A likelihood ratio appropach to family-based association studies with covariates

We introduce a procedure for association based analysis of nuclear families that allows for dichotomous and more general measurements of phenotype and inclusion of covariate information. Standard generalized linear models are used to relate phenotype and its predictors. Our test procedure, based on the likelihood ratio, unifies the estimation of all parameters through the likelihood itself and yields maximum likelihood estimates of the genetic relative risk and interaction parameters. Our method has advantages in modelling the covariate and gene-covariate interaction terms over recently proposed conditional score tests that include covariate information via a two-stage modelling approach. We apply our method in a study of human systemic lupus erythematosus and the C-reactive protein that includes sex as a covariate.

A Bayesian Analysis in the Presence of Covariates for Multivariate Survival Data: An example of Application

In this paper, we introduce a Bayesian analysis for survival multivariate data in the presence of a covariate vector and censored observations. Different ""frailties"" or latent variables are considered to capture the correlation among the survival times for the same individual. We assume Weibull or generalized Gamma distributions considering right censored lifetime data. We develop the Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods.

Bias-corrected estimators for dispersion models with dispersion covariates

In this paper we discuss bias-corrected estimators for the regression and the dispersion parameters in an extended class of dispersion models (Jorgensen, 1997b). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the O(n(-1)) bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results obtained by Botter and Cordeiro (1998), Cordeiro and McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The practical use of the formulae is that we can derive closed-form expressions for the O(n(-1)) biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the O(n(-1)) biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to order O(n(-1)) that are based on bootstrap methods. These estimators are compared by simulation. (C) 2011 Elsevier B.V. All rights reserved.

Modeling grouped survival data with time-dependent covariates

In this article, proportional hazards and logistic models for grouped survival data were extended to incorporate time-dependent covariates. The extension was motivated by a forestry experiment designed to compare five different water stresses in Eucalyptus grandis seedlings. The response was the seedling lifetime. The data set was grouped since there were just three occasions in which the seedlings was visited by the researcher. In each of these occasions also the shoot height was measured and therefore it is a time-dependent covariate. Both extended models were used in this example, and the results were very similar.

Early selection in open-pollinated Eucalyptus families based on competition covariates

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Covariates of high-risk human papillomavirus (HPV) infections are distinct for incident CIN1, CIN2 and CIN3 as disclosed by competing-risks regression models

Background: In addition to the oncogenic human papillomavirus (HPV), several cofactors are needed in cervical carcinogenesis, but whether the HPV covariates associated with incident i) CIN1 are different from those of incident ii) CIN2 and iii) CIN3 needs further assessment. Objectives: To gain further insights into the true biological differences between CIN1, CIN2 and CIN3, we assessed HPV covariates associated with incident CIN1, CIN2, and CIN3. Study Design and Methods: HPV covariates associated with progression to CIN1, CIN2 and CIN3 were analysed in the combined cohort of the NIS (n = 3,187) and LAMS study (n = 12,114), using competing-risks regression models (in panel data) for baseline HR-HPV-positive women (n = 1,105), who represent a sub-cohort of all 1,865 women prospectively followed-up in these two studies. Results: Altogether, 90 (4.8%), 39 (2.1%) and 14 (1.4%) cases progressed to CIN1, CIN2, and CIN3, respectively. Among these baseline HR-HPV-positive women, the risk profiles of incident GIN I, CIN2 and CIN3 were unique in that completely different HPV covariates were associated with progression to CIN1, CIN2 and CIN3, irrespective which categories (non-progression, CIN1, CIN2, CIN3 or all) were used as competing-risks events in univariate and multivariate models. Conclusions: These data confirm our previous analysis based on multinomial regression models implicating that distinct covariates of HR-HPV are associated with progression to CIN1, CIN2 and CIN3. This emphasises true biological differences between the three grades of GIN, which revisits the concept of combining CIN2 with CIN3 or with CIN1 in histological classification or used as a common end-point, e.g., in HPV vaccine trials.

THE ROLE OF AN EXPLICIT CAUSAL FRAMEWORK IN AFFECTED SIB PAIR DESIGNS WITH COVARIATES

The affected sib/relative pair (ASP/ARP) design is often used with covariates to find genes that can cause a disease in pathways other than through those covariates. However, such "covariates" can themselves have genetic determinants, and the validity of existing methods has so far only been argued under implicit assumptions. We propose an explicit causal formulation of the problem using potential outcomes and principal stratification. The general role of this formulation is to identify and separate the meaning of the different assumptions that can provide valid causal inference in linkage analysis. This separation helps to (a) develop better methods under explicit assumptions, and (b) show the different ways in which these assumptions can fail, which is necessary for developing further specific designs to test these assumptions and confirm or improve the inference. Using this formulation in the specific problem above, we show that, when the "covariate" (e.g., addiction to smoking) also has genetic determinants, then existing methods, including those previously thought as valid, can declare linkage between the disease and marker loci even when no such linkage exists. We also introduce design strategies to address the problem.

