abnormalities(29.7%)and right axis deviation with poor R wave progression(24.3%).Atrial fibrillation/flutter was detected in 24.3%.Echocardiography was performed in 97.3%of cases and cardiac MRI in 91.9%of cases.Ejection fraction was reduced in more than a half of patients(56.7%).An associated congenital heart disease was found in 16.2%.Heart failure therapy was administered in 35.1%of patients.The outcome was favorable in the vast majority of patients,with just one death.CONCLUSION ILVAH is a multifaceted entity with a so far unpredictable course,ranging from benign until the elderly to sudden death during adolescence.

THE STRONG LAW FOR THE P-L ESTIMATE IN THE LEFT TRUNCATED AND RIGHT CENSORED MODEL (I)

For the model with both left truncation and right censoring,suppose all the distributions are continuous. It is proved that the sampled cumulative hazard function Λ n and the product-limit estimate F n are strong consistent. For any nonnegative measurable , the almost sure convergences of ∫d Λ n and ∫dF n to the true values ∫d Λ and ∫dF respectively are obtained.The strong consistency of the estimator for the truncation probability is proved.

BIVARIATE ESTIMATION WITH LEFT-TRUNCATED DATA

In this article we construct a kernel estimate of the probability function from bivariate data when a component is subject to random left-truncation. We establish consistency and asymptotic normality of the proposed estimator using a strong approximation result. Simulation studies show that the proposed procedure gives a good estimate of the true density function even when the sample size is moderate.

Single-Index Quantile Regression with Left Truncated Data

The purpose of this paper is two fold.First,the authors investigate quantile regression(QR)estimation for single-index QR models when the response is subject to random left truncation.The random weights are introduced to deal with left truncated data and the associated iteration estimation method is proposed.The asymptotic properties for the proposed QR estimates of the index parameter and unknown link function are both obtained.Further,by combining the QR loss function and the adaptive LASSO penalization,a variable selection procedure for the index parameter is introduced and its oracle property is established.Second,a weighted empirical log-likelihood ratio of the index parameter based on the QR method is introduced and is proved to be asymptotic standard chi-square distribution.Furthermore,confidence regions of the index parameter can be constructed.The finite sample performance of the proposed methods are demonstrated.A real data analysis is also conducted to show the usefulness of the proposed approaches.

BAHADUR REPRESENTATION OF THEKERNEL QUANTILE ESTIMATOR UNDER TRUNCATED AND CENSORED DATA

In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right censored data. Under suitable conditions, with probability one, the exactconvergence rate of the remainder term in the representations is obtained. As a by-product, theLIL, the asymptotic normality for those kernel estimators are derived.