A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

Survival, population pize, and gonotrophic cycle duration of Nyssomyia neivai (Diptera: Psychodidae) at an endemic area of American Cutaneous Leishmaniasis in Southeastern Brazil

The survival, absolute population size, gonotrophic cycle duration, and temporal and spatial abundance of Nyssomyia neivai (Pinto) were studied in a rural area endemic for American cutaneous leishmaniasis (ACL) in Conchal, Sõo Paulo State, southeastern Brazil, using mark-release-recapture techniques and by monitoring population fluctuation. The monthly abundance exhibited a unimodal pattern, with forest and domicile habitats having the highest relative abundances. A total of 1,873 males and 3,557 females were marked and released during the six experiments, of which 4.1-13.0 per cent of males and 4.1-11.8 per cent of females were recaptured. Daily survivorship estimated from the decline in recaptures per day was 0.681 for males and 0.667 for females. Gonotrophic cycle duration was estimated to be 4.0 d. Absolute population size was calculated using the Lincoln Index and ranged from 861 to 4,612 males and from 2,187 to 19,739 females. The low proportion of females that reach the age when they are potentially infective suggests that N. neivai has a low biological capacity to serve as a vector and that factors such as high biting rates and opportunistic feeding behavior would be needed to enable Leishmania (Viannia) braziliensis Vianna transmission. This agreed with the epidemiological pattern of ACL in southeastern Brazil that is characterized by low incidence, with isolated cases acquired principally within domiciliary habitats

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.

Functional microarray analysis suggests repressed cell-cell signaling and cell survival-related modules inhibit progression of head and neck squamous cell carcinoma

Background: Cancer shows a great diversity in its clinical behavior which cannot be easily predicted using the currently available clinical or pathological markers. The identification of pathways associated with lymph node metastasis (N+) and recurrent head and neck squamous cell carcinoma (HNSCC) may increase our understanding of the complex biology of this disease. Methods: Tumor samples were obtained from untreated HNSCC patients undergoing surgery. Patients were classified according to pathologic lymph node status (positive or negative) or tumor recurrence (recurrent or non-recurrent tumor) after treatment (surgery with neck dissection followed by radiotherapy). Using microarray gene expression, we screened tumor samples according to modules comprised by genes in the same pathway or functional category. Results: The most frequent alterations were the repression of modules in negative lymph node (N0) and in non-recurrent tumors rather than induction of modules in N+ or in recurrent tumors. N0 tumors showed repression of modules that contain cell survival genes and in non-recurrent tumors cell-cell signaling and extracellular region modules were repressed. Conclusions: The repression of modules that contain cell survival genes in N0 tumors reinforces the important role that apoptosis plays in the regulation of metastasis. In addition, because tumor samples used here were not microdissected, tumor gene expression data are represented together with the stroma, which may reveal signaling between the microenvironment and tumor cells. For instance, in non-recurrent tumors, extracellular region module was repressed, indicating that the stroma and tumor cells may have fewer interactions, which disable metastasis development. Finally, the genes highlighted in our analysis can be implicated in more than one pathway or characteristic, suggesting that therapeutic approaches to prevent tumor progression should target more than one gene or pathway, specially apoptosis and interactions between tumor cells and the stroma.

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.

Log-modified Weibull regression models with censored data: Sensitivity and residual analysis

This paper proposes a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and we also present some ways to perform global influence. Besides, for different parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the modified deviance residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for a martingale-type residual in log-modified Weibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the modified deviance residual are performed to select appropriate models. (c) 2008 Elsevier B.V. All rights reserved.

Spatial portability of numerical models of leaf wetness duration based on empirical approaches

Leaf wetness duration (LWD) models based on empirical approaches offer practical advantages over physically based models in agricultural applications, but their spatial portability is questionable because they may be biased to the climatic conditions under which they were developed. In our study, spatial portability of three LWD models with empirical characteristics - a RH threshold model, a decision tree model with wind speed correction, and a fuzzy logic model - was evaluated using weather data collected in Brazil, Canada, Costa Rica, Italy and the USA. The fuzzy logic model was more accurate than the other models in estimating LWD measured by painted leaf wetness sensors. The fraction of correct estimates for the fuzzy logic model was greater (0.87) than for the other models (0.85-0.86) across 28 sites where painted sensors were installed, and the degree of agreement k statistic between the model and painted sensors was greater for the fuzzy logic model (0.71) than that for the other models (0.64-0.66). Values of the k statistic for the fuzzy logic model were also less variable across sites than those of the other models. When model estimates were compared with measurements from unpainted leaf wetness sensors, the fuzzy logic model had less mean absolute error (2.5 h day(-1)) than other models (2.6-2.7 h day(-1)) after the model was calibrated for the unpainted sensors. The results suggest that the fuzzy logic model has greater spatial portability than the other models evaluated and merits further validation in comparison with physical models under a wider range of climate conditions. (C) 2010 Elsevier B.V. All rights reserved.

