Estimating the size of a closed population by modeling latent and observed heterogeneity.

The paper extends the empirical likelihood (EL) approach of Liu et al. to a new and very flexible family of latent class models for capture-recapture data also allowing for serial dependence on previous capture history, conditionally on latent type and covariates. The EL approach allows to estimate the overall population size directly rather than by adding estimates conditional to covariate configurations. A Fisher-scoring algorithm for maximum likelihood estimation is proposed and a more efficient alternative to the traditional EL approach for estimating the non-parametric component is introduced; this allows us to show that the mapping between the non-parametric distribution of the covariates and the probabilities of being never captured is one-to-one and strictly increasing. Asymptotic results are outlined, and a procedure for constructing profile likelihood confidence intervals for the population size is presented. Two examples based on real data are used to illustrate the proposed approach and a simulation study indicates that, when estimating the overall undercount, the method proposed here is substantially more efficient than the one based on conditional maximum likelihood estimation, especially when the sample size is not sufficiently large.

A hidden Markov model for continuous longitudinal data with missing responses and dropout.

We propose a hidden Markov model for multivariate continuous longitudinal responses with covariates that accounts for three different types of missing pattern: (I) partially missing outcomes at a given time occasion, (II) completely missing outcomes at a given time occasion (intermittent pattern), and (III) dropout before the end of the period of observation (monotone pattern). The missing-at-random (MAR) assumption is formulated to deal with the first two types of missingness, while to account for the informative dropout, we rely on an extra absorbing state. Estimation of the model parameters is based on the maximum likelihood method that is implemented by an expectation-maximization (EM) algorithm relying on suitable recursions. The proposal is illustrated by a Monte Carlo simulation study and an application based on historical data on primary biliary cholangitis.

Male recognition bias in sex assignment based on visual stimuli.

According to previous ethnomethodological and cognitive studies on sex assignment, if a figure has male sexual characteristics people are more likely to think it is a man than they think it is a woman when the figure has female sexual characteristics. This bias in favor of male attribution is strongly reinforced when a penis is apparent in human nude pictures. In our contribution, we reported findings of three experiments aimed at replicating previous studies by administering the Sex/Gender Attribution Test for Adult (SGAT-A) created by digitally morphing the bodies of one human male and one human female model into realistic pictures. We observed the sex attribution and response time of 1706 young adult participants. A cross-cultural comparison was also carried out with a sample of young adult Chinese students. Findings substantially reconfirmed those obtained in previous studies. The male external genitalia overshadow any other features that might rather suggest a female identity. Indeed, when male external genitalia were exposed, the odds of male sex attribution were 5.688 compared to 1.823 female attribution when female external genitalia were shown. Moreover, the shortest response times were observed with masculine stimuli. Evolutionary and cultural determinants of the male sex bias are also discussed.

A spatio-temporal model based on discrete latent variables for the analysis of COVID-19 incidence.

We propose a model based on discrete latent variables, which are spatially associated and time specific, for the analysis of incident cases of SARS-CoV-2 infections. We assume that for each area the sequence of latent variables across time follows a Markov chain with initial and transition probabilities that also depend on latent variables in neighboring areas. The model is estimated by a Markov chain Monte Carlo algorithm based on a data augmentation scheme, in which the latent states are drawn together with the model parameters for each area and time. As an illustration we analyze incident cases of SARS-CoV-2 collected in Italy at regional level for the period from February 24, 2020, to January 17, 2021, corresponding to 48 weeks, where we use number of swabs as an offset. Our model identifies a common trend and, for every week, assigns each region to one among five distinct risk groups.

A multivariate statistical approach to predict COVID-19 count data with epidemiological interpretation and uncertainty quantification.

