Assessing influence in survival data with a cure fraction and covariates

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage were derived, analyzed and discussed in survival data with a cure fraction and covariates. The relevance of the approach was illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data is changed.

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model.

Influence diagnostics for polyhazard models in the presence of covariates

In this paper, we present various diagnostic methods for polyhazard models. Polyhazard models are a flexible family for fitting lifetime data. Their main advantage over the single hazard models, such as the Weibull and the log-logistic models, is to include a large amount of nonmonotone hazard shapes, as bathtub and multimodal curves. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. A discussion of the computation of the likelihood displacement as well as the normal curvature in the local influence method are presented. Finally, an example with real data is given for illustration.

Comparing the performance of geostatistical models with additional information from covariates for sewage plume characterization

In this work, kriging with covariates is used to model and map the spatial distribution of salinity measurements gathered by an autonomous underwater vehicle in a sea outfall monitoring campaign aiming to distinguish the effluent plume from the receiving waters and characterize its spatial variability in the vicinity of the discharge. Four different geostatistical linear models for salinity were assumed, where the distance to diffuser, the west-east positioning, and the south-north positioning were used as covariates. Sample variograms were fitted by the Mat`ern models using weighted least squares and maximum likelihood estimation methods as a way to detect eventual discrepancies. Typically, the maximum likelihood method estimated very low ranges which have limited the kriging process. So, at least for these data sets, weighted least squares showed to be the most appropriate estimation method for variogram fitting. The kriged maps show clearly the spatial variation of salinity, and it is possible to identify the effluent plume in the area studied. The results obtained show some guidelines for sewage monitoring if a geostatistical analysis of the data is in mind. It is important to treat properly the existence of anomalous values and to adopt a sampling strategy that includes transects parallel and perpendicular to the effluent dispersion.

Oestrogen replacement treatment and the risk of endometrial cancer : an assessment of the role of covariates

The relationship between oestrogen replacement treatment and the risk of endometrial cancer was analysed in a case-control study of 158 histologically confirmed incident cases below the age of 75 and 468 controls in hospital for acute, non-neoplastic, non-hormone-related conditions conducted in the Swiss Canton of Vaud in 1988-1992. Overall, 60 (38%) cases vs. 93 (20%) controls had ever used oestrogen replacement treatment: the corresponding multiple logistic regression relative risk (RR) was 2.7 (95% confidence interval, CI: 1.7-4.1). The risk was directly related to duration of use, and rose to 5.1 (95% CI: 2.7-9.8) for > 5 year-use. The RR was still significantly elevated 10 or more years after stopping use (RR = 2.3, 95% CI: 1.2-4.5). When the role of covariates was considered, a significant interaction was observed with body mass index (RR for long-term oestrogen use = 6.0 for lean or normal weight women vs. 2.4 for overweight women). There was also a hint of a negative interaction with oral contraceptive (OC) use, since the RR for oestrogens was higher (or restricted) to women who had never used OC (RR = 5.4, for long-term oestrogen use), as compared with those who had used OC, who showed no significant evidence of association with oestrogens (RR = 0.9 for long-term use). There was no significant interaction with cigarette smoking. Thus, this study confirms the presence of a strong association between oestrogen replacement treatment and endometrial cancer risk, since in the late 1980s or early 1990s about 25% of cases could be attributed to oestrogen replacement treatment in this Swiss population. Further, it confirms the presence of significant negative interactions of oestrogen use with obesity, and, possibly, with OC as well.

Robust parametric indirect estimates of the expected cost of a hospital stay with covariates and censored data.

We consider the problem of estimating the mean hospital cost of stays of a class of patients (e.g., a diagnosis-related group) as a function of patient characteristics. The statistical analysis is complicated by the asymmetry of the cost distribution, the possibility of censoring on the cost variable, and the occurrence of outliers. These problems have often been treated separately in the literature, and a method offering a joint solution to all of them is still missing. Indirect procedures have been proposed, combining an estimate of the duration distribution with an estimate of the conditional cost for a given duration. We propose a parametric version of this approach, allowing for asymmetry and censoring in the cost distribution and providing a mean cost estimator that is robust in the presence of extreme values. In addition, the new method takes covariate information into account.

