Individual prediction of automobile bodily injury claims liabilities

[spa] La mayoría de siniestros con daños corporales se liquidan mediante negociación, llegando a juicio menos del 5% de los casos. Una estrategia de negociación bien definida es, por tanto, fundamental para las compañías aseguradoras. En este artículo asumimos que la compensación monetaria concedida en juicio es la máxima cuantía que debería ser ofrecida por el asegurador en el proceso de negociación. Usando una base de datos real, implementamos un modelo log-lineal para estimar la máxima oferta de negociación. Perturbaciones no-esféricas son detectadas. Correlación ocurre cuando más de una siniestro se liquida en la misma sentencia judicial. Heterocedasticidad por grupos se debe a la influencia de la valoración del forense en la indemnización final.

Problematic Internet use is associated with substance use in young adolescents.

AIM: This study examined whether problematic Internet use was associated with substance use among young adolescents and assessed whether this association accounted for the use of tobacco, alcohol, cannabis and other drugs. METHODS: Using the Internet Addiction Test, we divided a representative sample of 3067 adolescents in Switzerland (mean age 14 years) into regular and problematic Internet users. We performed a bivariate analysis and two logistic regression models, to analyse substances separately and simultaneously, and developed a log-linear model to define the associations between significant variables. RESULTS: Problematic Internet users were more likely to be female, to use substances, to come from nonintact families, to report poor emotional well-being and to be below average students. The first model showed significant associations between problematic users and each substance, with adjusted odds ratios of 2.05 for tobacco, 1.72 for alcohol, 1.94 for cannabis and 2.73 for other drugs. Only smoking remained significant in the second model, with an adjusted odds ratio of 1.71. CONCLUSION: Problematic Internet use is associated with other risky behaviours and may be an important early predictor of adolescent substance use. Therefore, it should be included in the psychosocial screening of adolescents.

Parent-adolescent relationship in youths with a chronic condition.

BACKGROUND: Suffering from a chronic disease or disability (CDD) during adolescence can be a burden for both the adolescents and their parents. The aim of the present study is to assess how living with a CDD during adolescence, the quality of parent-adolescent relationship (PAR) and the adolescent's psychosocial development interact with each other. METHODS: Using the Swiss Multicenter Adolescent Survey on Health 2002 (SMASH02) database, we compared adolescents aged 16-20 years with a CDD (n = 760) with their healthy peers (n = 6493) on sociodemographics, adolescents' general and psychosocial health, interparental relationship and PAR. RESULTS: Bivariate analyses showed that adolescents with a CDD had a poorer psychosocial health and a more difficult relationship with their parents. The log-linear model indirectly linked CDD and poor PAR through four variables: two of the adolescents' psychosocial health variables (suicide attempt and sensation seeking), the need for help regarding difficulties with parents and a highly educated mother that acted as a protective factor, allowing for a better parent-adolescent with a CDD relationship. CONCLUSION: It is essential for health professionals taking care of adolescents with a CDD to distinguish between issues in relation with the CDD from other psychosocial difficulties, in order to help these adolescents and their parents deal with them appropriately and thus maintain a healthy PAR.

Forecasting the maximum compensation offer in the automobile BI claims negotiation process

Most motor bodily injury (BI) claims are settled by negotiation, with fewer than 5% of cases going to court. A well-defined negotiation strategy is thus very useful for insurance companies. In this paper we assume that the monetary compensation awarded in court is the upper amount to be offered by the insurer in the negotiation process. Using a real database, a log-linear model is implemented to estimate the maximal offer. Non-spherical disturbances are detected. Correlation occurs when various claims are settled in the same judicial verdict. Group wise heteroscedasticity is due to the influence of the forensic valuation on the final compensation amount. An alternative approximation based on generalized inference theory is applied to estimate confidence intervals on variance components, since classical interval estimates may be unreliable for datasets with unbalanced structures.

Comparing diagnostic tests with missing data

When missing data occur in studies designed to compare the accuracy of diagnostic tests, a common, though naive, practice is to base the comparison of sensitivity, specificity, as well as of positive and negative predictive values on some subset of the data that fits into methods implemented in standard statistical packages. Such methods are usually valid only under the strong missing completely at random (MCAR) assumption and may generate biased and less precise estimates. We review some models that use the dependence structure of the completely observed cases to incorporate the information of the partially categorized observations into the analysis and show how they may be fitted via a two-stage hybrid process involving maximum likelihood in the first stage and weighted least squares in the second. We indicate how computational subroutines written in R may be used to fit the proposed models and illustrate the different analysis strategies with observational data collected to compare the accuracy of three distinct non-invasive diagnostic methods for endometriosis. The results indicate that even when the MCAR assumption is plausible, the naive partial analyses should be avoided.

