THE LOG-BURR XII REGRESSION MODEL FOR GROUPED SURVIVAL DATA

The log-Burr XII regression model for grouped survival data is evaluated in the presence of many ties. The methodology for grouped survival data is based on life tables, where the times are grouped in k intervals, and we fit discrete lifetime regression models to the data. The model parameters are estimated by maximum likelihood and jackknife methods. To detect influential observations in the proposed model, diagnostic measures based on case deletion, so-called global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to these measures, the total local influence and influential estimates are also used. We conduct Monte Carlo simulation studies to assess the finite sample behavior of the maximum likelihood estimators of the proposed model for grouped survival. A real data set is analyzed using a regression model for grouped data.

The impact of climate on Leptospirosis in Sao Paulo, Brazil

In this work, we correlate the daily number of human leptospirosis cases with several climatic factors. We used a negative binomial model that considers hospital daily admissions due to leptospirosis as the dependent variable, and the climatic variables of daily precipitation pattern, and maximum and minimum temperature as independent variables. We calculated the monthly leptospirosis admission probabilities from the precipitation and maximum temperature variables. The month of February showed the highest probability, although values were also high during the spring months. The month of February also showed the highest number of hospital admissions. Another interesting result is that, for every 20 mm precipitation, there was an average increase of 31.5% in hospital admissions. Additionally, the relative risk of leptospirosis varied from 1.1 to 2.0 when the precipitation varied from 20 to 140 mm.

The Poisson-exponential regression model under different latent activation schemes

In this paper, a new family of survival distributions is presented. It is derived by considering that the latent number of failure causes follows a Poisson distribution and the time for these causes to be activated follows an exponential distribution. Three different activation schemes are also considered. Moreover, we propose the inclusion of covariates in the model formulation in order to study their effect on the expected value of the number of causes and on the failure rate function. Inferential procedure based on the maximum likelihood method is discussed and evaluated via simulation. The developed methodology is illustrated on a real data set on ovarian cancer.

A log-Birnbaum-Saunders regression model with asymmetric errors

This paper introduces a skewed log-Birnbaum-Saunders regression model based on the skewed sinh-normal distribution proposed by Leiva et al. [A skewed sinh-normal distribution and its properties and application to air pollution, Comm. Statist. Theory Methods 39 (2010), pp. 426-443]. Some influence methods, such as the local influence and generalized leverage, are presented. Additionally, we derived the normal curvatures of local influence under some perturbation schemes. An empirical application to a real data set is presented in order to illustrate the usefulness of the proposed model.

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.

A log-linear regression model for the beta-Birnbaum-Saunders distribution with censored data

The beta-Birnbaum-Saunders (Cordeiro and Lemonte, 2011) and Birnbaum-Saunders (Birnbaum and Saunders, 1969a) distributions have been used quite effectively to model failure times for materials subject to fatigue and lifetime data. We define the log-beta-Birnbaum-Saunders distribution by the logarithm of the beta-Birnbaum-Saunders distribution. Explicit expressions for its generating function and moments are derived. We propose a new log-beta-Birnbaum-Saunders regression model that can be applied to censored data and be used more effectively in survival analysis. We obtain the maximum likelihood estimates of the model parameters for censored data and investigate influence diagnostics. The new location-scale regression model is modified for the possibility that long-term survivors may be presented in the data. Its usefulness is illustrated by means of two real data sets. (C) 2011 Elsevier B.V. All rights reserved.

Knowledge Flows and Networks: the Interplay between Local and Global Linkages within Bangalore IT Cluster

This doctoral work gains deeper insight into the dynamics of knowledge flows within and across clusters, unfolding their features, directions and strategic implications. Alliances, networks and personnel mobility are acknowledged as the three main channels of inter-firm knowledge flows, thus offering three heterogeneous measures to analyze the phenomenon. The interplay between the three channels and the richness of available research methods, has allowed for the elaboration of three different papers and perspectives. The common empirical setting is the IT cluster in Bangalore, for its distinguished features as a high-tech cluster and for its steady yearly two-digit growth around the service-based business model. The first paper deploys both a firm-level and a tie-level analysis, exploring the cases of 4 domestic companies and of 2 MNCs active the cluster, according to a cluster-based perspective. The distinction between business-domain knowledge and technical knowledge emerges from the qualitative evidence, further confirmed by quantitative analyses at tie-level. At firm-level, the specialization degree seems to be influencing the kind of knowledge shared, while at tie-level both the frequency of interaction and the governance mode prove to determine differences in the distribution of knowledge flows. The second paper zooms out and considers the inter-firm networks; particularly focusing on the role of cluster boundary, internal and external networks are analyzed, in their size, long-term orientation and exploration degree. The research method is purely qualitative and allows for the observation of the evolving strategic role of internal network: from exploitation-based to exploration-based. Moreover, a causal pattern is emphasized, linking the evolution and features of the external network to the evolution and features of internal network. The final paper addresses the softer and more micro-level side of knowledge flows: personnel mobility. A social capital perspective is here developed, which considers both employees’ acquisition and employees’ loss as building inter-firm ties, thus enhancing company’s overall social capital. Negative binomial regression analyses at dyad-level test the significant impact of cluster affiliation (cluster firms vs non-cluster firms), industry affiliation (IT firms vs non-IT fims) and foreign affiliation (MNCs vs domestic firms) in shaping the uneven distribution of personnel mobility, and thus of knowledge flows, among companies.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

