Characterizing quantile-varying covariate effects under the accelerated failure time model.

An important task in survival analysis is choosing a structure for the relationship between covariates of interest and the time-to-event outcome. For example, the accelerated failure time (AFT) model structures each covariate effect as a constant multiplicative shift in the outcome distribution across all survival quantiles. Though parsimonious, this structure cannot detect or capture effects that differ across quantiles of the distribution, a limitation that is analogous to only permitting proportional hazards in the Cox model. To address this, we propose a general framework for quantile-varying multiplicative effects under the AFT model. Specifically, we embed flexible regression structures within the AFT model and derive a novel formula for interpretable effects on the quantile scale. A regression standardization scheme based on the g-formula is proposed to enable the estimation of both covariate-conditional and marginal effects for an exposure of interest. We implement a user-friendly Bayesian approach for the estimation and quantification of uncertainty while accounting for left truncation and complex censoring. We emphasize the intuitive interpretation of this model through numerical and graphical tools and illustrate its performance through simulation and application to a study of Alzheimer's disease and dementia.

Relative effects of climate factors and malaria control interventions on changes of parasitaemia risk in Burkina Faso from 2014 to 2017/2018.

BACKGROUND: In Burkina Faso, the prevalence of malaria has decreased over the past two decades, following the scale-up of control interventions. The successful development of malaria parasites depends on several climatic factors. Intervention gains may be reversed by changes in climatic factors. In this study, we investigated the role of malaria control interventions and climatic factors in influencing changes in the risk of malaria parasitaemia. METHODS: Bayesian logistic geostatistical models were fitted on Malaria Indicator Survey data from Burkina Faso obtained in 2014 and 2017/2018 to estimate the effects of malaria control interventions and climatic factors on the temporal changes of malaria parasite prevalence. Additionally, intervention effects were assessed at regional level, using a spatially varying coefficients model. RESULTS: Temperature showed a statistically important negative association with the geographic distribution of parasitaemia prevalence in both surveys; however, the effects of insecticide-treated nets (ITNs) use was negative and statistically important only in 2017/2018. Overall, the estimated number of infected children under the age of 5 years decreased from 704,202 in 2014 to 290,189 in 2017/2018. The use of ITNs was related to the decline at national and regional level, but coverage with artemisinin-based combination therapy only at regional level. CONCLUSION: Interventions contributed more than climatic factors to the observed change of parasitaemia risk in Burkina Faso during the period of 2014 to 2017/2018. Intervention effects varied in space. Longer time series analyses are warranted to determine the differential effect of a changing climate on malaria parasitaemia risk.

Varying-coefficients for regional quantile via KNN-based LASSO with applications to health outcome study.

Health outcomes, such as body mass index and cholesterol levels, are known to be dependent on age and exhibit varying effects with their associated risk factors. In this paper, we propose a novel framework for dynamic modeling of the associations between health outcomes and risk factors using varying-coefficients (VC) regional quantile regression via K-nearest neighbors (KNN) fused Lasso, which captures the time-varying effects of age. The proposed method has strong theoretical properties, including a tight estimation error bound and the ability to detect exact clustered patterns under certain regularity conditions. To efficiently solve the resulting optimization problem, we develop an alternating direction method of multipliers (ADMM) algorithm. Our empirical results demonstrate the efficacy of the proposed method in capturing the complex age-dependent associations between health outcomes and their risk factors.

Multistate modeling and structure selection for multitype recurrent events and terminal event data.

In cardiovascular disease studies, a large number of risk factors are measured but it often remains unknown whether all of them are relevant variables and whether the impact of these variables is changing with time or remains constant. In addition, more than one kind of cardiovascular disease events can be observed in the same patient and events of different types are possibly correlated. It is expected that different kinds of events are associated with different covariates and the forms of covariate effects also vary between event types. To tackle these problems, we proposed a multistate modeling framework for the joint analysis of multitype recurrent events and terminal event. Model structure selection is performed to identify covariates with time-varying coefficients, time-independent coefficients, and null effects. This helps in understanding the disease process as it can detect relevant covariates and identify the temporal dynamics of the covariate effects. It also provides a more parsimonious model to achieve better risk prediction. The performance of the proposed model and selection method is evaluated in numerical studies and illustrated on a real dataset from the Atherosclerosis Risk in Communities study.

Analysis of Prognostic Factors of Low-Grade Gliomas in Adults Using Time-Dependent Competing Risk Models: A Population Study Based on the Surveillance, Epidemiology, and End Results Database.

