A segmented regression model for event history data: an application to the fertility patterns in Italy

We propose a segmented discrete-time model for the analysis of event history data in demographic research. Through a unified regression framework, the model provides estimates of the effects of explanatory variables and jointly accommodates flexibly non-proportional differences via segmented relationships. The main appeal relies on ready availability of parameters, changepoints, and slopes, which may provide meaningful and intuitive information on the topic. Furthermore, specific linear constraints on the slopes may also be set to investigate particular patterns. We investigate the intervals between cohabitation and first childbirth and from first to second childbirth using individual data for Italian women from the Second National Survey on Fertility. The model provides insights into dramatic decrease of fertility experienced in Italy, in that it detects a ‘common’ tendency in delaying the onset of childbearing for the more recent cohorts and a ‘specific’ postponement strictly depending on the educational level and age at cohabitation.     

Support provided by elderly in Italy: a hierarchical analysis of ego networks controlling for alter–overlapping

Statistical Methods & Applications - Providing support outside the household can be considered an actual sign of an active social life for the elderly. Adopting an ego–network...     

The Poisson-exponential model for recurrent event data: an application to bowel motility data

This paper presents a new parametric model for recurrent events, in which the time of each recurrence is associated to one or multiple latent causes and no information is provided about the responsible cause for the event. This model is characterized by a rate function and it is based on the Poisson-exponential distribution, namely the distribution of the maximum among a random number (truncated Poisson distributed) of exponential times. The time of each recurrence is then given by the maximum lifetime value among all latent causes. Inference is based on a maximum likelihood approach. A simulation study is performed in order to observe the frequentist properties of the estimation procedure for small and moderate sample sizes. We also investigated likelihood-based tests procedures. A real example from a gastroenterology study concerning small bowel motility during fasting state is used to illustrate the methodology. Finally, we apply the proposed model to a real data set and compare it with the classical Homogeneous Poisson model, which is a particular case.     

A novel Bayesian regression model for counts with an application to health data

Discrete data are collected in many application areas and are often characterised by highly-skewed distributions. An example of this, which is considered in this paper, is the number of visits to a specialist, often taken as a measure of demand in healthcare. A discrete Weibull regression model was recently proposed for regression problems with a discrete response and it was shown to possess desirable properties. In this paper, we propose the first Bayesian implementation of this model. We consider a general parametrization, where both parameters of the discrete Weibull distribution can be conditioned on the predictors, and show theoretically how, under a uniform non-informative prior, the posterior distribution is proper with finite moments. In addition, we consider closely the case of Laplace priors for parameter shrinkage and variable selection. Parameter estimates and their credible intervals can be readily calculated from their full posterior distribution. A simulation study and the analysis of four real datasets of medical records show promises for the wide applicability of this approach to the analysis of count data. The method is implemented in the R package BDWreg.     

Frailty modeling for clustered survival data: an application to birth interval in Bangladesh

The present work demonstrates an application of random effects model for analyzing birth intervals that are clustered into geographical regions. Observations from the same cluster are assumed to be correlated because usually they share certain unobserved characteristics between them. Ignoring the correlations among the observations may lead to incorrect standard errors of the estimates of parameters of interest. Beside making the comparisons between Cox's proportional hazards model and random effects model for analyzing geographically clustered time-to-event data, important demographic and socioeconomic factors that may affect the length of birth intervals of Bangladeshi women are also reported in this paper.     

Statistical learning procedures for monitoring regulatory compliance: an application to fisheries data

Summary.  As a special case of statistical learning, ensemble methods are well suited for the analysis of opportunistically collected data that involve many weak and sometimes specialized predictors, especially when subject-matter knowledge favours inductive approaches. We analyse data on the incidental mortality of dolphins in the purse-seine fishery for tuna in the eastern Pacific Ocean. The goal is to identify those rare purse-seine sets for which incidental mortality would be expected but none was reported. The ensemble method random forests is used to classify sets according to whether mortality was (response 1) or was not (response 0) reported. To identify questionable reporting practice, we construct 'residuals' as the difference between the categorical response (0,1) and the proportion of trees in the forest that classify a given set as having mortality. Two uses of these residuals to identify suspicious data are illustrated. This approach shows promise as a means of identifying suspect data gathered for environmental monitoring.     

