Pseudo-likelihood Method Research Articles

Proprotein convertase subtilisin/kexin type 9 levels and the risk of cardiovascular events in statin-treated patients with cardiovascular disease

Abstract Background Previous studies have not found a consistent association between circulating proprotein convertase subtilisin/kexin type 9 (PCSK9) levels and the risk of cardiovascular events. Although PCSK9 is cleaved by furin and becomes biologically inactive, previous studies have employed measurement methods which cannot distinguish furin-cleaved and uncleaved form of PCSK9. Methods This study is a prespecified sub-study of the REAL-CAD study which is a prospective, multicenter, randomized trial to compare high- versus low-dose statin in patients with stable coronary artery disease (CAD). The substudy primary endpoint was a composite of major adverse cerebrovascular and cardiovascular events (MACCE) defined as a composite of cardiovascular death, nonfatal myocardial infarction, nonfatal ischemic stroke, or unstable angina requiring emergency hospitalization. In a case-cohort study, sub-cohort was randomly selected samples from the total cohort as tripling the number of cases with MACCE. Serum mature (uncleaved) and furin-cleaved PCSK9 levels obtained at 6 months after randomization were measured among participants who subsequently developed MACCE and among randomly selected participants. Their relationships with cardiovascular events were assessed according to the quartiles. Cox proportional hazards model was used to calculate hazard ratios (HRs) with 95% confidence intervals (CI). Results From 1,478 patients in the sub-cohort, the Cox proportional hazards models with a pseudolikelihood method for case-cohort design revealed that the risk of primary endpoint in patients in the highest quartile of mature PCSK9 concentrations was similar to the lowest quartile (HR 0.809; 95%CI, 0.541-1.209). Similarly, HRs for the highest to lowest quartiles of furin-cleaved PCSK9s was 0.948 [95%CI, 0.645-1.392] (P=0.784). As compared to the lowest quartile, both serum mature and furin-cleaved PCSK9 levels did not predict the cardiovascular events. Conclusions Serum mature and furin-cleaved PCSK9 levels did not provide useful information in the assessment of future cardiovascular events in statin-treated patients with stable CAD.Study FlowThe weighted Kaplan-Meier cueves

Benchmarking South African water utilities using three efficiency analysis methods

ABSTRACT This paper compares efficiency scores from the data envelopment analysis (DEA), stochastic frontier analysis (SFA), and stochastic non-parametric envelopment of data (StoNED) methods in the context of regulating South African water utilities. We estimate cost efficiency based on cross-sectional data from 102 South African water utilities in the period 2013/14. We compare the impact of methodological choices on the efficiency scores. For StoNED, we compare scores from two different estimation techniques (method of moments and pseudolikelihood). We also use the naïve method of averaging (NMA) and compare its results to those generated by the other methods. Results show that the choice of method has an impact on efficiency estimates and monetary cost reduction targets. When water sector regulators in the developing countries intend to benchmark utilities based on each of these methods, heterogeneity and the operating environments of utilities should be considered before deciding on the estimation method.

Serum mature and furin-cleaved proprotein convertase subtilisin/kexin type 9 levels and their association with cardiovascular events in statin-treated patients with cardiovascular disease

Previous studies have not found a consistent association between circulating proprotein convertase subtilisin/kexin type 9 (PCSK9) levels and the risk of cardiovascular events partly due to measurement methods that cannot distinguish between uncleaved and furin-cleaved forms of PCSK9. This is a prespecified sub-study of the REAL-CAD study which is a prospective, multicenter, randomized trial to compare high- versus low-dose statin in patients with stable coronary artery disease (CAD). The primary endpoint was major adverse cerebrovascular and cardiovascular events (MACCE) defined as a composite of cardiovascular death, nonfatal myocardial infarction, nonfatal ischemic stroke, or unstable angina requiring emergency hospitalization. In this case-cohort study, serum mature (uncleaved) and furin-cleaved PCSK9 levels obtained at 6 months after randomization were measured among 426 participants who developed MACCE (cases) and 1,478 randomly selected participants (sub-cohort). From 1,478 patients in sub-cohort, the Cox proportional hazards models with a pseudolikelihood method for case-cohort design revealed that the risk of the primary endpoint in patients with the highest quartile of mature PCSK9 levels was similar to that in the lowest quartile (hazard ration [HR] 0.809; 95% confidence intervals [CI], 0.541-1.209). Similarly, the HR for the highest to lowest quartiles of furin-cleaved PCSK9 was 0.948 [95% CI, 0.645-1.392] (P = 0.784). Compared to the lowest quartile, neither serum mature nor furin-cleaved PCSK9 levels predicted MACCE. In a large-scale secondary prevention cohort, serum mature and furin-cleaved PCSK9 levels did not provide useful information for predicting future cardiovascular events in statin-treated patients with stable CAD.

