General Semiparametric Shared Frailty Model Estimation and Simulation with frailtySurv

The R package frailtySurv for simulating and fitting semi-parametric shared frailty models is introduced. Package frailtySurv implements semi-parametric consistent estimators for a variety of frailty distributions, including gamma, log-normal, inverse Gaussian and power variance function, and provides consistent estimators of the standard errors of the parameters' estimators. The parameters' estimators are asymptotically normally distributed, and therefore statistical inference based on the results of this package, such as hypothesis testing and confidence intervals, can be performed using the normal distribution. Extensive simulations demonstrate the flexibility and correct implementation of the estimator. Two case studies performed with publicly available datasets demonstrate applicability of the package. In the Diabetic Retinopathy Study, the onset of blindness is clustered by patient, and in a large hard drive failure dataset, failure times are thought to be clustered by the hard drive manufacturer and model

Frailty models

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Residual Diagnostics and Statistical Inference for Shared Frailty Models

Frailty models are commonly used for analyzing clustered survival data and accounting for unobserved heterogeneity. Shared frailty models are random-effect models in which the frailties are shared among individuals within groups. Several R packages, such as survival, frailtyEM, fraltypack, frailtysurv, and frailtyHL, are available for fitting shared frailty models. However, little research has been conducted to compare their performances, leaving users without clear guidance in selecting an appropriate tool for analyzing clustered survival data. The first study in this thesis aims to address this gap by providing an overview of current R packages for fitting shared frailty models and comparing their performances through simulation studies. After fitting a shared frailty model, model diagnostics are an essential part of the modelling process. The use of residuals in assessing model adequacy is a conventional tool for normal regression. In the second study of this thesis, we propose to use the Z-residual for detecting the non-linearity in the shared frailty model. Through a simulation study, we investigate the power of Z residuals in detecting non-linear effects in covariates and demonstrate their effectiveness in diagnosing models using real data on the survival of acute myeloid leukemia patients. Typically, all residuals in survival analysis are calculated using the full dataset, resulting in a bias problem due to double usage of the dataset. In the third study of this thesis, we propose applying cross-validation methods to compute residuals for diagnosing a semi-parametric shared frailty model and investigate the performance of cross-validatory Z-residual for diagnosing a shared frailty model with non-parametric baseline hazards. We compare Z-residuals calculated through three methods: without cross-validation (No-CV) method which is the basic algorithm, 10-fold cross-validation (10-fold) and leave-one-out cross-validation (LOOCV). Through simulation studies, we investigate their performances in the detection of nonlinear effects in covariates and identification of the outliers in the dataset through graphical visualization and overall GOF test. We also compared No-CV Z-residual and LOOCV Z-residual in a real data application for identifying outliers for a kidney infection dataset. Finally, in the fourth study of this thesis, we extended the Z residual to diagnose the proportional hazards assumption and compare it with existing residual methods

Efficacy and durability of multifactorial intervention on mortality and MACEs:a randomized clinical trial in type-2 diabetic kidney disease

Background: Multiple modifiable risk factors for late complications in patients with diabetic kidney disease (DKD), including hyperglycemia, hypertension and dyslipidemia, increase the risk of a poor outcome. DKD is associated with a very high cardiovascular risk, which requires simultaneous treatment of these risk factors by implementing an intensified multifactorial treatment approach. However, the efficacy of a multifactorial intervention on major fatal/non-fatal cardiovascular events (MACEs) in DKD patients has been poorly investigated. Methods: Nephropathy in Diabetes type 2 (NID-2) study is a multicentre, cluster-randomized, open-label clinical trial enrolling 395 DKD patients with albuminuria, diabetic retinopathy (DR) and negative history of CV events in 14 Italian diabetology clinics. Centres were randomly assigned to either Standard-of-Care (SoC) (n = 188) or multifactorial intensive therapy (MT, n = 207) of main cardiovascular risk factors (blood pressure 40/50 mg/dL for men/women and < 175 mg/dL, respectively). Primary endpoint was MACEs occurrence by end of follow-up phase. Secondary endpoints included single components of primary endpoint and all-cause death. Results: At the end of intervention period (median 3.84 and 3.40 years in MT and SoC group, respectively), targets achievement was significantly higher in MT. During 13.0 years (IQR 12.4–13.3) of follow-up, 262 MACEs were recorded (116 in MT vs. 146 in SoC). The adjusted Cox shared-frailty model demonstrated 53% lower risk of MACEs in MT arm (adjusted HR 0.47, 95%CI 0.30–0.74, P = 0.001). Similarly, all-cause death risk was 47% lower (adjusted HR 0.53, 95%CI 0.29–0.93, P = 0.027). Conclusion: MT induces a remarkable benefit on the risk of MACEs and mortality in high-risk DKD patients. Clinical Trial Registration ClinicalTrials.gov number, NCT00535925. https://clinicaltrials.gov/ct2/show/NCT0053592