Statistical learning theory for fitting multimodal distribution to rainfall data: an application

The promising methodology of the “Statistical Learning Theory” for the estimation of multimodal distribution is thoroughly studied. The “tail” is estimated through Hill's, UH and moment methods. The threshold value is determined by nonparametric bootstrap and the minimum mean square error criterion. Further, the “body” is estimated by the nonparametric structural risk minimization method of the empirical distribution function under the regression set-up. As an illustration, rainfall data for the meteorological subdivision of Orissa, India during the period 1871–2006 are used. It is shown that Hill's method has performed the best for tail density. Finally, the combined estimated “body” and “tail” of the multimodal distribution is shown to capture the multimodality present in the data.     

Some non-parametric tests for duration dependence: an application to UK business cycle data

A distinction between Fisher's implied data-generating process for Monte Carlo cycles and the more general Markov process leads to non-parametric tests for duration dependence. Tests are based on the method of moments, Tauchen's generalized method of moments (GMM) procedure, and a statistic whose null distribution probability limit is zero. Using finite-sample critical values obtained by Monte Carlo methods, our test results are remarkably consistent. The null distribution of the GMM test statistic for samples of the size considered is distinctly non-normal, so that asymptotic critical values give erroneous results. The tests are applied to UK business cycle data for 1854-1992. There is evidence for duration dependence in expansions but not in contractions.     

A clustering approach to detect multiple outliers in linear functional relationship model for circular data

Outlier detection has been used extensively in data analysis to detect anomalous observation in data. It has important applications such as in fraud detection and robust analysis, among others. In this paper, we propose a method in detecting multiple outliers in linear functional relationship model for circular variables. Using the residual values of the Caires and Wyatt model, we applied the hierarchical clustering approach. With the use of a tree diagram, we illustrate the detection of outliers graphically. A Monte Carlo simulation study is done to verify the accuracy of the proposed method. Low probability of masking and swamping effects indicate the validity of the proposed approach. Also, the illustrations to two sets of real data are given to show its practical applicability.     

A 3-parameter Gompertz distribution for survival data with competing risks,with an application to breast cancer data

The cumulative incidence function is of great importance in the analysis of survival data when competing risks are present. Parametric modeling of such functions, which are by nature improper, suggests the use of improper distributions. One frequently used improper distribution is that of Gompertz, which captures only monotone hazard shapes. In some applications, however, subdistribution hazard estimates have been observed with unimodal shapes. An extension to the Gompertz distribution is presented which can capture unimodal as well as monotone hazard shapes. Important properties of the proposed distribution are discussed, and the proposed distribution is used to analyze survival data from a breast cancer clinical trial.     

Multistate survival models for transitions and reverse transitions: an application to contraceptive use data

This paper extends the use of the multistate proportional hazards model proposed by R. Kay for transitions, reverse transitions, and repeated transitions. A simple method of testing the equality of vectors of parameters for transitions and repeated transitions is also shown in addition to estimates for the underlying cumulative hazards for different types of transition. The multistate survival models applied to contraceptive use data collected by the International Center for Diarrheal Disease Research, Bangladesh, for the period January 1978 to December 1982 provide useful findings relating to interstate transitions. The author stresses the need to not treat separately states of contraceptive use given their link to the acceptance of the first method, transitions from one method to another, first method discontinuation, periods of non-use, the use of subsequent methods, loss to follow-up, the use of irreversible methods, and subsequent periods of non-use. Religion is an important indicator for the acceptance of an irreversible method as a first or subsequent method; compared to women of other religions, Muslims were less likely to accept an irreversible method as a first or subsequent method. Religion is not, however, associated with the acceptance or subsequent use of a reversible method or with discontinuation of a reversible method. Higher age in the study area is associated with both lower acceptance and longer continuation of a method. Women with a larger number of living sons tend to accept their first method and subsequent methods at an higher rate than women with fewer or no sons. As for educational status, women with higher education proved to be serious users of contraception, although women with less or no education tend to accept an irreversible method at an higher rate than the women with an higher level of education. Further, the desire for more children is a strong predictor for non-use of a method even if contraception is used to space births. The score test suggested in the paper for testing the equality of parameters in models 1-4 reveals that there is no significant difference in the parameters of the models. This paper shows that the factors which affect the acceptance of any reversible method of contraception are different from those for an irreversible method. Moreover, the factors which affect a transition differ from those for a reverse transition in the case of adopting reversible methods.     

