Cure rate models for heterogeneous competing causes.

Cure rate models have been widely studied to analyze time-to-event data with a cured fraction of patients. In this type of model, the number of concurrent causes is assumed to be a random variable. However, in practice, it is natural to admit that the distribution of the number of competing causes is different from individual to individual. Our proposal is to assume that the number of competing causes belongs to a class of a finite mixture of competing causes distributions. We assume the number of malignant cells follow a mixture of two power series distributions and suppose that the time to the event of interest follows a Weibull distribution. We consider the proportion of the cured number of competing causes depending on covariates, allowing direct modeling of the cure rate. The proposed model includes several well-known models as special cases and defines many new special models. An expectation-maximization algorithm is proposed for parameter estimation, where the expectation step involves the computation of the expected number of concurrent causes for each individual. A Monte Carlo simulation is performed to assess the behavior of the estimation method. In order to show the potential for the practice of our model, we apply it to the real medical data set from a population-based study of incident cases of cutaneous melanoma diagnosed in the state of São Paulo, Brazil, illustrating that the model proposed can outperform traditional models in terms of model fitting.

Misinformation Caused Increased Urban Mobility and the End of Social Confinement Before the Second Wave of COVID-19 in Amazonia.

Tendentious projections about COVID-19 in Brazil provided an appealing excuse for individuals and decision-makers to justify poor choices during a critical phase of the pandemic. The erroneous results likely contributed to premature resumption of in-person school classes and easing of restrictions on social contact, favoring the resurgence of COVID-19. In Manaus, the largest city in the Amazon region, the COVID-19 pandemic did not end in 2020 of its own accord, but rather rebounded in a disastrous second wave of the disease.

Misinformation caused increased urban mobility and the end of social confinement before the second wave of COVID-19 in Amazonia

Tendentious projections about COVID-19 in Brazil provided an appealing excuse for individuals and decision-makers to justify poor choices during a critical phase of the pandemic. The erroneous results likely contributed to premature resumption of in-person school classes and easing of restrictions on social contact, favoring the resurgence of COVID-19. In Manaus, the largest city in the Amazon region, the COVID-19 pandemic did not end in 2020 of its own accord, but rather rebounded in a disastrous second wave of the disease.

Dynamics of COVID-19 in Amazonia: A history of government denialism and the risk of a third wave.

The city of Manaus (the capital of Brazil's state of Amazonas) has become a key location for understanding the dynamics of the global pandemic of COVID-19. Different groups of scientists have foreseen different scenarios, such as the second wave or that Manaus could escape such a wave by having reached herd immunity. Here we test five hypotheses that explain the second wave of COVID-19 in Manaus: 1) The greater transmissibility of the Amazonian (gamma or P.1) variant is responsible for the second wave; 2) SARS-CoV-2 infection levels during the first wave were overestimated by those foreseeing herd immunity, and the population remained below this threshold when the second wave began at the beginning of December 2020; 3) Antibodies acquired from infection by one lineage do not confer immunity against other lineages; 4) Loss of immunity has generated a feedback phenomenon among infected people, which could generate future waves, and 5) A combination of the foregoing hypotheses. We also evaluated the possibility of a third wave in Manaus despite advances in vaccination, the new wave being due to the introduction of the delta variant in the region and the loss of immunity from natural contact with the virus. We developed a multi-strain SEIRS (Susceptible-Exposed-Infected-Removed-Susceptible) model and fed it with data for Manaus on mobility, COVID-19 hospitalizations, numbers of cases and deaths. Our model contemplated the current vaccination rates for all vaccines applied in Manaus and the individual protection rates already known for each vaccine. Our results indicate that the SARS-CoV-2 gamma (P.1) strain that originated in the Amazon region is not the cause of the second wave of COVID-19 in Manaus, but rather this strain originated during the second wave and became predominant in January 2021. Our multi-strain SEIRS model indicates that neither the doubled transmission rate of the gamma variant nor the loss of immunity alone is sufficient to explain the sudden rise of hospitalizations in late December 2020. Our results also indicate that the most plausible explanation for the current second wave is a SARS-CoV-2 infection level at around 50% of the population in early December 2020, together with loss of population immunity and early relaxation of restrictive measures. The most-plausible model indicates that contact with one strain does not provide protection against other strains and that the gamma variant has a transmissibility rate twice that of the original SARS-CoV-2 strain. Our model also shows that, despite the advance of vaccination, and even if future vaccination advances at a steady pace, the introduction of the delta variant or other new variants could cause a new wave of COVID-19.