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.

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

The objetive of this work was to evaluate the influence of intergenotypic competition in open-pollinated families of Eucalyptus and its effects on early selection efficiency. Two experiments were carried out, in which the timber volume was evaluated at three ages, in a randomized complete block design. Data from the three years of evaluation (experiment 1, at 2, 4, and 7 years; and experiment 2, at 2, 5, and 7 years) were analyzed using mixed models. The following were estimated: variance components, genetic parameters, selection gains, effective number, early selection efficiency, selection gain per unit time, and coincidence of selection with and without the use of competition covariates. Competition effect was nonsignificant for ages under three years, and adjustment using competition covariates was unnecessary. Early selection for families is effective; families that have a late growth spurt are more vulnerable to competition, which markedly impairs ranking at the end of the cycle. Early selection is efficient according to all adopted criteria, and the age of around three years is the most recommended, given the high efficiency and accuracy rate in the indication of trees and families. The addition of competition covariates at the end of the cycle improves early selection efficiency for almost all studied criteria.

Family-based association analysis with ordered categorical phenotypes, covariates and interactions

Genetic association analyses of family-based studies with ordered categorical phenotypes are often conducted using methods either for quantitative or for binary traits, which can lead to suboptimal analyses. Here we present an alternative likelihood-based method of analysis for single nucleotide polymorphism (SNP) genotypes and ordered categorical phenotypes in nuclear families of any size. Our approach, which extends our previous work for binary phenotypes, permits straightforward inclusion of covariate, gene-gene and gene-covariate interaction terms in the likelihood, incorporates a simple model for ascertainment and allows for family-specific effects in the hypothesis test. Additionally, our method produces interpretable parameter estimates and valid confidence intervals. We assess the proposed method using simulated data, and apply it to a polymorphism in the c-reactive protein (CRP) gene typed in families collected to investigate human systemic lupus erythematosus. By including sex interactions in the analysis, we show that the polymorphism is associated with anti-nuclear autoantibody (ANA) production in females, while there appears to be no effect in males.

Meta-analysis: a unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality

OBJECTIVES: This contribution provides a unifying concept for meta-analysis integrating the handling of unobserved heterogeneity, study covariates, publication bias and study quality. It is important to consider these issues simultaneously to avoid the occurrence of artifacts, and a method for doing so is suggested here. METHODS: The approach is based upon the meta-likelihood in combination with a general linear nonparametric mixed model, which lays the ground for all inferential conclusions suggested here. RESULTS: The concept is illustrated at hand of a meta-analysis investigating the relationship of hormone replacement therapy and breast cancer. The phenomenon of interest has been investigated in many studies for a considerable time and different results were reported. In 1992 a meta-analysis by Sillero-Arenas et al. concluded a small, but significant overall effect of 1.06 on the relative risk scale. Using the meta-likelihood approach it is demonstrated here that this meta-analysis is due to considerable unobserved heterogeneity. Furthermore, it is shown that new methods are available to model this heterogeneity successfully. It is argued further to include available study covariates to explain this heterogeneity in the meta-analysis at hand. CONCLUSIONS: The topic of HRT and breast cancer has again very recently become an issue of public debate, when results of a large trial investigating the health effects of hormone replacement therapy were published indicating an increased risk for breast cancer (risk ratio of 1.26). Using an adequate regression model in the previously published meta-analysis an adjusted estimate of effect of 1.14 can be given which is considerably higher than the one published in the meta-analysis of Sillero-Arenas et al. In summary, it is hoped that the method suggested here contributes further to a good meta-analytic practice in public health and clinical disciplines.

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.