RESUMO

This article extends the semiparametric mixed model for longitudinal censored data with Gaussian errors by considering the Student's t $$ t $$ -distribution. This model allows us to consider a flexible, functional dependence of an outcome variable over the covariates using nonparametric regression. Moreover, the proposed model takes into account the correlation between observations by using random effects. Penalized likelihood equations are applied to derive the maximum likelihood estimates that appear to be robust against outlying observations with respect to the Mahalanobis distance. We estimate nonparametric functions using smoothing splines under an EM-type algorithm framework. Finally, the proposed approach's performance is evaluated through extensive simulation studies and an application to two datasets from acquired immunodeficiency syndrome clinical trials.

Assuntos

Síndrome da Imunodeficiência Adquirida , Síndrome da Imunodeficiência Adquirida/terapia , Simulação por Computador , Humanos , Funções Verossimilhança , Modelos Estatísticos , Distribuição Normal , Estudantes

RESUMO

BACKGROUND AND PURPOSE: Conventional magnetic resonance images (MRI) has limitations in distinguishing primary from secondary brain tumors. Proton magnetic resonance spectroscopy (1H-MRS) allows evaluation of the concentration of metabolites in a brain lesion and, hence, better characterization of the tumor. Considering that an accurate diagnosis determines the choice of treatment, our purpose was to assess the usefulness of spectroscopy data for differentiating between primary and secondary brain neoplasms. MATERIALS AND METHODS: We undertook a retrospective analysis of 61 MRI and 1H-MRS images of patients with histologically confirmed tumors (30 primary tumors and 31 metastatic tumors). The metabolite ratios of Cho/Cr and NAA/Cr at short TE were determined from spectroscopic curves, with a single voxel positioned in the enhancing tumor. Additional variables analyzed along with the metabolites, like as age and gender, allowed the construction of a logistic regression model to predict the tumor's nature. The statistical analysis was done using the R software (version 4.0.3 R Core Team, 2020). RESULTS: The mean NAA/Cr and Cho/Cr ratios were higher in secondary tumors, with a good correlation between NAA/Cr and Cho/Cr (r = 0.61). The mean age of patients with primary tumors was lower than for secondary tumors (43.9 vs 55.9, respectively). Receiver operating characteristic analysis yielded a cut-off value of 0.4 for the NAA/Cr ratio with an accuracy of 73.8%, a sensitivity of 73.3% and a specificity of 74.2% in predicting metastatic tumors. CONCLUSION: The model was reasonable in predicting the nature of the tumor and provides an additional tool for analyzing brain tumors.

Assuntos

Neoplasias Encefálicas , Ácido Aspártico , Neoplasias Encefálicas/diagnóstico , Colina/metabolismo , Creatina/metabolismo , Humanos , Espectroscopia de Ressonância Magnética/métodos , Espectroscopia de Prótons por Ressonância Magnética , Estudos Retrospectivos , Sensibilidade e Especificidade

RESUMO

In longitudinal studies, repeated measures are collected over time and hence they tend to be serially correlated. These studies are commonly analyzed using linear mixed models (LMMs), and in this article we consider an extension of the skew-normal/independent LMM, where the error term has a dependence structure, such as damped exponential correlation or autoregressive correlation of order p. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously when continuous repeated measures are serially correlated. For this robust model, we present an efficient EM-type algorithm for parameters estimation via maximum likelihood and the observed information matrix is derived analytically to account for standard errors. The methodology is illustrated through an application to schizophrenia data and some simulation studies. The proposed algorithm and methods are implemented in the new R package skewlmm.

Assuntos

Algoritmos , Modelos Estatísticos , Simulação por Computador , Humanos , Modelos Lineares , Estudos Longitudinais , Análise Multivariada

RESUMO

Mixed-effects models, with modifications to accommodate censored observations (LMEC/NLMEC), are routinely used to analyze measurements, collected irregularly over time, which are often subject to some upper and lower detection limits. This paper presents a likelihood-based approach for fitting LMEC/NLMEC models with autoregressive of order p dependence of the error term. An EM-type algorithm is developed for computing the maximum likelihood estimates, obtaining as a byproduct the standard errors of the fixed effects and the likelihood value. Moreover, the constraints on the parameter space that arise from the stationarity conditions for the autoregressive parameters in the EM algorithm are handled by a reparameterization scheme, as discussed in Lin and Lee (2007). To examine the performance of the proposed method, we present some simulation studies and analyze a real AIDS case study. The proposed algorithm and methods are implemented in the new R package ARpLMEC.

Assuntos

Funções Verossimilhança , Simulação por Computador , Humanos , Modelos Lineares , Estudos Longitudinais , Carga Viral

RESUMO

In biomedical studies on HIV RNA dynamics, viral loads generate repeated measures that are often subjected to upper and lower detection limits, and hence these responses are either left- or right-censored. Linear and non-linear mixed-effects censored (LMEC/NLMEC) models are routinely used to analyse these longitudinal data, with normality assumptions for the random effects and residual errors. However, the derived inference may not be robust when these underlying normality assumptions are questionable, especially the presence of outliers and thick-tails. Motivated by this, Matos et al. (2013b) recently proposed an exact EM-type algorithm for LMEC/NLMEC models using a multivariate Student's-t distribution, with closed-form expressions at the E-step. In this paper, we develop influence diagnostics for LMEC/NLMEC models using the multivariate Student's-t density, based on the conditional expectation of the complete data log-likelihood. This partially eliminates the complexity associated with the approach of Cook (1977, 1986) for censored mixed-effects models. The new methodology is illustrated via an application to a longitudinal HIV dataset. In addition, a simulation study explores the accuracy of the proposed measures in detecting possible influential observations for heavy-tailed censored data under different perturbation and censoring schemes.