Locally Efficient Estimation with Current Status Data and High Dimensional Covariates

In biostatistical applications, interest often focuses on the estimation of the distribution of time T between two consecutive events. If the initial event time is observed and the subsequent event time is only known to be larger or smaller than an observed monitoring time, then the data is described by the well known singly-censored current status model, also known as interval censored data, case I. We extend this current status model by allowing the presence of a time-dependent process, which is partly observed and allowing C to depend on T through the observed part of this time-dependent process. Because of the high dimension of the covariate process, no globally efficient estimators exist with a good practical performance at moderate sample sizes. We follow the approach of Robins and Rotnitzky (1992) by modeling the censoring variable, given the time-variable and the covariate-process, i.e., the missingness process, under the restriction that it satisfied coarsening at random. We propose a generalization of the simple current status estimator of the distribution of T and of smooth functionals of the distribution of T, which is based on an estimate of the missingness. In this estimator the covariates enter only through the estimate of the missingness process. Due to the coarsening at random assumption, the estimator has the interesting property that if we estimate the missingness process more nonparametrically, then we improve its efficiency. We show that by local estimation of an optimal model or optimal function of the covariates for the missingness process, the generalized current status estimator for smooth functionals become locally efficient; meaning it is efficient if the right model or covariate is consistently estimated and it is consistent and asymptotically normal in general. Estimation of the optimal model requires estimation of the conditional distribution of T, given the covariates. Any (prior) knowledge of this conditional distribution can be used at this stage without any risk of losing root-n consistency. We also propose locally efficient one step estimators. Finally, we show some simulation results.

Smooth Hazard Function Estimation for Interval Censored Data with Time Varying Covariates

In this paper we propose methods for smooth hazard estimation of a time variable where that variable is interval censored. These methods allow one to model the transformed hazard in terms of either smooth (smoothing splines) or linear functions of time and other relevant time varying predictor variables. We illustrate the use of this method on a dataset of hemophiliacs where the outcome, time to seroconversion for HIV, is interval censored and left-truncated.

A Nonstationary Negative Binomial Time Series with Time-Dependent Covariates: Enterococcus Counts in Boston Harbor

Boston Harbor has had a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predictor. Without further restrictions, this function is not identifiable in the presence of time-dependent covariates; consequently we use a basis orthogonal to the space spanned by the covariates and use penalized quasi-likelihood (PQL) for estimation. We conclude that Enterococcus counts were greatly reduced near the Nut Island Treatment Plant (NITP) outfalls following the transfer of wastewaters from NITP to the Deer Island Treatment Plant (DITP) and that the transfer of wastewaters from Boston Harbor to the offshore diffusers in Massachusetts Bay reduced the Enterococcus counts near the DITP outfalls.

Survival Analysis with Large Dimensional Covariates: An Application in Microarray Studies

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time (AFT) model. Assessment of the two methods is conducted through simulation studies and through analysis of microarray data obtained from a set of patients with diffuse large B-cell lymphoma where time to survival is of interest. The approaches are shown to match or exceed the predictive performance of a Cox-based and an AFT-based variable selection method. The methods are moreover shown to be much more computationally efficient than their respective Cox- and AFT- based counterparts.

Associations between mood, anxiety or substance use disorders and inflammatory markers after adjustment for multiple covariates in a population-based study.

Inflammation is one possible mechanism underlying the associations between mental disorders and cardiovascular diseases (CVD). However, studies on mental disorders and inflammation have yielded inconsistent results and the majority did not adjust for potential confounding factors. We examined the associations of several pro-inflammatory cytokines (IL-1β, IL-6 and TNF-α) and high sensitive C-reactive protein (hsCRP) with lifetime and current mood, anxiety and substance use disorders (SUD), while adjusting for multiple covariates. The sample included 3719 subjects, randomly selected from the general population, who underwent thorough somatic and psychiatric evaluations. Psychiatric diagnoses were made with a semi-structured interview. Major depressive disorder was subtyped into "atypical", "melancholic", "combined atypical-melancholic" and "unspecified". Associations between inflammatory markers and psychiatric diagnoses were assessed using multiple linear and logistic regression models. Lifetime bipolar disorders and atypical depression were associated with increased levels of hsCRP, but not after multivariate adjustment. After multivariate adjustment, SUD remained associated with increased hsCRP levels in men (β = 0.13 (95% CI: 0.03,0.23)) but not in women. After multivariate adjustment, lifetime combined and unspecified depression were associated with decreased levels of IL-6 (β = -0.27 (-0.51,-0.02); β = -0.19 (-0.34,-0.05), respectively) and TNF-α (β = -0.16 (-0.30,-0.01); β = -0.10 (-0.19,-0.02), respectively), whereas current combined and unspecified depression were associated with decreased levels of hsCRP (β = -0.20 (-0.39,-0.02); β = -0.12 (-0.24,-0.01), respectively). Our data suggest that the significant associations between increased hsCRP levels and mood disorders are mainly attributable to the effects of comorbid disorders, medication as well as behavioral and physical CVRFs.