Mário de Castro

A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79–88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix ‘Kw’) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

Fractal dimension applied to plant identification

This article discusses methods to identify plants by analysing leaf complexity based on estimating their fractal dimension. Leaves were analyzed according to the complexity of their internal and external shapes. A computational program was developed to process, analyze and extract the features of leaf images, thereby allowing for automatic plant identification. Results are presented from two experiments, the first to identify plant species from the Brazilian Atlantic forest and Brazilian Cerrado scrublands, using fifty leaf samples from ten different species, and the second to identify four different species from genus Passiflora, using twenty leaf samples for each class. A comparison is made of two methods to estimate fractal dimension (box-counting and multiscale Minkowski). The results are discussed to determine the best approach to analyze shape complexity based on the performance of the technique, when estimating fractal dimension and identifying plants.

Surrogate endpoints for prostate cancer-specific mortality after radiotherapy and androgen suppression therapy in men with localised or locally advanced prostate cancer: an analysis of two randomised trials

BACKGROUND Androgen suppression therapy and radiotherapy are used to treat locally advanced prostate cancer. 3 years of androgen suppression confers a small survival benefit compared with 6 months of therapy in this setting, but is associated with more toxic effects. Early identification of men in whom radiotherapy and 6 months of androgen suppression is insufficient for cure is important. Thus, we assessed whether prostate-specific antigen (PSA) values can act as an early surrogate for prostate cancer-specific mortality (PCSM). METHODS We systematically reviewed randomised controlled trials that showed improved overall and prostate cancer-specific survival with radiotherapy and 6 months of androgen suppression compared with radiotherapy alone and measured lowest PSA concentrations (PSA nadir) and those immediately after treatment (PSA end). We assessed a cohort of 734 men with localised or locally advanced prostate cancer from two eligible trials in the USA and Australasia that randomly allocated participants between Feb 2, 1996, and Dec 27, 2001. We used Prentice criteria to assess whether reported PSA nadir or PSA end concentrations of more than 0·5 ng/mL were surrogates for PCSM. FINDINGS Men treated with radiotherapy and 6 months of androgen suppression in both trials were significantly less likely to have PSA end and PSA nadir values of more than 0·5 ng/mL than were those treated with radiotherapy alone (p<0·0001). Presence of candidate surrogates (ie, PSA end and PSA nadir values >0·5 ng/mL) alone and when assessed in conjunction with the randomised treatment group increased risk of PCSM in the US trial (PSA nadir p=0·0016; PSA end p=0·017) and Australasian trial (PSA nadir p<0·0001; PSA end p=0·0012). In both trials, the randomised treatment group was no longer associated with PCSM (p ≥ 0·20) when the candidate surrogates were included in the model. Therefore, both PSA metrics satisfied Prentice criteria for surrogacy. INTERPRETATION After radiotherapy and 6 months of androgen suppression, men with PSA end values exceeding 0·5 ng/mL should be considered for long-term androgen suppression and those with localised or locally advanced prostate cancer with PSA nadir values exceeding 0·5 ng/mL should be considered for inclusion in randomised trials investigating the use of drugs that have extended survival in castration-resistant metastatic prostate cancer. FUNDING None.

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.

A Bayesian Long-term Survival Model Parametrized in the Cured Fraction

The main goal of this paper is to investigate a cure rate model that comprehends some well-known proposals found in the literature. In our work the number of competing causes of the event of interest follows the negative binomial distribution. The model is conveniently reparametrized through the cured fraction, which is then linked to covariates by means of the logistic link. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis in the proposed model. The procedure is illustrated with a numerical example.

The beta generalized gamma distribution

For the first time, a new five-parameter distribution, called the beta generalized gamma distribution, is introduced and studied. It contains at least 25 special sub-models such as the beta gamma, beta Weibull, beta exponential, generalized gamma (GG), Weibull and gamma distributions and thus could be a better model for analysing positive skewed data. The new density function can be expressed as a linear combination of GG densities. We derive explicit expressions for moments, generating function and other statistical measures. The elements of the expected information matrix are provided. The usefulness of the new model is illustrated by means of a real data set.

A flexible model for survival data with a cure rate: a Bayesian approach

In this paper we deal with a Bayesian analysis for right-censored survival data suitable for populations with a cure rate. We consider a cure rate model based on the negative binomial distribution, encompassing as a special case the promotion time cure model. Bayesian analysis is based on Markov chain Monte Carlo (MCMC) methods. We also present some discussion on model selection and an illustration with a real data set.

Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the models goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease.

Detection of analytical bias

The main object of this paper is to consider maximum likelihood estimators for models used in detection of analytical bias. We consider the regression model proposed in Ripley and Thompson (Analyst, 112, 1987, p. 377) with an EM-type algorithm for computing maximum likelihood estimators and obtain consistent estimators for the asymptotic variance of the maximum likelihood estimators, which seems not to be available in the literature. Wald type statistics are proposed for testing hypothesis related to the bias of the analytical methods with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels. The main conclusion is that proposed approaches in the literature underestimate the covariance matrix of the maximum likelihood estimators. Results of simulation studies and applications to real data sets are reported to illustrate comparisons with other approaches.

A hands-on approach for fitting long-term survival models under the GAMLSS framework

In many data sets from clinical studies there are patients insusceptible to the occurrence of the event of interest. Survival models which ignore this fact are generally inadequate. The main goal of this paper is to describe an application of the generalized additive models for location, scale, and shape (GAMLSS) framework to the fitting of long-term survival models. In this work the number of competing causes of the event of interest follows the negative binomial distribution. In this way, some well known models found in the literature are characterized as particular cases of our proposal. The model is conveniently parameterized in terms of the cured fraction, which is then linked to covariates. We explore the use of the gamlss package in R as a powerful tool for inference in long-term survival models. The procedure is illustrated with a numerical example.