Semiparametric Research Articles

Exploring shared frailty models for cluster-specific risk estimation: A study on diabetes patients with a history of acute coronary syndrome

This study proposes the use of semiparametric log-normal shared frailty models to analyze time-to-event data for individuals with similar features referred to as clusters. Shared frailty models are useful for modeling and estimating common risk in the lifetimes of individuals in these clusters. While various methods have been proposed for estimating shared frailty models, few studies have explored the use of the pseudo-full-likelihood method. In this study, the pseudo-full-likelihood and hierarchical likelihood approaches were used to construct and estimate parameter estimates and check for asymptotic properties via simulations. Log-normal semiparametric frailty model was used to obtain cluster-specific frailty based on the semiparametric log-normal shared frailty distribution. The results of both methods were compared, and prediction intervals for a random effect were obtained. To further investigate the existence of shared frailty in diabetes patients and a history of acute coronary syndrome (STEMI and NSTEMI), data from UK Biobank was used. The results suggest the presence of frailty within the clusters and indicate cluster time dependence in the study population. Overall, this study highlights the potential benefits of using the pseudo-full-likelihood method in shared frailty modeling and provides insights into the impact of observed variabilities on hazards within clusters.

Application of Semi-parametric Spatial Lag Model in the Study of the Relationship Between Innovation Efficiency and Industrial Development in China’s Pharmaceutical Manufacturing Industry

Application of Semi-parametric Spatial Lag Model in the Study of the Relationship Between Innovation Efficiency and Industrial Development in China’s Pharmaceutical Manufacturing Industry

Copula-based analysis of dependent current status data with semiparametric linear transformation model.

This paper discusses regression analysis of current status data with dependent censoring, a problem that often occurs in many areas such as cross-sectional studies, epidemiological investigations and tumorigenicity experiments. Copula model-based methods are commonly employed to tackle this issue. However, these methods often face challenges in terms of model and parameter identification. The primary aim of this paper is to propose a copula-based analysis for dependent current status data, where the association parameter is left unspecified. Our method is based on a general class of semiparametric linear transformation models and parametric copulas. We demonstrate that the proposed semiparametric model is identifiable under certain regularity conditions from the distribution of the observed data. For inference, we develop a sieve maximum likelihood estimation method, using Bernstein polynomials to approximate the nonparametric functions involved. The asymptotic consistency and normality of the proposed estimators are established. Finally, to demonstrate the effectiveness and practical applicability of our method, we conduct an extensive simulation study and apply the proposed method to a real data example.

A general semi-parametric elliptical distribution model for semi-supervised learning

ABSTRACT This research proposes a novel semi-parametric elliptical distribution model for application in semi-supervised learning tasks. We use labelled and unlabelled data to develop a pseudo maximum likelihood method for estimation and classification. The proposed estimator outperforms the estimator based solely on labelled data and achieves the semi-parametric efficiency bound with a suitable size of unlabelled data. We efficiently maximise the objective function by utilising low-dimensional groupwise pseudo-likelihood functions in a block coordinate descent manner while ensuring numerical stability and convergence through appropriate bandwidth selectors and initial parameter estimates. Additionally, the study comprehensively investigates the impact of labelled and unlabelled data on the pseudo maximum likelihood estimator and classifier. Simulation studies and empirical data applications illustrate the superiority of our methodology.

Optimal subsampling for semi-parametric accelerated failure time models with massive survival data using a rank-based approach.

Subsampling is a practical strategy for analyzing vast survival data, which are progressively encountered across diverse research domains. While the optimal subsampling method has been applied to inferences for Cox models and parametric accelerated failure time (AFT) models, its application to semi-parametric AFT models with rank-based estimation have received limited attention. The challenges arise from the non-smooth estimating function for regression coefficients and the seemingly zero contribution from censored observations in estimating functions in the commonly seen form. To address these challenges, we develop optimal subsampling probabilities for both event and censored observations by expressing the estimating functions through a well-defined stochastic process. Meanwhile, we apply an induced smoothing procedure to the non-smooth estimating functions. As the optimal subsampling probabilities depend on the unknown regression coefficients, we employ a two-step procedure to obtain a feasible estimation method. An additional benefit of the method is its ability to resolve the issue of underestimation of the variance when the subsample size approaches the full sample size. We validate the performance of our estimators through a simulation study and apply the methods to analyze the survival time of lymphoma patients in the surveillance, epidemiology, and end results program.