Does using stepwise variable selection to build sequential path analysis models make sense?

Causal inference methods - mainly path analysis and structural equation modeling - offer plant physiologists information about cause-and-effect relationships among plant traits. Recently, an unusual approach to causal inference through stepwise variable selection has been proposed and used in various works on plant physiology. The approach should not be considered correct from a biological point of view. Here, it is explained why stepwise variable selection should not be used for causal inference, and shown what strange conclusions can be drawn based upon the former analysis when one aims to interpret cause-and-effect relationships among plant traits.

Benefit of antiretroviral therapy on survival of human immunodeficiency virus-infected patients admitted to an intensive care unit

Objective: To evaluate the impact of antiretroviral therapy (ART) and the prognostic factors for in-intensive care unit (ICU) and 6-month mortality in human immunodeficiency virus (HIV)-infected patients. Design: A retrospective cohort study was conducted in patients admitted to the ICU from 1996 through 2006. The follow-up period extended for 6 months after ICU admission. Setting: The ICU of a tertiary-care teaching hospital at the Universidade de Sao Paulo, Brazil. Participants: A total of 278 HIV-infected patients admitted to the ICU were selected. We excluded ICU readmissions (37), ICU admissions who stayed less than 24 hours (44), and patients with unavailable medical charts (36). Outcome Measure: In-ICU and 6-month mortality. Main Results: Multivariate logistic regression analysis and Cox proportional hazards models demonstrated that the variables associated with in-ICU and 6-month mortality were sepsis as the cause of admission (odds ratio [OR] = 3.16 [95% confidence interval [CI] 1.65-6.06]); hazards ratio [HR] = 1.37 [95% Cl 1.01-1.88)), an Acute Physiology and Chronic Health Evaluation 11 score >19 [OR = 2.81 (95% CI 1.57-5.04); HR = 2.18 (95% CI 1.62-2.94)], mechanical ventilation during the first 24 hours [OR = 3.92 (95% CI 2.20-6.96); HR = 2.25 (95% CI 1.65-3.07)], and year of ICU admission [OR = 0.90 (95% CI 0.81-0.99); HR = 0.92 [95% CI 0.87-0.97)]. CD4 T-cell count <50 cells/mm(3) Was only associated with ICU mortality [OR = 2.10 (95% Cl 1.17-3.76)]. The use of ART in the ICU was negatively predictive of 6-month mortality in the Cox model [HR = 0.50 (95% CI 0.35-0.71)], especially if this therapy was introduced during the first 4 days of admission to the ICU [HR = 0.58 (95% CI 0.41-0.83)]. Regarding HIV-infected patients admitted to ICU without using ART, those who have started this treatment during ICU, stay presented a better prognosis when time and potential confounding factors were adjusted for [HR 0.55 (95% CI 0.31-0.98)]. Conclusions: The ICU outcome of HIV-infected patients seems to be dependent not only on acute illness severity, but also on the administration of antiretroviral treatment. (Crit Care Med 2009; 37: 1605-1611)

Squamous Cell Carcinoma of the Tongue and Floor of the Mouth: Analysis of Survival Rate and Independent Prognostic Factors in the Amazon Region

Oral squamous cell carcinoma (OSCC) accounts for more than 95% of all malignant neoplasms in the oral cavity. Although several studies have shown the epidemiology of this cancer in Brazil, there do not seem to be any studies that describe the prognostic factors related to OSCC in the Amazon region. Therefore, the aim of this study was to determine the survival rate and prognostic significance of different factors in patients from this region affected by OSCC. Data from 85 patients with histologically confirmed squamous cell carcinoma of the tongue and floor of the mouth identified from the Ofir Loyola Hospital archives were collected and analyzed using univariate (log-rank test) and multivariate (Cox proportional hazard model) tests. The overall 5-year survival rate was found to be 27%. Univariate analysis showed that the 5-year survival rate was significantly higher for younger (<= 45 y) female patients, patients with T1-2 tumors and clinically clear neck nodes (N0), patients with early stage cancers (AJCC stage I-II), and patients treated with surgical procedures. However, multivariate analysis showed that the 5-year survival rate was significantly higher only in the younger patients and those who underwent surgical treatment. The age of the patient at the moment of diagnosis and treatment with surgical procedures were the only independent prognostic factors that affected the 5-year survival rate of the patients in this region.