BACKGROUND: Because of multiple competing death outcomes and time-varying coefficients, using a Cox regression model to analyze the prognostic factors of low-grade gliomas (LGG) may lead to a possible bias. Therefore, we adopted time-dependent competing risk models to obtain accurate prognostic factors for LGG. METHODS: In this retrospective cohort study, data were extracted from patients enrolled in the Surveillance, Epidemiology, and End Results (SEER) database between 2000 and 2018. Univariate analysis was performed using the cumulative incidence function (CIF) and Kaplan-Meier (KM) function. Time-dependent competing risk and Cox regression models were used in the multivariable analysis. RESULTS: A total of 2581 patients were diagnosed with low-grade glioma, among whom 889 died from low-grade glioma, 114 died from other causes, and the rest were alive. The time-dependent competing risk models indicated that age, sex, marital status, primary tumor site, histological type, tumor diameter, surgery, and year of diagnosis were significantly associated with low-grade glioma-specific death, and the relative effect of age, tumor diameter, surgery, oligodendroglioma, and mixed glioma on low-grade glioma-specific death changed over time. Compared with the competing risk models, the Cox regression model misestimated the hazard ratio (HR) of covariates on the outcome and even produced false-negative results. CONCLUSIONS: The time-dependent competing risk models were better than the Cox regression model for evaluating the impact of covariates on low-grade glioma-specific mortality in the presence of competing risks and time-varying coefficients. The models identified the prognostic factors of LGG more accurately than the Cox regression model.

Dynamic semiparametric transformation models for recurrent event data with a terminal event.

Recurrent event data with a terminal event commonly arise in many longitudinal follow-up studies. This article proposes a class of dynamic semiparametric transformation models for the marginal mean functions of the recurrent events with a terminal event, where some covariate effects may be time-varying. An estimation procedure is developed for the model parameters, and the asymptotic properties of the resulting estimators are established. In addition, relevant significance tests are suggested for examining whether or not covariate effects vary with time, and a model checking procedure is presented for assessing the adequacy of the proposed models. The finite sample performance of the proposed estimators is examined through simulation studies, and an application to a medical cost study of chronic heart failure patients is provided.

How many asymptomatic cases were unconfirmed in the US COVID-19 pandemic? The evidence from a serological survey.

A serological survey from CDC revealed more than 10% of individuals in America probably resolving or past infection with SARS-CoV-2 at the end of 2020, which illustrated there were massive unconfirmed asymptomatic infected people by contrast with the reported cases numbers. Asymptomatic patients as one of the crucial reasons for the COVID-19 pandemic being tough to contain, estimating the number of unconfirmed ones including the active infected and having cured in this population, is of great guiding significance for formulating epidemic prevention and control policies. This paper proposes a varying coefficient Susceptible-Infected-Removed-Susceptible (vSIRS) model to obtain the time series data of the unconfirmed asymptomatic infected numbers. Moreover, due to the time-varying coefficients, we can effectively track the situation changes of the COVID-19 intervened by related policy support and medical care level through this epidemiological model. A novel two-stage approach with a programming problem is correspondingly developed to accomplish the estimation of the unknown parameters in the vSIRS model. Subsequently, by leveraging seroprevalence data, daily reported cases data, and other clinical information, we apply the vSIRS model to analyze the evolution of COVID-19 in America. The modeling results show millions of active asymptomatic infected individuals were unconfirmed during the autumn and winter of 2020, which was a momentous factor for driving American COVID-19 pandemic.

An additive hazards frailty model with semi-varying coefficients.

Proportional hazards frailty models have been extensively investigated and used to analyze clustered and recurrent failure times data. However, the proportional hazards assumption in the models may not always hold in practice. In this paper, we propose an additive hazards frailty model with semi-varying coefficients, which allows some covariate effects to be time-invariant while other covariate effects to be time-varying. The time-varying and time-invariant regression coefficients are estimated by a set of estimating equations, whereas the frailty parameter is estimated by the moment method. The large sample properties of the proposed estimators are established. The finite sample performance of the estimators is examined by simulation studies. The proposed model and estimation are illustrated with an analysis of data from a rehospitalization study of colorectal cancer patients.

Spatially varying age-period-cohort analysis with application to US mortality, 2002-2016.