Semiparametric Additive Modeling of the Restricted Mean Survival Time.

Analysis of the restricted mean survival time (RMST) has become increasingly common in biomedical studies during the last decade as a means of estimating treatment or covariate effects on survival. Advantages of RMST over the hazard ratio (HR) include increased interpretability and lack of reliance on the often tenuous proportional hazards assumption. Some authors have argued that RMST regression should generally be the frontline analysis as opposed to methods based on counting process increments. However, in order for the use of the RMST to be more mainstream, it is necessary to broaden the range of data structures to which pertinent methods can be applied. In this report, we address this issue from two angles. First, most of existing methodological development for directly modeling RMST has focused on multiplicative models. An additive model may be preferred due to goodness of fit and/or parameter interpretation. Second, many settings encountered nowadays feature high-dimensional categorical (nuisance) covariates, for which parameter estimation is best avoided. Motivated by these considerations, we propose stratified additive models for direct RMST analysis. The proposed methods feature additive covariate effects. Moreover, nuisance factors can be factored out of the estimation, akin to stratification in Cox regression, such that focus can be appropriately awarded to the parameters of chief interest. Large-sample properties of the proposed estimators are derived, and a simulation study is performed to assess finite-sample performance. In addition, we provide techniques for evaluating a fitted model with respect to risk discrimination and predictive accuracy. The proposed methods are then applied to liver transplant data to estimate the effects of donor characteristics on posttransplant survivaltime.

Hybrid Modeling for On-Line Fermentation Optimization and Scale-Up: A Review

Modeling is a crucial tool in the biomanufacturing industry, namely in fermentation processes. This work discusses both mechanistic and data-driven models, each with unique benefits and application potential. It discusses semi-parametric hybrid modeling, a growing field that combines these two types of models for more accurate and easy result extrapolation. The characteristics and structure of such hybrid models will be examined. Moreover, its versatility will be highlighted, showing its usefulness in various stages of process development, including real-time monitoring and optimization. Scale-up remains one of the most relevant topics in fermentation processes, as it is important to have reproducible critical quality attributes, such as titer and yield, on larger scales. Furthermore, the process still relies on empirical correlations and iterative optimization. For these reasons, it is important to improve scale-up predictions, through e.g., the use of digital tools. Perspectives will be presented on the potential that hybrid modeling has by predicting performance across different process scales. This could provide more efficient and reliable biomanufacturing processes that require less resource consumption through experimentation.

Resolving the Stellar-Collapse and Hierarchical-Merger Origins of the Coalescing Black Holes.

Spin and mass properties provide essential clues in distinguishing the origins of coalescing black holes (BHs). With a dedicated semiparametric population model for the coalescing binary black holes (BBHs), we identify two distinct categories of BHs among the GWTC-3 events, which is favored over the one population scenario by a logarithmic Bayes factor (lnB) of 7.5. One category, with a mass ranging from ∼25M_{⊙} to ∼80M_{⊙}, is distinguished by the high spin magnitudes (∼0.75) and consistent with the hierarchical merger origin. The other category, characterized by low spins, has a sharp mass cutoff at ∼40M_{⊙}, which is natural for the stellar-collapse origin and in particular the pair-instability explosion of massive stars. We infer the local hierarchical merger rate density as 0.46_{-0.24}^{+0.61} Gpc^{-3} yr^{-1}. Additionally, we find that a fraction of the BBHs has a cosine-spin-tilt-angle distribution concentrated preferentially around 1, and the fully isotropic distribution for spin orientation is disfavored by a lnB of -6.3, suggesting that the isolated field evolution channels are contributing to the total population.