Survival, Population Size, and Gonotrophic Cycle Duration of Nyssomyia neivai (Diptera: Psychodidae) at an Endemic Area of American Cutaneous Leishmaniasis in Southeastern Brazil

The survival, absolute population size, gonotrophic cycle duration, and temporal and spatial abundance of Nyssomyia neivai (Pinto) were studied in a rural area endemic for American cutaneous leishmaniasis (ACL) in Conchal, Sao Paulo State, southeastern Brazil, using mark-release-recapture techniques and by monitoring population fluctuation. The monthly abundance exhibited a unimodal pattern, with forest and domicile habitats having the highest relative abundances. A total of 1,873 males and 3,557 females were marked and released during the six experiments, of which 4.1-13.0% of males and 4.1-11.8% of females were recaptured. Daily survivorship estimated from the decline in recaptures per day was 0.681 for males and 0.667 for females. Gonotrophic cycle duration was estimated to be 4.0 d. Absolute population size was calculated using the Lincoln Index and ranged from 861 to 4,612 males and from 2,187 to 19,739 females. The low proportion of females that reach the age when they are potentially infective suggests that N. neivai has a low biological capacity to serve as a vector and that factors such as high biting rates and opportunistic feeding behavior would be needed to enable Leishmania (Viannia) braziliensis Vianna transmission. This agreed with the epidemiological pattern of ACL in southeastern Brazil that is characterized by low incidence, with isolated cases acquired principally within domiciliary habitats.

Bayesian analysis and constraints on kinematic models from union SNIa

The kinematic expansion history of the universe is investigated by using the 307 supernovae type Ia from the Union Compilation set. Three simple model parameterizations for the deceleration parameter ( constant, linear and abrupt transition) and two different models that are explicitly parametrized by the cosmic jerk parameter ( constant and variable) are considered. Likelihood and Bayesian analyses are employed to find best fit parameters and compare models among themselves and with the flat Lambda CDM model. Analytical expressions and estimates for the deceleration and cosmic jerk parameters today (q(0) and j(0)) and for the transition redshift (z(t)) between a past phase of cosmic deceleration to a current phase of acceleration are given. All models characterize an accelerated expansion for the universe today and largely indicate that it was decelerating in the past, having a transition redshift around 0.5. The cosmic jerk is not strongly constrained by the present supernovae data. For the most realistic kinematic models the 1 sigma confidence limits imply the following ranges of values: q(0) is an element of [-0.96, -0.46], j(0) is an element of [-3.2,-0.3] and z(t) is an element of [0.36, 0.84], which are compatible with the Lambda CDM predictions, q(0) = -0.57 +/- 0.04, j(0) = -1 and z(t) = 0.71 +/- 0.08. We find that even very simple kinematic models are equally good to describe the data compared to the concordance Lambda CDM model, and that the current observations are not powerful enough to discriminate among all of them.

Destructive weighted Poisson cure rate models

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow a compound weighted Poisson distribution. This model is more flexible in terms of dispersion than the promotion time cure model. Moreover, it gives an interesting and realistic interpretation of the biological mechanism of the occurrence of event of interest as it includes a destructive process of the initial risk factors in a competitive scenario. In other words, what is recorded is only from the undamaged portion of the original number of risk factors.

COM-Poisson cure rate survival models and an application to a cutaneous melanoma data

In this paper, we develop a flexible cure rate survival model by assuming the number of competing causes of the event of interest to follow the Conway-Maxwell Poisson distribution. This model includes as special cases some of the well-known cure rate models discussed in the literature. Next, we discuss the maximum likelihood estimation of the parameters of this cure rate survival model. Finally, we illustrate the usefulness of this model by applying it to a real cutaneous melanoma data. (C) 2009 Elsevier B.V. All rights reserved.