Many public health databases index disease counts by age groups and calendar periods within geographic regions (e.g., states, districts, or counties). Issues around relative risk estimation in small areas are well-studied; however, estimating trend parameters that vary across geographic regions has received less attention. Additionally, small counts (e.g., $<10$) in most publicly accessible databases are censored, further complicating age-period-cohort (APC) analysis in small areas. Here, we present a novel APC model with left-censoring and spatially varying intercept and trends, estimated with correlations among contiguous geographic regions. Like traditional models, our model captures population-scale trends, but it can also be used to characterize geographic disparities in relative risk and age-adjusted trends over time. To specify the joint distribution of our three spatially varying parameters, we adapt the generalized multivariate conditional autoregressive prior, previously used for multivariate disease mapping. Specified in this manner, region-specific parameters are correlated spatially, and also to one another. Estimation is performed using the No-U-Turn Hamiltonian Monte Carlo sampler in Stan. We conduct a simulation study to assess the performance of the proposed model relative to the standard model, and conclude with an application to US state-level opioid overdose mortality in men and women aged 15-64 years.

Predictive generalized varying-coefficient longitudinal model.

We propose a nonparametric bivariate varying coefficient generalized linear model to predict a mean response trajectory in the future given an individual's characteristics at present or an earlier time point in a longitudinal study. Given the measurement time of the predictors, the coefficients vary as functions of the future time over which the prediction of the mean response is concerned and illustrate the dynamic association between the future response and the earlier measured predictors. We use a nonparametric approach that takes advantage of features of both the kernel and the spline methods for estimation. The resulting coefficient estimator is asymptotically consistent under mild regularity conditions. We also develop a new bootstrap approach to construct simultaneous confidence bands for statistical inference about the coefficients and the predicted response trajectory based on the coverage rate of bootstrap estimates. We use the Framingham Heart Study to illustrate the methodology. The proposed procedure is applied to predict the probability trajectory of hypertension risk given individuals' health condition in early adulthood and to examine the impact of risk factors in early adulthood on a long-term risk of hypertension over several decades.

Competing barnacle species with a time dependent reproduction rate.

A simple competition model with time varying periodic coefficients, in which two species use different reproduction strategies, is explored in this paper. The two species considered comprise a native species which reproduces once a year over a short time period and an invasive species which is capable of reproducing throughout the entire year. A monotonicity property of the model is instrumental for its analysis. The model reveals that the time difference between the peak of reproduction for the two species is a critical factor in determining the outcome of competition between these species. The impact of climate change and an anthropogenic disturbance, comprising the creation of additional substrate, is also investigated using a modified model. The results of this paper describe how climate change will favour the invasive species by reducing the time period between the reproductive peaks of the two species and how the addition of new substrates is likely to endanger a small population of either of the two species, depending on the timing of the introduction of the substrates.

Tree-based modeling of time-varying coefficients in discrete time-to-event models.

Hazard models are popular tools for the modeling of discrete time-to-event data. In particular two approaches for modeling time dependent effects are in common use. The more traditional one assumes a linear predictor with effects of explanatory variables being constant over time. The more flexible approach uses the class of semiparametric models that allow the effects of the explanatory variables to vary smoothly over time. The approach considered here is in between these modeling strategies. It assumes that the effects of the explanatory variables are piecewise constant. It allows, in particular, to evaluate at which time points the effect strength changes and is able to approximate quite complex variations of the change of effects in a simple way. A tree-based method is proposed for modeling the piecewise constant time-varying coefficients, which is embedded into the framework of varying-coefficient models. One important feature of the approach is that it automatically selects the relevant explanatory variables and no separate variable selection procedure is needed. The properties of the method are investigated in several simulation studies and its usefulness is demonstrated by considering two real-world applications.

Assessing the impact of sleep time on truck driver performance using a recurrent event model.

Driver fatigue is a major safety concern for commercial truck drivers and is directly related to the total hours of sleep prior to a working shift. To evaluate changes in driving performance over a long on-duty driving period, we propose a mixed Poisson process recurrent-event model with time-varying coefficients. We use data from 96 commercial truck drivers whose trucks were instrumented with an advanced in situ data acquisition system. The driving performance is measured by unintentional lane deviation events, a known performance deterioration related to fatigue. Driver sleep time and other activities are extracted from a detailed activity register. The time-varying coefficients are used to model the baseline intensity and difference among three cohorts of shifts in which the driver slept less than 7 hours, between 7 to 9 hours, and more than 9 hours prior to driving. We use the penalized B-splines approach to model the time-varying coefficients and an expectation-maximization algorithm with embedded penalized quasi-likelihood approximation for parameter estimation. Simulation studies show that the proposed model fits low and high event rate data well. The results show a significantly higher intensity after 8 hours of on-duty driving for shifts with less than 7 hours of sleep prior to work. The study also shows drivers tend to self-adjust sleep duration, total driving hours, and breaks. This study provides crucial insight into the impact of sleep time on driving performance for commercial truck drivers and highlights the on-road safety implications of insufficient sleep and breaks while driving.