Brazil's COVID-19 Epicenter in Manaus: How Much of the Population Has Already Been Exposed and Are Vulnerable to SARS-CoV-2?

Is Brazil's COVID-19 epicenter really approaching herd immunity? A recent study estimated that in October 2020 three-quarters of the population of Manaus (the capital of the largest state in the Brazilian Amazon) had contact with SARS-CoV-2. We show that 46% of the Manaus population having had contact with SARS-CoV-2 at that time is a more plausible estimate, and that Amazonia is still far from herd immunity. The second wave of COVID-19 is now evident in Manaus. We predict that the pandemic of COVID-19 will continue throughout 2021, given the duration of naturally acquired immunity of only 240 days and the slow pace of vaccination. Manaus has a large percentage of the population that is susceptible (35 to 45% as of May 17, 2021). Against this backdrop, measures to restrict urban mobility and social isolation are still necessary, such as the closure of schools and universities, since the resumption of these activities in 2020 due to the low attack rates of SARS-CoV-2 was the main trigger for the second wave in Manaus.

Dynamics of COVID-19 in Amazonia: a history of government denialism and the risk of a third wave

The city of Manaus (the capital of Brazil’s state of Amazonas) has become a key location for understanding the dynamics of the global pandemic of COVID-19. Different groups of scientists have foreseen different scenarios, such as the second wave or that Manaus could escape such a wave by having reached herd immunity. Here we test five hypotheses that explain the second wave of COVID-19 in Manaus: 1) The greater transmissibility of the Amazonian (gamma or P.1) variant is responsible for the second wave; 2) SARS-CoV-2 infection levels during the first wave were overestimated by those foreseeing herd immunity, and the population remained below this threshold when the second wave began at the beginning of December 2020; 3) Antibodies acquired from infection by one lineage do not confer immunity against other lineages; 4) Loss of immunity has generated a feedback phenomenon among infected people, which could generate future waves, and 5) A combination of the foregoing hypotheses. We also evaluated the possibility of a third wave in Manaus despite advances in vaccination, the new wave being due to the introduction of the delta variant in the region and the loss of immunity from natural contact with the virus. We developed a multi-strain SEIRS (Susceptible-Exposed-Infected-Removed-Susceptible) model and fed it with data for Manaus on mobility, COVID-19 hospitalizations, numbers of cases and deaths. Our model contemplated the current vaccination rates for all vaccines applied in Manaus and the individual protection rates already known for each vaccine. Our results indicate that the SARS-CoV-2 gamma (P.1) strain that originated in the Amazon region is not the cause of the second wave of COVID-19 in Manaus, but rather this strain originated during the second wave and became predominant in January 2021. Our multi-strain SEIRS model indicates that neither the doubled transmission rate of the gamma variant nor the loss of immunity alone is sufficient to explain the sudden rise of hospitalizations in late December 2020. Our results also indicate that the most plausible explanation for the current second wave is a SARS-CoV-2 infection level at around 50% of the population in early December 2020, together with loss of population immunity and early relaxation of restrictive measures. The most-plausible model indicates that contact with one strain does not provide protection against other strains and that the gamma variant has a transmissibility rate twice that of the original SARS-CoV-2 strain. Our model also shows that, despite the advance of vaccination, and even if future vaccination advances at a steady pace, the introduction of the delta variant or other new variants could cause a new wave of COVID-19.