Unraveling the interplay between mental workload, occupational fatigue, physiological responses and cognitive performance in office workers

Recently, cognitive demands in workplaces have surged significantly. This study explored the intricate relationship among mental workload (MWL), occupational fatigue, physiological responses, and cognitive performance in office workers by using collective semi-parametric models. One hundred office workers were selected from twenty offices involved in cognitive performance. MWL was assessed through the NASA Task Load Index (NASA-TLX), and occupational fatigue was measured using the Persian version of the Swedish Occupational Fatigue Inventory. Physiological responses, including respiratory rate, the electrical conductivity of the skin (ECS), Heart Rate (HR), and other heart-related parameters, were recorded from the participants during a work shift. Selective and Divided Attention tests were chosen to evaluate workers' cognitive function based on cognitive task analysis. The mean of MWL and occupational fatigue scores were 66.28 ± 11.76 and 1.62 ± 1.07, respectively. There was a significant moderate correlation between two dimensions, mental demand (0.429) and frustration (0.409), with functional fatigue. Also, Significant and, of course, nonlinear relationships were observed between MWL and HR (R2 = 0.44, P-value < 0.001) and ECS (R2 = 0.45, P-value < 0.001) and reaction time in selected (R2 = 0.34, P-value < 0.001) and divided test (R2 = 0.48, P-value < 0.001). Similarly, nonlinear relationships were observed between physiological responses and cognitive performance with fatigue among participants who had experienced higher levels of occupational fatigue. The MWL and fatigue seem to have a significant and non-linear effect on physiological parameters such as HR and ECS and cognitive parameters such as reaction time. Moreover, MWL can influence the dimension of functional fatigue of workers.

Semiparametric varying-coefficient additive hazards model for informatively interval-censored failure time data

The analysis of interval-censored data with informative observation processes has recently attracted much attention and a few methods have been developed. However, all of the existing methods assume that covariate effects are constant and this may not be true sometimes in practice. To address this, in this paper, we propose a varying-coefficient additive hazards model and in the proposed method, frailty variables are used to describe the dependence between the failure time and the informative observation process. For inference, a Bernstein polynomials-based, two-step sieve maximum likelihood method is developed and the proposed method can be easily implemented. Furthermore, the resulting estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the proposed approach works well for practical situations. The proposed method is applied to a cardiac allograft vasculopathy (CAV) study that motivated this investigation.

Risk factors for COVID-19 and their association with mortality in Ecuadorian patients admitted to the ICU: A retrospective cohort multicentric study.

Several risk factors were associated with mortality in patients with coronavirus disease 2019 (COVID-19) infection in intensive care units (ICU). We assessed the effect of risk factors related to the characteristics and clinical history of the population, laboratory test results, drug management, and type of ventilation on the probability of survival/discharge from the ICU. A retrospective cohort multicentric study of adults with COVID-19 admitted to the ICU between March 2020 and December 2021. Data were collected from 6 hospitals in 5 cities in Ecuador. The primary outcome was ICU survival/discharge. Survival analysis was conducted using semi-parametric Cox proportional hazards models. Of those admitted to the ICU with COVID-19, (n = 991), mean age was 56.76 ± 13.14, and 65.9% were male. Regarding the primary outcome, 51.1% (n = 506) died and 48.9% (n = 485) survived. Of the group that died, their mean age was higher than the survivors (60.7 vs 52.60 years, respectively), and they had a higher prevalence of comorbidities such as arterial hypertension (37.2% vs 20.4%, respectively) and diabetes mellitus (26.9% vs 15.7%, respectively), with P < .001. In ventilatory management, 32.7% of patients used noninvasive ventilation and high-flow nasal cannula, and 67.3% required invasive ventilatory support. After adjusting for confounders, Cox regression analysis showed that patients were less likely to be discharged alive from the ICU if they met the following conditions: arterial hypertension (hazard ratio [HR] = 0.83 95% CI 0.723-0.964), diabetes mellitus (HR = 0.80 95% CI 0.696-0.938), older than 62 years (HR = 0.86 95% CI 0.790-0.956), obese (body mass index ≥ 30) (HR = 0.78 95% CI 0.697-0.887), 1 unit increase in SOFA score (HR = 0.94 95% CI 0.937-0.961), PaO2/FiO2 ratio <100 mm Hg (HR = 0.84 95% CI 0.786-0.914), and the use of invasive mechanical ventilation (HR = 0.68 95% CI 0.614-0.769). Risk factors associated with increased mortality were older age, obesity, arterial hypertension, and diabetes. Factors such as male gender, chronic obstructive pulmonary disease, acute kidney injury, and cancer reported in other investigations did not have the same effect on mortality in our study.