Birnbaum-Saunders nonlinear regression models

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [Rieck, J.R., Nedelman, J.R., 1991. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33, 51-60]. We discuss maximum-likelihood estimation for the parameters of the model, and derive closed-form expressions for the second-order biases of these estimates. Our formulae are easily computed as ordinary linear regressions and are then used to define bias corrected maximum-likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Two empirical applications are analysed and discussed. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Preparação e carcterização de complexos multicomponentes contendo ciclodextrinas e benznidazol

The benznidazole (BNZ) is the only alternative for Chagas disease treatment in Brazil. This drug has low solubility, which restricts its dissolution rate. Thus, the present work aimed to study the BNZ interactions in binary systems with beta cyclodextrin (β-CD) and hydroxypropyl-beta cyclodextrin (HP-β-CD), in order to increase the apparent aqueous solubility of drug. The influence of seven hydrophilic polymers, triethanolamine (TEA) and 1-methyl-2- pyrrolidone (NMP) in benznidazole apparent aqueous solubility, as well as the formation of inclusion complexes was also investigated. The interactions in solution were predicted and investigated using phase solubility diagram methodology, nuclear magnetic resonance of protons (RMN) and molecular modeling. Complexes were obtained in solid phase by spray drying and physicochemical characterization included the UV-Vis spectrophotometric spectroscopy in the infrared region, scanning electron microscopy, X-ray diffraction and dissolution drug test from the different systems. The increment on apparent aqueous solubility of drug was achieved with a linear type (AL) in presence of both cyclodextrins at different pH values. The hydrophilic polymers and 1-methyl-2-pyrrolidone contributes to the formation of inclusion complexes, while the triethanolamine decreased the complex stability constant (Kc). The log-linear model applied for solubility diagrams revealed that both triethanolamine and 1-methyl-2-pyrrolidone showed an action cosolvent (both solvents) and complexing (1-methyl-2-pyrrolidone). The best results were obtained with complexes involving 1-methyl-2-pyrrolidone and hydroxypropylbeta- cyclodextrin, with an increased of benznidazole solubility in 27.9 and 9.4 times, respectively. The complexes effectiveness was proven by dissolution tests, in which the ternary complexes and physical mixtures involving 1-methyl- 2-pyrrolidone and both cyclodextrins investigated showed better results, showing the potential use as novel pharmaceutical ingredient, that leads to increased benznidazole bioavailability

Temporal Trends of Asthma Mortality Rates in Brazil from 1980 to 2010

Objective. Mortality from asthma has varied among countries during the last several decades. This study aimed to identify temporal trends of asthma mortality in Brazil from 1980 to 2010. Method. We analyzed 6840 deaths of patients aged 5-34 years that occurred in Brazil with the underlying cause of asthma. We applied a log-linear model using Poisson regression to verify peaks and trends. We also calculated the point estimation and 95% confidence interval (CI 95%) of the annual percent change (APC) of the mortality rates, and the average annual percent change (AAPC) for 2001-2010. Results. A decline was observed from 1980 to 1992 [APC = -3.4 (-5.0 to -1.8)], followed by a nonsignificant rise until 1996 [APC = 6.8 (-1.4 to 15.6)], and a new downward trend from 1997 to 2010 [APC = -2.7 (-3.9 to -1.6)]. The APCs varied according to age strata: 5-14 years from 1980 to 2010 [-0.3 (-1.1 to 0.5)]; 15-24 years from 1980 to 1991 [-2.1 (-5.0 to 0.9)], from 1992 to 1996 [6.8 (-6.7 to 22.2)], and from 1997 to 2010 [-3.9 (-5.7 to -2.0)]; 24-25 years from 1980 to 1992 [-2.5 (-4.6 to -0.3)], from 1993 to 1995 [12.0 (-21.1 to 59.1)], and from 1996-2010 [-1.7 (-3.0 to -0.4)]. AAPC from 2001 to 2010 was -1.7 (-3.0 to -0.4); the decline for this period was significant for patients over 15 years old, women, and those living in the Southeast region. Conclusion. Asthma mortality rates in Brazil have been declining since the late 1990s.

DECOMPOSITION OF REGRESSION ESTIMATORS TO EXPLORE THE INFLUENCE OF "UNMEASURED" TIME-VARYING CONFOUNDERS

In environmental epidemiology, exposure X and health outcome Y vary in space and time. We present a method to diagnose the possible influence of unmeasured confounders U on the estimated effect of X on Y and to propose several approaches to robust estimation. The idea is to use space and time as proxy measures for the unmeasured factors U. We start with the time series case where X and Y are continuous variables at equally-spaced times and assume a linear model. We define matching estimator b(u)s that correspond to pairs of observations with specific lag u. Controlling for a smooth function of time, St, using a kernel estimator is roughly equivalent to estimating the association with a linear combination of the b(u)s with weights that involve two components: the assumptions about the smoothness of St and the normalized variogram of the X process. When an unmeasured confounder U exists, but the model otherwise correctly controls for measured confounders, the excess variation in b(u)s is evidence of confounding by U. We use the plot of b(u)s versus lag u, lagged-estimator-plot (LEP), to diagnose the influence of U on the effect of X on Y. We use appropriate linear combination of b(u)s or extrapolate to b(0) to obtain novel estimators that are more robust to the influence of smooth U. The methods are extended to time series log-linear models and to spatial analyses. The LEP plot gives us a direct view of the magnitude of the estimators for each lag u and provides evidence when models did not adequately describe the data.