Bayesian inference for the log-symmetric autoregressive conditional duration model.

This paper adapts Hamiltonian Monte Carlo methods for application in log-symmetric autoregressive conditional duration models. These recent models are based on a class of log-symmetric distributions. In this class, it is possible to model both median and skewness of the duration time distribution. We use the Bayesian approach to estimate the model parameters of some log-symmetric autoregressive conditional duration models and evaluate their performance using a Monte Carlo simulation study. The usefulness of the estimation methodology is demonstrated by analyzing a high frequency financial data set from the German DAX of 2016.

On a new piecewise regression model with cure rate: Diagnostics and application to medical data.

In this article, we discuss an extension of the classical negative binomial cure rate model with piecewise exponential distribution of the time to event for concurrent causes, which enables the modeling of monotonic and non-monotonic hazard functions (ie, the shape of the hazard function is not assumed as in traditional parametric models). This approach produces a flexible cure rate model, depending on the choice of time partition. We discuss local influence on this negative binomial power piecewise exponential model. We report on Monte Carlo simulation studies and application of the model to real melanoma and leukemia datasets.

How Brazil's President turned the country into a global epicenter of COVID-19.

In this manuscript, we point out that the federal government headed by President Bolsonaro has pursued a political agenda that contributed to the spread of COVID-19, transforming the country into a major repository for SARS-CoV-2 and its variants, thus representing a risk for worldwide containment efforts. Furthermore his actions are also weakening democratic institutions, which could counter his political agenda, effectively facilitating the spread of COVID-19. Thus, the perpetuation of the COVID-19 pandemic in Brazil is due to human behaviour factors, especially high-level public decision makers.

Weighted Lindley frailty model: estimation and application to lung cancer data.

In this paper, we propose a novel frailty model for modeling unobserved heterogeneity present in survival data. Our model is derived by using a weighted Lindley distribution as the frailty distribution. The respective frailty distribution has a simple Laplace transform function which is useful to obtain marginal survival and hazard functions. We assume hazard functions of the Weibull and Gompertz distributions as the baseline hazard functions. A classical inference procedure based on the maximum likelihood method is presented. Extensive simulation studies are further performed to verify the behavior of maximum likelihood estimators under different proportions of right-censoring and to assess the performance of the likelihood ratio test to detect unobserved heterogeneity in different sample sizes. Finally, to demonstrate the applicability of the proposed model, we use it to analyze a medical dataset from a population-based study of incident cases of lung cancer diagnosed in the state of São Paulo, Brazil.

The First Case of Immunity Loss and SARS-CoV-2 Reinfection by the Same Virus Lineage in Amazonia.

We report the first confirmed record of a SARS-CoV-2 immunity loss and reinfection for the Amazon region and for Brazil by the same virus lineage. The patient presented an asymptomatic condition the first time and an aggravated one after reinfection. We raise the possibility of a recessive genotype in the Amazonian population that does not generate an immune memory response to SARS-CoV-2.

Brazil’s COVID-19 epicenter in Manaus: how much of the population has already been exposed and are vulnerable to SARS-CoV-2?

Is Brazil’s COVID-19 epicenter really approaching herd immunity? A recent study estimated that in October 2020 three-quarters of the population of Manaus (the capital of the largest state in the Brazilian Amazon) had contact with SARS-CoV-2. We show that 46% of the Manaus population having had contact with SARS-CoV-2 at that time is a more plausible estimate, and that Amazonia is still far from herd immunity. The second wave of COVID-19 is now evident in Manaus. We predict that the pandemic of COVID-19 will continue throughout 2021, given the duration of naturally acquired immunity of only 240 days and the slow pace of vaccination. Manaus has a large percentage of the population that is susceptible (35 to 45% as of May 17, 2021). Against this backdrop, measures to restrict urban mobility and social isolation are still necessary, such as the closure of schools and universities, since the resumption of these activities in 2020 due to the low attack rates of SARS-CoV-2 was the main trigger for the second wave in Manaus.