Falls: A marker of preclinical Alzheimer disease: A cohort study protocol

INTRODUCTION: Progression to symptomatic Alzheimer disease (AD) occurs slowly over a series of preclinical stages. Declining functional mobility may be an early indicator of loss of brain network integration and may lead to an increased risk of experiencing falls. It is unknown whether measures of functional mobility and falls are preclinical markers of AD. The purpose of this study is to examine (1) the relationship between falls and functional mobility with AD biomarkers to determine when falls occur within the temporal progression to symptomatic Alzheimer disease, and (2) the attentional compared with perceptual/motor systems that underlie falls and functional mobility changes seen with AD. METHODS AND ANALYSIS: This longitudinal cohort study will be conducted at the Knight Alzheimer Disease Research Center. Approximately 350 cognitively normal participants (with and without preclinical AD) will complete an in-home visit every year for 4 years. During each yearly assessment, functional mobility will be assessed using the Performance Oriented Mobility Assessment, Timed Up and Go, and Timed Up and Go dual task. Data regarding falls (including number and severity) will be collected monthly by self-report and confirmed through interviews. This study will leverage ongoing neuropsychological assessments and neuroimaging (including molecular imaging using positron emission tomography and MRI) performed by the Knight Alzheimer Disease Research Center. Relationships between falls and biomarkers of amyloid, tau and neurodegeneration will be evaluated. ETHICS AND DISSEMINATION: This study was approved by the Washington University in St. Louis Institutional Review Board (reference number 201807135). Written informed consent will be obtained in the home prior to the collection of any study data. Results will be published in peer-reviewed publications and presented at national and international conferences. TRIAL REGISTRATION NUMBER: NCT04949529; Pre-results

MULTI-PARAMETRIC COPULA ESTIMATION BASED ON MOMENTS METHOD UNDER CENSORING

This thesis combines two interesting branches of statistics: survival analysis and copula theory. The primary objective is to extend the copula theory results via semi-parametric estimation, under censored data. More precisely, we are interested by a copulas semi-parametric estimation, based on the classical moments estimation method, adapted for bivariate censored data. There are various kinds of censoring, we are only look at doubly and singly right-censored data. As theoretical results, general formulas were proved with analytical forms of the obtained estimators. According to early research, many asymptotic results obtained in the framework of non-parametric statistics for right-censored observations are based on the Kaplan Meier estimator, which estimates the survival function. Taking into account the results of Lopez and Saint-Pierre (2012) [72], Gribkova and Lopez (2015) [39], the asymptotic normality of the empirical survival copula was established for the two cases of censoring. The dependence structure between the bivariate survival times was modeled under the assumption that the underlying copula is Archimedean. Accounting for various censoring patterns (singly or doubly censored), a simulation study was performed efficiency and robustness of the new estimator proposed. Individual random parameters, which are commonly understood as frailty parameters, are another tool frequently employed for modeling multivariate survival data. We implemented this model for two-variable survival data using Archimedean copulas in the final part of the thesis. The frailty variables considered here are latent variables that are not observed, are nevertheless one-dimensional. In the example presented, this variable characterized the effect of the individual on the recurrence time. Then we looked at Clayton-Oakes copulas in particular, and even the model with gamma-type frailty. For each of these two models, the copulas used for the bivariate survival functions are the same. Even so, the marginal survival functions are modeled in different ways. The applications for health-related survival data were next examined