For the analysis of COVID-19 pandemic data, we propose Bayesian multinomial and Dirichlet-multinomial autoregressive models for time-series of counts of patients in mutually exclusive and exhaustive observational categories, defined according to the severity of the patient status and the required treatment. Categories include hospitalized in regular wards (H) and in intensive care units (ICU), together with deceased (D) and recovered (R). These models explicitly formulate assumptions on the transition probabilities between these categories across time, thanks to a flexible formulation based on parameters that a priori follow normal distributions, possibly truncated to incorporate specific hypotheses having an epidemiological interpretation. The posterior distribution of model parameters and the transition matrices are estimated by a Markov chain Monte Carlo algorithm that also provides predictions and allows us to compute the reproduction number Rt . All estimates and predictions are endowed with an accuracy measure obtained thanks to the Bayesian approach. We present results concerning data collected during the first wave of the pandemic in Italy and Lombardy and study the effect of nonpharmaceutical interventions. Suitable discrepancy measures defined to check and compare models show that the Dirichlet-multinomial model has an adequate fit and provides good predictive performance in particular for H and ICU patients.

A shared-parameter continuous-time hidden Markov and survival model for longitudinal data with informative dropout.

A shared-parameter approach for jointly modeling longitudinal and survival data is proposed. With respect to available approaches, it allows for time-varying random effects that affect both the longitudinal and the survival processes. The distribution of these random effects is modeled according to a continuous-time hidden Markov chain so that transitions may occur at any time point. For maximum likelihood estimation, we propose an algorithm based on a discretization of time until censoring in an arbitrary number of time windows. The observed information matrix is used to obtain standard errors. We illustrate the approach by simulation, even with respect to the effect of the number of time windows on the precision of the estimates, and by an application to data about patients suffering from mildly dilated cardiomyopathy.

Bedside sonography assessment of extravascular lung water increase after major pulmonary resection in non-small cell lung cancer patients.

BACKGROUND: Extra vascular lung water (EVLW) following pulmonary resection increases due to fluid infusion and rises in capillary surface and permeability of the alveolar capillary membranes. EVLW increase clinically correlates to pulmonary oedema and it may generate impairments of gas exchanges and acute lung injury. An early and reliable assessment of postoperative EVLW, especially following major pulmonary resection, is useful in terms of reducing the risk of postoperative complications. The currently used methods, though satisfying these criteria, tend to be invasive and cumbersome and these factors might limit its use. The presence and burden of EVLW has been reported to correlate with sonographic B-line artefacts (BLA) assessed by lung ultrasound (LUS). This observational study investigated if bedside LUS could detect EVLW increases after major pulmonary resection. Due to the clinical association between EVLW increase and impairment of gas exchange, secondary aims of the study included investigating for associations between any observed EVLW increases and both respiratory ratio (PaO2/FiO2) and fluid retention, measured by brain natriuretic peptide (BNP). METHODS: Overall, 74 major pulmonary resection patients underwent bedside LUS before surgery and at postoperative days 1 and 4, in the inviolate hemithorax which were divided into four quadrants. BLA were counted with a four-level method. The respiratory ratio PaO2/FiO2 and fluid retention were both assessed. RESULTS: BLA resulted being increased at postoperative day 1 (OR 9.25; 95% CI, 5.28-16.20; P<0.0001 vs. baseline), and decreased at day 4 (OR 0.50; 95% CI, 0.31-0.80; P=0.004 vs. day 1). Moreover, the BLA increase was associated with both increased BNP (OR 1.005; 95% CI, 1.003-1.008; P<0.0001) and body weight (OR 1.040; 95% CI, 1.008-1.073; P=0.015). Significant inverse correlations were observed between the BLA values and the PaO2/FiO2 respiratory ratios. CONCLUSIONS: Our results suggest that LUS, due to its non-invasiveness, affordability and capacity to detect increases in EVLW, might be useful in better managing postoperative patients.

A multilevel latent Markov model for the evaluation of nursing homes' performance.