How Brazil’s President turned the country into a global epicenter of COVID-19

In this manuscript, we point out that the federal government headed by President Bolsonaro has pursued a political agenda that contributed to the spread of COVID-19, transforming the country into a major repository for SARS-CoV-2 and its variants, thus representing a risk for worldwide containment efforts. Furthermore his actions are also weakening democratic institutions, which could counter his political agenda, effectively facilitating the spread of COVID-19. Thus, the perpetuation of the COVID-19 pandemic in Brazil is due to human behaviour factors, especially high-level public decision makers.

The first case of immunity loss and SARS-CoV-2 reinfection by the same virus lineage in Amazonia

We report the first confirmed record of a SARS-CoV-2 immunity loss and reinfection for the Amazon region and for Brazil by the same virus lineage. The patient presented an asymptomatic condition the first time and an aggravated one after reinfection. We raise the possibility of a recessive genotype in the Amazonian population that does not generate an immune memory response to SARS-CoV-2.

A new cure rate model with flexible competing causes with applications to melanoma and transplantation data.

In this article, we introduce a long-term survival model in which the number of competing causes of the event of interest follows the zero-modified geometric (ZMG) distribution. Such distribution accommodates equidispersion, underdispersion, and overdispersion and captures deflation or inflation of zeros in the number of lesions or initiated cells after the treatment. The ZMG distribution is also an appropriate alternative for modeling clustered samples when the number of competing causes of the event of interest consists of two subpopulations, one containing only zeros (cure proportion), while in the other (noncure proportion) the number of competing causes of the event of interest follows a geometric distribution. The advantage of this assumption is that we can measure the cure proportion in the initiated cells. Furthermore, the proposed model can yield greater or lower cure proportion than that of the geometric distribution when modeling the number of competing causes. In this article, we present some statistical properties of the proposed model and use the maximum likelihood method to estimate the model parameters. We also conduct a Monte Carlo simulation study to evaluate the performance of the estimators. We present and discuss two applications using real-world medical data to assess the practical usefulness of the proposed model.

Parametric modal regression with varying precision.

In this paper, we propose a simple parametric modal linear regression model where the response variable is gamma distributed using a new parameterization of this distribution that is indexed by mode and precision parameters, that is, in this new regression model, the modal and precision responses are related to a linear predictor through a link function and the linear predictor involves covariates and unknown regression parameters. The main advantage of our new parameterization is the straightforward interpretation of the regression coefficients in terms of the mode of the positive response variable, as is usual in the context of generalized linear models, and direct inference in parametric mode regression based on the likelihood paradigm. Furthermore, we discuss residuals and influence diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. Finally, we illustrate the usefulness of the new model by two applications, to biology and demography.

Incorporation of frailties into a cure rate regression model and its diagnostics and application to melanoma data.

Cure rate models have been widely studied to analyze time-to-event data with a cured fraction of patients. Our proposal consists of incorporating frailty into a cure rate model, as an alternative to the existing models to describe this type of data, based on the Birnbaum-Saunders distribution. Such a distribution has theoretical arguments to model medical data and has shown empirically to be a good option for their analysis. An advantage of the proposed model is the possibility to jointly consider the heterogeneity among patients by their frailties and the presence of a cured fraction of them. In addition, the number of competing causes is described by the negative binomial distribution, which absorbs several particular cases. We consider likelihood-based methods to estimate the model parameters and to derive influence diagnostics for this model. We assess local influence on the parameter estimates under different perturbation schemes. Deriving diagnostic tools is needed in all statistical modeling, which is another novel aspect of our proposal. Numerical evaluation of the considered model is performed by Monte Carlo simulations and by an illustration with melanoma data, both of which show its good performance and its potential applications. Particularly, the illustration confirms the importance of statistical diagnostics in the modeling.

Birnbaum-Saunders frailty regression models: Diagnostics and application to medical data.

In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum-Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum-likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real-world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.