Cause-specific hazard Cox models with partly interval censoring - Penalized likelihood estimation using Gaussian quadrature.

The cause-specific hazard Cox model is widely used in analyzing competing risks survival data, and the partial likelihood method is a standard approach when survival times contain only right censoring. In practice, however, interval-censored survival times often arise, and this means the partial likelihood method is not directly applicable. Two common remedies in practice are (i) to replace each censoring interval with a single value, such as the middle point; or (ii) to redefine the event of interest, such as the time to diagnosis instead of the time to recurrence of a disease. However, the mid-point approach can cause biased parameter estimates. In this article, we develop a penalized likelihood approach to fit semi-parametric cause-specific hazard Cox models, and this method is general enough to allow left, right, and interval censoring times. Penalty functions are used to regularize the baseline hazard estimates and also to make these estimates less affected by the number and location of knots used for the estimates. We will provide asymptotic properties for the estimated parameters. A simulation study is designed to compare our method with the mid-point partial likelihood approach. We apply our method to the Aspirin in Reducing Events in the Elderly (ASPREE) study, illustrating an application of our proposed method.

Semiparametric Structural Equation Models with Interval-Censored Data

Structural equation models offer a valuable tool for delineating the complicated interrelationships among multiple variables, including observed and latent variables. Over the last few decades, structural equation models have successfully analyzed complete and right-censored survival data, exemplified by wide applications in psychological, social, or genomic studies. However, the existing methodology for structural equation modeling is not concerned with interval-censored data, a type of coarse survival data arising typically from periodic examinations for the occurrence of asymptomatic disease. The present study aims to fill this gap and provide a flexible semiparametric structural equation modeling framework. A general class of factor-augmented transformation models is proposed to model the interval-censored outcome of interest in the presence of latent risk factors. An expectation–maximization algorithm is subtly designed to conduct the nonparametric maximum likelihood estimation. Furthermore, the asymptotic properties of the proposed estimators are established by leveraging the empirical process theory. The numerical results obtained from extensive simulations and an application to the Alzheimer’s disease data set demonstrate the proposed method’s empirical performance and practical utility.

Outcome risk model development for heterogeneity of treatment effect analyses: a comparison of non-parametric machine learning methods and semi-parametric statistical methods