The seasonal sensitivity of brown bear denning phenology in response to climatic variability.

BACKGROUND: For brown bears (Ursus arctos), hibernation is a critical part of the annual life cycle because energy savings during hibernation can be crucial for overwintering, and females give birth to cubs at that time. For hibernation to be a useful strategy, timing is critical. However, environmental conditions vary greatly, which might have a negative effect on the functionality of the evolved biological time-keeping. Here, we used a long-term dataset (69 years) on brown bear denning phenology recorded in 12 Russian protected areas and quantified the phenological responses to variation in temperature and snow depth. Previous studies analyzing the relationship between climate and denning behavior did not consider that the brown bear response to variation in climatic factors might vary through a period preceding den entry and exit. We hypothesized that there is a seasonal sensitivity pattern of bear denning phenology in response to variation in climatic conditions, such that the effect of climatic variability will be pronounced only when it occurs close to den exit and entry dates. RESULTS: We found that brown bears are most sensitive to climatic variations around the observed first den exit and last entry dates, such that an increase/decrease in temperature in the periods closer to the first den exit and last entry dates have a greater influence on the denning dates than in other periods. CONCLUSIONS: Our study shows that climatic factors are modulating brown bear hibernation phenology and provide a further structuring of this modulation. The sensitivity of brown bears to changes in climatic factors during hibernation might affect their ability to cope with global climate change. Therefore, understanding these processes will be essential for informed management of biodiversity in a changing world.

Semiparametric varying-coefficient regression analysis of recurrent events with applications to treatment switching.

This paper investigates the semiparametric statistical methods for recurrent events. The mean number of the recurrent events are modeled with the generalized semiparametric varying-coefficient model that can flexibly model three types of covariate effects: time-constant effects, time-varying effects, and covariate-varying effects. We assume that the time-varying effects are unspecified functions of time and the covariate-varying effects are parametric functions of an exposure variable specified up to a finite number of unknown parameters. Different link functions can be selected to provide a rich family of models for recurrent events data. The profile estimation methods are developed for the parametric and nonparametric components. The asymptotic properties are established. We also develop some hypothesis testing procedures to test validity of the parametric forms of covariate-varying effects. The simulation study shows that both estimation and hypothesis testing procedures perform well. The proposed method is applied to analyze a data set from an acyclovir study and investigate whether acyclovir treatment reduces the mean relapse recurrences.

Selection of effects in Cox frailty models by regularization methods.

In all sorts of regression problems, it has become more and more important to deal with high-dimensional data with lots of potentially influential covariates. A possible solution is to apply estimation methods that aim at the detection of the relevant effect structure by using penalization methods. In this article, the effect structure in the Cox frailty model, which is the most widely used model that accounts for heterogeneity in survival data, is investigated. Since in survival models one has to account for possible variation of the effect strength over time the selection of the relevant features has to distinguish between several cases, covariates can have time-varying effects, time-constant effects, or be irrelevant. A penalization approach is proposed that is able to distinguish between these types of effects to obtain a sparse representation that includes the relevant effects in a proper form. It is shown in simulations that the method works well. The method is applied to model the time until pregnancy, illustrating that the complexity of the influence structure can be strongly reduced by using the proposed penalty approach.

Time-dependent impact of age and comorbidities on long-term overall survival after liver resection.

BACKGROUND & AIMS: Advanced age and comorbidities are known to be associated with increased perioperative risks after liver resection. However, the precise impact of these variables on long-term overall survival (OS) remains unclear. Thus, the aim of this study was to evaluate the confounder-adjusted, time-dependent effect of age and comorbidities on OS following hepatectomy for primary and secondary malignancies. METHODS: From a prospective database of 1.143 liver resections, 763 patients treated for primary and secondary malignancies were included. For time-varying OS calculations, a Cox-Aalen model was fitted. The confounder-adjusted hazard was compared with mortality tables of the German population. RESULTS: Overall, age (P = 0.003) and comorbidities (P = 0.001) were associated with shortened OS. However, time-dependent analysis indicated that age and comorbidities had no impact on OS within 39 and 55 months after resection respectively. From this time on, a significant decline in OS was shown. Subgroup analysis indicated an earlier increase of the effect of age in patients with hepatocellular carcinoma (17 months) than in those with colorectal metastases (70 months). The confounder-adjusted hazard of 70-year-old patients was increased post-operatively but dropped 66 months after surgery, and the risk of death was comparable to the general population 78 months after resection. At this time, one-third of patients aged 70 years and older were still alive. CONCLUSIONS: With regard to long-term outcome, liver resection for both primary and secondary malignancies should not be categorically denied due to age and comorbidities. This information should be considered for the patient selection process and informed consent.