An ordinal logistic regression model with misclassification of the outcome variable and categorical covariate

Ordinal outcomes are frequently employed in diagnosis and clinical trials. Clinical trials of Alzheimer's disease (AD) treatments are a case in point using the status of mild, moderate or severe disease as outcome measures. As in many other outcome oriented studies, the disease status may be misclassified. This study estimates the extent of misclassification in an ordinal outcome such as disease status. Also, this study estimates the extent of misclassification of a predictor variable such as genotype status. An ordinal logistic regression model is commonly used to model the relationship between disease status, the effect of treatment, and other predictive factors. A simulation study was done. First, data based on a set of hypothetical parameters and hypothetical rates of misclassification was created. Next, the maximum likelihood method was employed to generate likelihood equations accounting for misclassification. The Nelder-Mead Simplex method was used to solve for the misclassification and model parameters. Finally, this method was applied to an AD dataset to detect the amount of misclassification present. The estimates of the ordinal regression model parameters were close to the hypothetical parameters. β1 was hypothesized at 0.50 and the mean estimate was 0.488, β2 was hypothesized at 0.04 and the mean of the estimates was 0.04. Although the estimates for the rates of misclassification of X1 were not as close as β1 and β2, they validate this method. X 1 0-1 misclassification was hypothesized as 2.98% and the mean of the simulated estimates was 1.54% and, in the best case, the misclassification of k from high to medium was hypothesized at 4.87% and had a sample mean of 3.62%. In the AD dataset, the estimate for the odds ratio of X 1 of having both copies of the APOE 4 allele changed from an estimate of 1.377 to an estimate 1.418, demonstrating that the estimates of the odds ratio changed when the analysis includes adjustment for misclassification. ^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

Effects of informative censoring on the hazard function: Application to the proportional hazards regression model

The standard analyses of survival data involve the assumption that survival and censoring are independent. When censoring and survival are related, the phenomenon is known as informative censoring. This paper examines the effects of an informative censoring assumption on the hazard function and the estimated hazard ratio provided by the Cox model.^ The limiting factor in all analyses of informative censoring is the problem of non-identifiability. Non-identifiability implies that it is impossible to distinguish a situation in which censoring and death are independent from one in which there is dependence. However, it is possible that informative censoring occurs. Examination of the literature indicates how others have approached the problem and covers the relevant theoretical background.^ Three models are examined in detail. The first model uses conditionally independent marginal hazards to obtain the unconditional survival function and hazards. The second model is based on the Gumbel Type A method for combining independent marginal distributions into bivariate distributions using a dependency parameter. Finally, a formulation based on a compartmental model is presented and its results described. For the latter two approaches, the resulting hazard is used in the Cox model in a simulation study.^ The unconditional survival distribution formed from the first model involves dependency, but the crude hazard resulting from this unconditional distribution is identical to the marginal hazard, and inferences based on the hazard are valid. The hazard ratios formed from two distributions following the Gumbel Type A model are biased by a factor dependent on the amount of censoring in the two populations and the strength of the dependency of death and censoring in the two populations. The Cox model estimates this biased hazard ratio. In general, the hazard resulting from the compartmental model is not constant, even if the individual marginal hazards are constant, unless censoring is non-informative. The hazard ratio tends to a specific limit.^ Methods of evaluating situations in which informative censoring is present are described, and the relative utility of the three models examined is discussed. ^

Gender disparities in utilization, unmet need and expenditure for mental health care

Objectives: To compare mental health care utilization regarding the source, types, and intensity of mental health services received, unmet need for services, and out of pocket cost among non-institutionalized psychologically distressed women and men. ^ Method: Cross-sectional data for 19,325 non-institutionalized mentally distressed adult respondents to the “The National Survey on Drug Use and Health” (NSDUH), for the years 2006 -2008, representing over twenty-nine millions U.S. adults was analyzed. To assess the relative odds for women compared to men, logistic regression analysis was used for source of service, for types of barriers, for unmet need and cost; zero inflated negative binomial regression for intensity of utilization; and ordinal logistic regression analysis for quantifying out-of-pocket expenditure. ^ Results: Overall, 43% of mentally distressed adults utilized a form of mental health treatment; representing 12.6 million U.S psychologically distressed adults. Females utilized more mental health care compared to males in the previous 12 months (OR: 1. 70; 95% CI: 1.54, 1.83). Similarly, females were 54% more likely to get help for psychological distress in an outpatient setting and females were associated with an increased probability of using medication for mental distress (OR: 1.72; 95% CI: 1.63, 1.98). Women were 1.25 times likelier to visit a mental health center (specialty care) than men. ^ Females were positively associated with unmet needs (OR: 1.50; 95% CI: 1.29, 1.75) after taking into account predisposing, enabling, and need (PEN) characteristics. Women with perceived unmet needs were 23% (OR: 0.77; 95% CI: 0.59, 0.99) less likely than men to report societal accommodation (stigma) as a barrier to mental health care. At any given cutoff point, women were 1.74 times likelier to be in the higher payment categories for inpatient out of pocket cost when other variables in the model are held constant. Conclusions: Women utilize more specialty mental healthcare, report more unmet need, and pay more inpatient out of pocket costs than men. These gender disparities exist even after controlling for predisposing, enabling, and need variables. Creating policies that not only provide mental health care access but also de-stigmatize mental illness will bring us one step closer to eliminating gender disparities in mental health care.^