The periodic evaluation of health care services is a primary concern for many institutions. We consider services provided by nursing homes with the aim of ranking a set of these structures with respect to their effect on resident health status. Since the overall health status is not directly observable, and given the longitudinal and multilevel structure of the available data, we rely on latent variable models and, in particular, on a multilevel latent Markov model where residents and nursing homes are the first and the second level units, respectively. The model includes individual covariates to account for resident characteristics. The impact of nursing home membership is modelled through a pair of random effects affecting the initial distribution and the transition probabilities between different levels of health status. Through the prediction of these random effects we obtain a ranking of the nursing homes. Furthermore, the proposed model accounts for nonignorable dropout due to resident death, which typically occurs in these contexts. The motivating dataset is gathered from the Long Term Care Facilities programme, a health care protocol implemented in Umbria (Italy). Our results show that differences in performance between nursing homes are statistically significant.

A joint model for longitudinal and survival data based on an AR(1) latent process.

A critical problem in repeated measurement studies is the occurrence of nonignorable missing observations. A common approach to deal with this problem is joint modeling the longitudinal and survival processes for each individual on the basis of a random effect that is usually assumed to be time constant. We relax this hypothesis by introducing time-varying subject-specific random effects that follow a first-order autoregressive process, AR(1). We also adopt a generalized linear model formulation to accommodate for different types of longitudinal response (i.e. continuous, binary, count) and we consider some extended cases, such as counts with excess of zeros and multivariate outcomes at each time occasion. Estimation of the parameters of the resulting joint model is based on the maximization of the likelihood computed by a recursion developed in the hidden Markov literature. This maximization is performed on the basis of a quasi-Newton algorithm that also provides the information matrix and then standard errors for the parameter estimates. The proposed approach is illustrated through a Monte Carlo simulation study and the analysis of certain medical datasets.

A Nonparametric Multidimensional Latent Class IRT Model in a Bayesian Framework.

We propose a nonparametric item response theory model for dichotomously-scored items in a Bayesian framework. The model is based on a latent class (LC) formulation, and it is multidimensional, with dimensions corresponding to a partition of the items in homogenous groups that are specified on the basis of inequality constraints among the conditional success probabilities given the latent class. Moreover, an innovative system of prior distributions is proposed following the encompassing approach, in which the largest model is the unconstrained LC model. A reversible-jump type algorithm is described for sampling from the joint posterior distribution of the model parameters of the encompassing model. By suitably post-processing its output, we then make inference on the number of dimensions (i.e., number of groups of items measuring the same latent trait) and we cluster items according to the dimensions when unidimensionality is violated. The approach is illustrated by two examples on simulated data and two applications based on educational and quality-of-life data.

Evaluation of Student Performance through a Multidimensional Finite Mixture IRT Model.

In the Italian academic system, a student can enroll for an exam immediately after the end of the teaching period or can postpone it; in this second case the exam result is missing. We propose an approach for the evaluation of a student performance throughout the course of study, accounting also for nonattempted exams. The approach is based on an item response theory model that includes two discrete latent variables representing student performance and priority in selecting the exams to take. We explicitly account for nonignorable missing observations as the indicators of attempted exams also contribute to measure the performance (within-item multidimensionality). The model also allows for individual covariates in its structural part.

[Employment status and perceived health in Italy: data from the European Union Statistics on Income and Living Conditions (EU-SILC) longitudinal study]. / Condizione occupazionale e salute percepita in Italia: evidenze da dati longitudinali EU-SILC.

The aim of this study was to investigate the relationship between employment status (permanent employment, fixed-term employment, unemployment, other) and perceived health status in a sample of the Italian population. Data was obtained from the European Union Statistics on Income and Living Condition (EU-SILC) study during the period 2009 - 2012. The sample consists of 4,848 individuals, each with a complete record of observations during four years for a total of 19,392 observations. The causal relationship between perceived/self-reported health status and employment status was tested using a global logit model (STATA). Our results confirm a significant association between employment status and perceived health, as well as between perceived health status and economic status. Unemployment that was dependent on an actual lack of work opportunities and not from individual disability was found to be the most significant determinant of perceived health status; a higher educational level produces a better perceived health status.

Preterm Birth: Analysis of Longitudinal Data on Siblings Based on Random-Effects Logit Models.