BackgroundIn randomized clinical trials, treatment effects may vary, and this possibility is referred to as heterogeneity of treatment effect (HTE). One way to quantify HTE is to partition participants into subgroups based on individual’s risk of experiencing an outcome, then measuring treatment effect by subgroup. Given the limited availability of externally validated outcome risk prediction models, internal models (created using the same dataset in which heterogeneity of treatment analyses also will be performed) are commonly developed for subgroup identification. We aim to compare different methods for generating internally developed outcome risk prediction models for subject partitioning in HTE analysis.MethodsThree approaches were selected for generating subgroups for the 2,441 participants from the United States enrolled in the ASPirin in Reducing Events in the Elderly (ASPREE) randomized controlled trial. An extant proportional hazards-based outcomes predictive risk model developed on the overall ASPREE cohort of 19,114 participants was identified and was used to partition United States’ participants by risk of experiencing a composite outcome of death, dementia, or persistent physical disability. Next, two supervised non-parametric machine learning outcome classifiers, decision trees and random forests, were used to develop multivariable risk prediction models and partition participants into subgroups with varied risks of experiencing the composite outcome. Then, we assessed how the partitioning from the proportional hazard model compared to those generated by the machine learning models in an HTE analysis of the 5-year absolute risk reduction (ARR) and hazard ratio for aspirin vs. placebo in each subgroup. Cochran’s Q test was used to detect if ARR varied significantly by subgroup.ResultsThe proportional hazard model was used to generate 5 subgroups using the quintiles of the estimated risk scores; the decision tree model was used to generate 6 subgroups (6 automatically determined tree leaves); and the random forest model was used to generate 5 subgroups using the quintiles of the prediction probability as risk scores. Using the semi-parametric proportional hazards model, the ARR at 5 years was 15.1% (95% CI 4.0–26.3%) for participants with the highest 20% of predicted risk. Using the random forest model, the ARR at 5 years was 13.7% (95% CI 3.1–24.4%) for participants with the highest 20% of predicted risk. The highest outcome risk group in the decision tree model also exhibited a risk reduction, but the confidence interval was wider (5-year ARR = 17.0%, 95% CI= -5.4–39.4%). Cochran’s Q test indicated ARR varied significantly only by subgroups created using the proportional hazards model. The hazard ratio for aspirin vs. placebo therapy did not significantly vary by subgroup in any of the models. The highest risk groups for the proportional hazards model and random forest model contained 230 participants each, while the highest risk group in the decision tree model contained 41 participants.ConclusionsThe choice of technique for internally developed models for outcome risk subgroups influences HTE analyses. The rationale for the use of a particular subgroup determination model in HTE analyses needs to be explicitly defined based on desired levels of explainability (with features importance), uncertainty of prediction, chances of overfitting, and assumptions regarding the underlying data structure. Replication of these analyses using data from other mid-size clinical trials may help to establish guidance for selecting an outcomes risk prediction modelling technique for HTE analyses.

Bayesian Estimation of the Semiparametric Spatial Lag Model

This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to sample all the parameters. The paper conducts numerical simulations to validate the proposed Bayesian estimation theory using a numerical example. The simulation results demonstrate satisfactory estimation performance of the parameter part and the fitting performance of the nonparametric function under different spatial weight matrix settings. Furthermore, the paper applies the constructed model and its estimation method to an empirical study on the relationship between economic growth and carbon emissions in China, illustrating the practical application value of the theoretical results.

Sign‐flip inference for spatial regression with differential regularisation

SummaryWe address the problem of performing inference on the linear and nonlinear terms of a semiparametric spatial regression model with differential regularisation. For the linear term, we propose a new resampling procedure, based on (partial) sign‐flipping of an appropriate transformation of the residuals of the model. The proposed resampling scheme can mitigate the bias effect induced by the differential regularisation. We prove that the proposed test is asymptotically exact. Moreover, we show, by simulation studies, that it enjoys very good control of Type‐I error also in small sample scenarios, differently from parametric alternatives. Additionally, we show that the proposed test has higher power with respect than recently proposed nonparametric tests on the linear term of semiparametric regression models with differential regularisation. Concerning the nonlinear term, we develop three different inference approaches: a parametric one and two nonparametric alternatives. The nonparametric tests are based on a sign‐flip approach. One of these is proved to be asymptotically exact, while the other is proved to be exact also for finite samples. Simulation studies highlight the good control of Type‐I error of the nonparametric approaches with respect the parametric test, while retaining high power.

Semi-supervised Double Deep Learning Temporal Risk Prediction (SeDDLeR) with Electronic Health Records