Reliability analysis of encapsulation methods for lead -based paint through an accelerated life testing

The adverse health effects of long-term exposure to lead are well established, with major uptake into the human body occurring mainly through oral ingestion by young children. Lead-based paint was frequently used in homes built before 1978, particularly in inner-city areas. Minority populations experience the effects of lead poisoning disproportionately. ^ Lead-based paint abatement is costly. In the United States, residents of about 400,000 homes, occupied by 900,000 young children, lack the means to correct lead-based paint hazards. The magnitude of this problem demands research on affordable methods of hazard control. One method is encapsulation, defined as any covering or coating that acts as a permanent barrier between the lead-based paint surface and the environment. ^ Two encapsulants were tested for reliability and effective life span through an accelerated lifetime experiment that applied stresses exceeding those encountered under normal use conditions. The resulting time-to-failure data were used to extrapolate the failure time under conditions of normal use. Statistical analysis and models of the test data allow forecasting of long-term reliability relative to the 20-year encapsulation requirement. Typical housing material specimens simulating walls and doors coated with lead-based paint were overstressed before encapsulation. A second, un-aged set was also tested. Specimens were monitored after the stress test with a surface chemical testing pad to identify the presence of lead breaking through the encapsulant. ^ Graphical analysis proposed by Shapiro and Meeker and the general log-linear model developed by Cox were used to obtain results. Findings for the 80% reliability time to failure varied, with close to 21 years of life under normal use conditions for encapsulant A. The application of product A on the aged gypsum and aged wood substrates yielded slightly lower times. Encapsulant B had an 80% reliable life of 19.78 years. ^ This study reveals that encapsulation technologies can offer safe and effective control of lead-based paint hazards and may be less expensive than other options. The U.S. Department of Health and Human Services and the CDC are committed to eliminating childhood lead poisoning by 2010. This ambitious target is feasible, provided there is an efficient application of innovative technology, a goal to which this study aims to contribute. ^

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Work-to-family spillover: Gender differences in Hungary

It is crucial to understand the role that labor market positions might play in creating gender differences in work–life balance. One theoretical approach to understanding this relationship is the spillover theory. The spillover theory argues that an individual’s life domains are integrated; meaning that well-being can be transmitted between life domains. Based on data collected in Hungary in 2014, this paper shows that work-to-family spillover does not affect both genders the same way. The effect of work on family life tends to be more negative for women than for men. Two explanations have been formulated in order to understand this gender inequality. According to the findings of the analysis, gender is conditionally independent of spillover if financial status and flexibility of work are also incorporated into the analysis. This means that the relative disadvantage for women in terms of spillover can be attributed to their lower financial status and their relatively low access to flexible jobs. In other words, the gender inequalities in work-to-family spillover are deeply affected by individual labor market positions. The observation of the labor market’s effect on work–life balance is especially important in Hungary since Hungary has one of the least flexible labor arrangements in Europe. A marginal log-linear model, which is a method for categorical multivariate analysis, has been applied in this analysis.

Development of error correction techniques for nitrate-N load estimation models

Excess nutrient loads carried by streams and rivers are a great concern for environmental resource managers. In agricultural regions, excess loads are transported downstream to receiving water bodies, potentially causing algal blooms, which could lead to numerous ecological problems. To better understand nutrient load transport, and to develop appropriate water management plans, it is important to have accurate estimates of annual nutrient loads. This study used a Monte Carlo sub-sampling method and error-corrected statistical models to estimate annual nitrate-N loads from two watersheds in central Illinois. The performance of three load estimation methods (the seven-parameter log-linear model, the ratio estimator, and the flow-weighted averaging estimator) applied at one-, two-, four-, six-, and eight-week sampling frequencies were compared. Five error correction techniques; the existing composite method, and four new error correction techniques developed in this study; were applied to each combination of sampling frequency and load estimation method. On average, the most accurate error reduction technique, (proportional rectangular) resulted in 15% and 30% more accurate load estimates when compared to the most accurate uncorrected load estimation method (ratio estimator) for the two watersheds. Using error correction methods, it is possible to design more cost-effective monitoring plans by achieving the same load estimation accuracy with fewer observations. Finally, the optimum combinations of monitoring threshold and sampling frequency that minimizes the number of samples required to achieve specified levels of accuracy in load estimation were determined. For one- to three-weeks sampling frequencies, combined threshold/fixed-interval monitoring approaches produced the best outcomes, while fixed-interval-only approaches produced the most accurate results for four- to eight-weeks sampling frequencies.

Censored Linear Regression Models For Irregularly Observed Longitudinal Data Using The Multivariate-t Distribution.

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

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.