INTRODUCTION: The literature about the determinants of a preterm birth is still controversial. We approach the analysis of these determinants distinguishing between woman's observable characteristics, which may change over time, and unobservable woman's characteristics, which are time invariant and explain the dependence between the typology (normal or preterm) of consecutive births. METHODS: We rely on a longitudinal dataset about 28,603 women who delivered for the first time in the period 2005-2013 in the Umbria Region (Italy). We consider singleton physiological pregnancies originating from natural conceptions with birthweight of at least 500 g and gestational age between 24 and 42 weeks; the overall number of deliveries is 34,224. The dataset is based on the Standard Certificates of Life Birth collected in the region in the same period. We estimate two types of logit model for the event that the birth is preterm. The first model is pooled and accounts for the information about possible previous preterm deliveries, including the lagged response among the covariates. The second model takes explicitly into account the longitudinal structure of data through the introduction of a random effect that summarizes all the (time invariant) unobservable characteristics of a woman affecting the probability of a preterm birth. RESULTS: The estimated models provide evidence that the probability of a preterm birth depends on certain woman's demographic and socioeconomic characteristics, other than on the previous history in terms of miscarriages and the baby's gender. Besides, as the random-effects model fits significantly better than the pooled model with lagged response, we conclude for a spurious state dependence between repeated preterm deliveries. CONCLUSION: The proposed analysis represents a useful tool to detect profiles of women with a high risk of preterm delivery. Such profiles are detected taking into account observable woman's demographic and socioeconomic characteristics as well as unobservable and time-constant characteristics, possibly related to the woman's genetic makeup. TRIAL REGISTRATION: Not applicable.

A discrete time event-history approach to informative drop-out in mixed latent Markov models with covariates.

Mixed latent Markov (MLM) models represent an important tool of analysis of longitudinal data when response variables are affected by time-fixed and time-varying unobserved heterogeneity, in which the latter is accounted for by a hidden Markov chain. In order to avoid bias when using a model of this type in the presence of informative drop-out, we propose an event-history (EH) extension of the latent Markov approach that may be used with multivariate longitudinal data, in which one or more outcomes of a different nature are observed at each time occasion. The EH component of the resulting model is referred to the interval-censored drop-out, and bias in MLM modeling is avoided by correlated random effects, included in the different model components, which follow common latent distributions. In order to perform maximum likelihood estimation of the proposed model by the expectation-maximization algorithm, we extend the usual forward-backward recursions of Baum and Welch. The algorithm has the same complexity as the one adopted in cases of non-informative drop-out. We illustrate the proposed approach through simulations and an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest, one continuous and the other binary.

Employment status and perceived health condition: longitudinal data from Italy.

BACKGROUND: The considerable increase of non-standard labor contracts, unemployment and inactivity rates raises the question of whether job insecurity and the lack of job opportunities affect physical and mental well-being differently from being employed with an open-ended contract. In this paper we offer evidence on the relationship between self-reported health and the employment status in Italy using the Survey on Household Income and Wealth (SHIW); another aim is to investigate whether these potential inequalities have changed with the recent economic downturn (time period 2006-2010). METHODS: We estimate an ordered logit model with self-reported health status (SRHS) as response variable based on a fixed-effects approach which has certain advantages with respect to the random-effects formulation: the fixed-effects nature of the model also allows us to solve the problems of incidental parameters and non-random selection of individuals into different labor market categories. RESULTS: We find that temporary workers, first-job seekers and unemployed individuals are worse off than permanent employees, especially males, young workers, and those living in the center and south of Italy. CONCLUSION: Health inequalities between permanent workers and job seekers widen over time for male and young workers, and arise in the north of the country as well.

Differences in birthweight outcomes: a longitudinal study based on siblings.

