A semiparametric approach to hidden Markov models under longitudinal observations

We propose a hidden Markov model for longitudinal count data where sources of unobserved heterogeneity arise, making data overdispersed. The observed process, conditionally on the hidden states, is assumed to follow an inhomogeneous Poisson kernel, where the unobserved heterogeneity is modeled in a generalized linear model (GLM) framework by adding individual-specific random effects in the link function. Due to the complexity of the likelihood within the GLM framework, model parameters may be estimated by numerical maximization of the log-likelihood function or by simulation methods; we propose a more flexible approach based on the Expectation Maximization (EM) algorithm. Parameter estimation is carried out using a non-parametric maximum likelihood (NPML) approach in a finite mixture context. Simulation results and two empirical examples are provided.     

A simple two-stage design for quantitative responses with application to a study in diabetic neuropathic pain

Two-stage designs offer substantial advantages for early phase II studies. The interim analysis following the first stage allows the study to be stopped for futility, or more positively, it might lead to early progression to the trials needed for late phase II and phase III. If the study is to continue to its second stage, then there is an opportunity for a revision of the total sample size. Two-stage designs have been implemented widely in oncology studies in which there is a single treatment arm and patient responses are binary. In this paper the case of two-arm comparative studies in which responses are quantitative is considered. This setting is common in therapeutic areas other than oncology. It will be assumed that observations are normally distributed, but that there is some doubt concerning their standard deviation, motivating the need for sample size review. The work reported has been motivated by a study in diabetic neuropathic pain, and the development of the design for that trial is described in detail.     

A copula-based Markov chain model for the analysis of binary longitudinal data

A fully parametric first-order autoregressive (AR(1)) model is proposed to analyse binary longitudinal data. By using a discretized version of a copula, the modelling approach allows one to construct separate models for the marginal response and for the dependence between adjacent responses. In particular, the transition model that is focused on discretizes the Gaussian copula in such a way that the marginal is a Bernoulli distribution. A probit link is used to take into account concomitant information in the behaviour of the underlying marginal distribution. Fixed and time-varying covariates can be included in the model. The method is simple and is a natural extension of the AR(1) model for Gaussian series. Since the approach put forward is likelihood-based, it allows interpretations and inferences to be made that are not possible with semi-parametric approaches such as those based on generalized estimating equations. Data from a study designed to reduce the exposure of children to the sun are used to illustrate the methods.     

Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model

The distribution of the aggregate claims in one year plays an important role in Actuarial Statistics for computing, for example, insurance premiums when both the number and size of the claims must be implemented into the model. When the number of claims follows a Poisson distribution the aggregated distribution is called the compound Poisson distribution. In this article we assume that the claim size follows an exponential distribution and later we make an extensive study of this model by assuming a bidimensional prior distribution for the parameters of the Poisson and exponential distribution with marginal gamma. This study carries us to obtain expressions for net premiums, marginal and posterior distributions in terms of some well-known special functions used in statistics. Later, a Bayesian robustness study of this model is made. Bayesian robustness on bidimensional models was deeply treated in the 1990s, producing numerous results, but few applications dealing with this problem can be found in the literature.     

Modeling the Adenoma and Serrated Pathway to Colorectal CAncer (ASCCA)

Several colorectal cancer (CRC) screening models have been developed describing the progression of adenomas to CRC. Currently, there is increasing evidence that serrated lesions can also develop into CRC. It is not clear whether screening tests have the same test characteristics for serrated lesions as for adenomas, but lower sensitivities have been suggested. Models that ignore this type of colorectal lesions may provide overly optimistic predictions of the screen‐induced reduction in CRC incidence. To address this issue, we have developed the Adenoma and Serrated pathway to Colorectal CAncer (ASCCA) model that includes the adenoma‐carcinoma pathway and the serrated pathway to CRC as well as characteristics of colorectal lesions. The model structure and the calibration procedure are described in detail. Calibration resulted in 19 parameter sets for the adenoma‐carcinoma pathway and 13 for the serrated pathway that match the age‐ and sex‐specific adenoma and serrated lesion prevalence in the COlonoscopy versus COlonography Screening (COCOS) trial, Dutch CRC incidence and mortality rates, and a number of other intermediate outcomes concerning characteristics of colorectal lesions. As an example, we simulated outcomes for a biennial fecal immunochemical test screening program and a hypothetical one‐time colonoscopy screening program. Inclusion of the serrated pathway influenced the predicted effectiveness of screening when serrated lesions are associated with lower screening test sensitivity or when they are not removed. To our knowledge, this is the first model that explicitly includes the serrated pathway and characteristics of colorectal lesions. It is suitable for the evaluation of the (cost)effectiveness of potential screening strategies for CRC.     

Die Bedeutung der Zinsschranke

The German Corporate Tax Reform Act of 2008 requires an adjustment of classic valuation concepts because it limits interest deduction from taxable income depending on the operating performance of the company. By using time- and state-contingent discount rates in a risk-neutral valuation with predetermined debt levels, a theoretically sound valuation result is obtained. However, a modified APV-concept which assumes deterministic debt over the planning horizon and constant leverage in the terminal value phase also yields consistent valuation results when two types of tax shields with different levels of risk are distinguished.     

Simulating space-time random fields with nonseparable Gneiting-type covariance functions

Statistics and Computing - Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which...     

Model averaging inconcentration–QT analyses

This article describes how a frequentist model averaging approach can be used for concentration–QT analyses in the context of thorough QTc studies. Based on simulations, we have concluded that starting from three candidate model families (linear, exponential, and Emax) the model averaging approach leads to treatment effect estimates that are quite robust with respect to the control of the type I error in nearly all simulated scenarios; in particular, with the model averaging approach, the type I error appears less sensitive to model misspecification than the widely used linear model. We noticed also few differences in terms of performance between the model averaging approach and the more classical model selection approach, but we believe that, despite both can be recommended in practice, the model averaging approach can be more appealing because of some deficiencies of model selection approach pointed out in the literature. We think that a model averaging or model selection approach should be systematically considered for conducting concentration–QT analyses. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of hazard rates for dependent random variables

In this paper, we define and study a new notion for the comparison of the hazard rates of two random variables taking into account their mutual dependence. Properties, applications and the comparison for a data set are given.     

Conditional VAR and Expected Shortfall: A New Functional Approach

We estimate two well-known risk measures, the value-at-risk (VAR) and the expected shortfall, conditionally to a functional variable (i.e., a random variable valued in some semi(pseudo)-metric space). We use nonparametric kernel estimation for constructing estimators of these quantities, under general dependence conditions. Theoretical properties are stated whereas practical aspects are illustrated on simulated data: nonlinear functional and GARCH(1,1) models. Some ideas on bandwidth selection using bootstrap are introduced. Finally, an empirical example is given through data of the S&P 500 time series.