Semi-varying coefficient multinomial logistic regression for disease progression risk prediction.

This paper proposes a risk prediction model using semi-varying coefficient multinomial logistic regression. We use a penalized local likelihood method to do the model selection and estimate both functional and constant coefficients in the selected model. The model can be used to improve predictive modelling when non-linear interactions between predictors are present. We conduct a simulation study to assess our method's performance, and the results show that the model selection procedure works well with small average numbers of wrong-selection or missing-selection. We illustrate the use of our method by applying it to classify the patients with early rheumatoid arthritis at baseline into different risk groups in future disease progression. We use a leave-one-out cross-validation method to assess its correct prediction rate and propose a recalibration framework to evaluate how reliable are the predicted risks. Copyright © 2016 John Wiley & Sons, Ltd.

Bayesian semiparametric model with spatially-temporally varying coefficients selection.

In spatiotemporal analysis, the effect of a covariate on the outcome usually varies across areas and time. The spatial configuration of the areas may potentially depend on not only the structured random intercept but also spatially varying coefficients of covariates. In addition, the normality assumption of the distribution of spatially varying coefficients could lead to potential biases of estimations. In this article, we proposed a Bayesian semiparametric space-time model where the spatially-temporally varying coefficient is decomposed as fixed, spatially varying, and temporally varying coefficients. We nonparametrically modeled the spatially varying coefficients of space-time covariates by using the area-specific Dirichlet process prior with weights transformed via a generalized transformation. We modeled the temporally varying coefficients of covariates through the dynamic model. We also took into account the uncertainty of inclusion of the spatially-temporally varying coefficients by variable selection procedure through determining the probabilities of different effects for each covariate. The proposed semiparametric approach shows its improvement compared with the Bayesian spatial-temporal models with normality assumption on spatial random effects and the Bayesian model with the Dirichlet process prior on the random intercept. We presented a simulation example to evaluate the performance of the proposed approach with the competing models. We used an application to low birth weight data in South Carolina as an illustration.

The impact of sustained malaria control in the Loreto region of Peru: a retrospective, observational, spatially-varying interrupted time series analysis of the PAMAFRO program.

Background: Although malaria control investments worldwide have resulted in dramatic declines in transmission since 2000, progress has stalled. In the Amazon, malaria resurgence has followed withdrawal of Global Fund support of the Project for Malaria Control in Andean Border Areas (PAMAFRO). We estimate intervention-specific and spatially-explicit effects of the PAMAFRO program on malaria incidence across the Loreto region of Peru, and consider the influence of the environmental risk factors in the presence of interventions. Methods: We conducted a retrospective, observational, spatial interrupted time series analysis of malaria incidence rates among people reporting to health posts across Loreto, Peru between the first epidemiological week of January 2001 and the last epidemiological week of December 2016. Model inference is at the smallest administrative unit (district), where the weekly number of diagnosed cases of Plasmodium vivax and Plasmodium falciparum were determined by microscopy. Census data provided population at risk. We include as covariates weekly estimates of minimum temperature and cumulative precipitation in each district, as well as spatially- and temporally-lagged malaria incidence rates. Environmental data were derived from a hydrometeorological model designed for the Amazon. We used Bayesian spatiotemporal modeling techniques to estimate the impact of the PAMAFRO program, variability in environmental effects, and the role of climate anomalies on transmission after PAMAFRO withdrawal. Findings: During the PAMAFRO program, incidence of P. vivax declined from 42.8 to 10.1 cases/1000 people/year. Incidence for P. falciparum declined from 14.3 to 2.5 cases/1000 people/year over this same period. The effects of PAMAFRO-supported interventions varied both by geography and species of malaria. Interventions were only effective in districts where interventions were also deployed in surrounding districts. Further, interventions diminished the effects of other prevailing demographic and environmental risk factors. Withdrawal of the program led to a resurgence in transmission. Increasing minimum temperatures and variability and intensity of rainfall events from 2011 onward and accompanying population displacements contributed to this resurgence. Interpretation: Malaria control programs must consider the climate and environmental scope of interventions to maximize effectiveness. They must also ensure financial sustainability to maintain local progress and commitment to malaria prevention and elimination efforts, as well as to offset the effects of environmental change that increase transmission risk. Funding: National Aeronautics and Space Administration, National Institutes of Health, Bill and Melinda Gates Foundation.