OBJECTIVES: We investigate the differences in birthweight between first- and second-borns, evaluating the impact of changes in pregnancy (e.g., gestational age), demographic (e.g., age), and social (e.g., education level, marital status) maternal characteristics. DATA AND METHODS: All analyses are performed on data collected in Umbria (Italy) taking into account a set of 792 women who delivered twice from 2005 to 2008. Firstly, we use a univariate paired t-test for the comparison between weights of first- and second-borns; Secondly, we use linear and nonlinear regression approaches in order to: (i) evaluate the effect of demographic and social maternal characteristics and (ii) predict the odds-ratio of low and high birthweight infants, respectively. RESULTS: We find that the birthweight of second-borns is significantly higher than that of first-borns. Statistically significant effects are related with a longer gestational age, an increased number of visits during the pregnancy, and the gender of infants. On the other hand, we do not observe any significant effect related with mother's age and with other characteristics of interest.

A new constant memory recursion for hidden Markov models.

We develop the recursion for hidden Markov (HM) models proposed by Bartolucci and Besag (2002), and we show how it may be used to implement an estimation algorithm for these models that requires an amount of memory not depending on the length of the observed series of data. This recursion allows us to obtain the conditional distribution of the latent state at every occasion, given the previous state and the observed data. With respect to the estimation algorithm based on the well-known Baum-Welch recursions, which requires an amount of memory that increases with the sample size, the proposed algorithm also has the advantage of not requiring dummy renormalizations to avoid numerical problems. Moreover, it directly allows us to perform global decoding of the latent sequence of states, without the need of a Viterbi method and with a consistent reduction of the memory requirement with respect to the latter. The proposed approach is compared, in terms of computing time and memory requirement, with the algorithm based on the Baum-Welch recursions and with the so-called linear memory algorithm of Churbanov and Winters-Hilt. The comparison is also based on a series of simulations involving an HM model for continuous time-series data.

Causal inference in paired two-arm experimental studies under noncompliance with application to prognosis of myocardial infarction.

Motivated by a study about prompt coronary angiography in myocardial infarction, we propose a method to estimate the causal effect of a treatment in two-arm experimental studies with possible noncompliance in both treatment and control arms. We base the method on a causal model for repeated binary outcomes (before and after the treatment), which includes individual covariates and latent variables for the unobserved heterogeneity between subjects. Moreover, given the type of noncompliance, the model assumes the existence of three subpopulations of subjects: compliers, never-takers, and always-takers. We estimate the model using a two-step estimator: at the first step, we estimate the probability that a subject belongs to one of the three subpopulations on the basis of the available covariates; at the second step, we estimate the causal effects through a conditional logistic method, the implementation of which depends on the results from the first step. The estimator is approximately consistent and, under certain circumstances, exactly consistent. We provide evidence that the bias is negligible in relevant situations. We compute standard errors on the basis of a sandwich formula. The application shows that prompt coronary angiography in patients with myocardial infarction may significantly decrease the risk of other events within the next 2 years, with a log-odds of about - 2. Given that noncompliance is significant for patients being given the treatment because of high-risk conditions, classical estimators fail to detect, or at least underestimate, this effect.

Effects of individual and social factors on preterm birth and low birth weight: empirical evidence from regional data in Italy.

OBJECTIVES: We examine the effects of mother's characteristics and socioeconomic condition on weight at birth and preterm delivery in an Italian region (Umbria). METHODS: The study concerns all live-born singleton infants in 2007 with at least a gestational age of 22 weeks. Information derived from the Standard Certificate of Live Birth was linked to information from census statistics, so as to obtain a deprivation index. RESULTS: On the basis of the fitting of two separate logistic regression models, we conclude that all individual socioeconomic factors are strongly associated with the outcomes at birth, apart from the deprivation index. Older and less educated mothers, and those with lower occupational level, have a higher probability to run into preterm delivery with respect to the other mothers. The relative risk ratios for low birth weight are significantly higher for older mothers, non-European, and not married. Lower weight rates are found in infants from complicated pregnancy and non-spontaneous conception. CONCLUSIONS: Effects of mother's characteristics on weight at birth and weeks of gestation are confirmed. The deprivation index does not affect these outcomes, showing the proper implementation of the Health System.