Dynamic predicting by landmarking as an alternative for multi-state modeling: an application to acute lymphoid leukemia data

This paper considers the problem of obtaining a dynamic prediction for 5-year failure free survival after bone marrow transplantation in ALL patients using data from the EBMT, the European Group for Blood and Marrow Transplantation. The paper compares the new landmark methodology as developed by the first author and the established multi-state modeling as described in a recent Tutorial in Biostatistics in Statistics in Medicine by the second author and colleagues. As expected the two approaches give similar results. The landmark methodology does not need complex modeling and leads to easy prediction rules. On the other hand, it does not give the insight in the biological processes as obtained for the multi-state model.     

Using data augmentation to correct for non-ignorable non-response when surrogate data are available: an application to the distribution of hourly pay

Summary.  The paper develops a data augmentation method to estimate the distribution function of a variable, which is partially observed, under a non-ignorable missing data mechanism, and where surrogate data are available. An application to the estimation of hourly pay distributions using UK Labour Force Survey data provides the main motivation. In addition to considering a standard parametric data augmentation method, we consider the use of hot deck imputation methods as part of the data augmentation procedure to improve the robustness of the method. The method proposed is compared with standard methods that are based on an ignorable missing data mechanism, both in a simulation study and in the Labour Force Survey application. The focus is on reducing bias in point estimation, but variance estimation using multiple imputation is also considered briefly.     

Bayesian factor analysis for spatially correlated data: application to cancer incidence data in Scotland

A hierarchical Bayesian factor model for multivariate spatially correlated data is proposed. Multiple cancer incidence data in Scotland are jointly analyzed, looking for common components, able to detect etiological factors of diseases hidden behind the data. The proposed method searches factor scores incorporating a dependence within observations due to a geographical structure. The great flexibility of the Bayesian approach allows the inclusion of prior opinions about adjacent regions having highly correlated observable and latent variables. The proposed model is an extension of a model proposed by Rowe (2003a) and starts from the introduction of separable covariance matrix for the observations. A Gibbs sampling algorithm is implemented to sample from the posterior distributions.     

A COVINDEX based on a GAM beta regression model with an application to the COVID-19 pandemic in Italy

Statistical Methods & Applications - Detecting changes in COVID-19 disease transmission over time is a key indicator of epidemic growth. Near real-time monitoring of the pandemic growth is...     

Joint generalized estimating equations for multivariate longitudinal binary outcomes with missing data: an application to acquired immune deficiency syndrome data

Summary.  In a large, prospective longitudinal study designed to monitor cardiac abnormalities in children born to women who are infected with the human immunodeficiency virus, instead of a single outcome variable, there are multiple binary outcomes (e.g. abnormal heart rate, abnormal blood pressure and abnormal heart wall thickness) considered as joint measures of heart function over time. In the presence of missing responses at some time points, longitudinal marginal models for these multiple outcomes can be estimated by using generalized estimating equations (GEEs), and consistent estimates can be obtained under the assumption of a missingness completely at random mechanism. When the missing data mechanism is missingness at random, i.e. the probability of missing a particular outcome at a time point depends on observed values of that outcome and the remaining outcomes at other time points, we propose joint estimation of the marginal models by using a single modified GEE based on an EM-type algorithm. The method proposed is motivated by the longitudinal study of cardiac abnormalities in children who were born to women infected with the human immunodeficiency virus, and analyses of these data are presented to illustrate the application of the method. Further, in an asymptotic study of bias, we show that, under a missingness at random mechanism in which missingness depends on all observed outcome variables, our joint estimation via the modified GEE produces almost unbiased estimates, provided that the correlation model has been correctly specified, whereas estimates from standard GEEs can lead to substantial bias.     

A new parametric family for modelling cumulative incidence functions: application to breast cancer data

Summary.  Competing risks situations can be encountered in many research areas such as medicine, social science and engineering. The main stream of analyses of those competing risks data has been nonparametric or semiparametric in the statistical literature. We propose a new parametric family to parameterize the cumulative incidence function completely. The new distribution is sufficiently flexible to fit various shapes of hazard patterns in survival data and increases the efficiency of the cumulative incidence estimates over the distribution-free approaches. A simple two-sample parametric test statistic is also proposed to compare the cumulative incidence functions between two groups at a given time point. The new parametric approach is illustrated by using breast cancer data sets from the National Surgical Adjuvant Breast and Bowel Project.