Background:Risk prediction plays a crucial role in planning for prevention, monitoring, and treatment. Electronic Health Records (EHRs) offer an expansive repository of temporal medical data encompassing both risk factors and outcome indicators essential for effective risk prediction. However, challenges emerge due to the lack of readily available gold-standard outcomes and the complex effects of various risk factors. Compounding these challenges are the false positives in diagnosis codes, and formidable task of pinpointing the onset timing in annotations. Objective:We develop a Semi-supervised Double Deep Learning Temporal Risk Prediction (SeDDLeR) algorithm based on extensive unlabeled longitudinal Electronic Health Records (EHR) data augmented by a limited set of gold standard labels on the binary status information indicating whether the clinical event of interest occurred during the follow-up period. Methods:The SeDDLeR algorithm calculates an individualized risk of developing future clinical events over time using each patient’s baseline EHR features via the following steps: (1) construction of an initial EHR-derived surrogate as a proxy for the onset status; (2) deep learning calibration of the surrogate along gold-standard onset status; and (3) semi-supervised deep learning for risk prediction combining calibrated surrogates and gold-standard onset status. To account for missing onset time and heterogeneous follow-up, we introduce temporal kernel weighting. We devise a Gated Recurrent Units (GRUs) module to capture temporal characteristics. We subsequently assess our proposed SeDDLeR method in simulation studies and apply the method to the Massachusetts General Brigham (MGB) Biobank to predict type 2 diabetes (T2D) risk. Results:SeDDLeR outperforms benchmark risk prediction methods, including Semi-parametric Transformation Model (STM) and DeepHit, with consistently best accuracy across experiments. SeDDLeR achieved the best C-statistics ( 0.815, SE 0.023; vs STM +.084, SE 0.030, P-value .004; vs DeepHit +.055, SE 0.027, P-value .024) and best average time-specific AUC (0.778, SE 0.022; vs STM + 0.059, SE 0.039, P-value .067; vs DeepHit + 0.168, SE 0.032, P-value <0.001) in the MGB T2D study. Conclusion:SeDDLeR can train robust risk prediction models in both real-world EHR and synthetic datasets with minimal requirements of labeling event times. It holds the potential to be incorporated for future clinical trial recruitment or clinical decision-making.

Comparison of Some Robust Methods of Difference Based Ridge Estimator in Semiparametric Regression Model

The semiparametric regression models have received a lot of attention from researchers recently because it combines parametric and nonparametric methods, it is one of the advanced topics in data analysis for various studies, which aims to find the best capabilities and a high level of efficiency. One of the most important semiparametric regression models is the partial linear regression model (PLM), which consists of a parametric component and a nonparametric component, for the purpose of estimating the parametric component, the difference method will be used to remove the nonparametric component. When the analysis hypotheses of the parametric component are not fulfilled, it will suffer from several problems, the most important of which is the problem of complete multicollinearity, besides the multicollinearity, there are also outliers in the data. In this research, the problems of multicollinearity and outliers of the semiparametric regression model were addressed, where simulation was used to generate data with different sample sizes and for different correlations and outlier ratios and for different methods such as [Difference Ridge based M robust with Nadaraya – Watson (DRMNW), Difference Ridge based S robust with Nadaraya – Watson (DRSNW), Difference Ridge based M robust with Smoothing spline (DRMSP), Difference Ridge based S robust with Smoothing spline (DRSSP)], the results showed that method Difference Ridge based M robust with Smoothing spline (DRMSP) is the best estimator.

Profile quasi-maximum likelihood estimation for semiparametric varying-coefficient spatial autoregressive panel models with fixed effects

Profile quasi-maximum likelihood estimation for semiparametric varying-coefficient spatial autoregressive panel models with fixed effects

Modelling Mixed-Frequency Time Series with Structural Change

AbstractPredictive ability of time series models is easily compromised in the presence of structural breaks, common among financial and economic variables amidst market shocks and policy regime shifts. We address this problem by estimating a semiparametric mixed-frequency model, that incorporate high frequency data either in the conditional mean or the conditional variance equation. The inclusion of high frequency data through non-parametric smoothing functions complements the low frequency data to capture possible non-linear relationships triggered by the structural change. Simulation studies indicate that in the presence of structural change, the varying frequency in the mean model provides improved in-sample fit and superior out-of-sample predictive ability relative to low frequency time series models. These hold across a broad range of simulation settings, such as varying time series lengths, nature of structural break points, and temporal dependencies. We illustrate the relative advantage of the method in predicting stock returns and foreign exchange rates in the case of the Philippines.