Distributed Pseudo-Likelihood Method for Community Detection in Large-Scale Networks

This paper proposes a distributed pseudo-likelihood method (DPL) to conveniently identify the community structure of large-scale networks. Specifically, we first propose a block-wise splitting method to divide large-scale network data into several subnetworks and distribute them among multiple workers. For simplicity, we assume the classical stochastic block model. Then, the DPL algorithm is iteratively implemented for the distributed optimization of the sum of the local pseudo-likelihood functions. At each iteration, the worker updates its local community labels and communicates with the master. The master then broadcasts the combined estimator to each worker for the new iterative steps. Based on the distributed system, DPL significantly reduces the computational complexity of the traditional pseudo-likelihood method using a single machine. Furthermore, to ensure statistical accuracy, we theoretically discuss the requirements of the worker sample size. Moreover, we extend the DPL method to estimate degree-corrected stochastic block models. The superior performance of the proposed distributed algorithm is demonstrated through extensive numerical studies and real data analysis.

Fast Calculation of Gaussian Process Multiple-Fold Cross-Validation Residuals and their Covariances

We generalize fast Gaussian process leave-one-out formulas to multiple-fold cross-validation, highlighting in turn the covariance structure of cross-validation residuals in simple and universal kriging frameworks. We illustrate how resulting covariances affect model diagnostics. We further establish in the case of noiseless observations that correcting for covariances between residuals in cross-validation-based estimation of the scale parameter leads back to maximum likelihood estimation. Also, we highlight in broader settings how differences between pseudo-likelihood and likelihood methods boil down to accounting or not for residual covariances. The proposed fast calculation of cross-validation residuals is implemented and benchmarked against a naive implementation, all in R. Numerical experiments highlight the substantial speed-ups that our approach enables. However, as supported by a discussion on main drivers of computational costs and by a numerical benchmark, speed-ups steeply decline as the number of folds (say, all sharing the same size) decreases. An application to a contaminant localization test case illustrates that the way of grouping observations in folds may affect model assessment and parameter fitting compared to leave-one-out. Overall, our results enable fast multiple-fold cross-validation, have consequences in model diagnostics, and pave the way to future work on hyperparameter fitting as well as on goal-oriented fold design. Supplementary materials for this article are available online.

Estimation of the causal effects of time-varying treatments in nested case-control studies using marginal structural Cox models.

When estimating the causal effects of time-varying treatments on survival in nested case-control (NCC) studies, marginal structural Cox models (Cox-MSMs) with inverse probability weights (IPWs) are a natural approach. However, calculating IPWs from the cases and controls is difficult because they are not random samples from the full cohort, and the number of subjects may be insufficient for calculation. To overcome these difficulties, we propose a method for calculating IPWs to fit Cox-MSMs to NCC sampling data. We estimate the IPWs using a pseudo-likelihood estimation method with an inverse probability of sampling weight using NCC samples, and additional samples of subjects who experience treatment changes and subjects whose follow-up is censored are required to calculate the weights. Our method only requires covariate histories for the samples. The confidence intervals are calculated from the robust variance estimator for the NCC sampling data. We also derive the asymptotic properties of the estimator of Cox-MSM under NCC sampling. The proposed methods will allow researchers to apply several case-control matching methods to improve statistical efficiency. A simulation study was conducted to evaluate the finite sample performance of the proposed method. We also applied our method to a motivating pharmacoepidemiological study examining the effect of statins on the incidence of coronary heart disease. The proposed method may be useful for estimating the causal effects of time-varying treatments in NCC studies.

Evaluating the Efficiency of Restricted Pseudo Likelihood Estimation in Balanced and Unbalanced Clustered Binary Data Models

Clustered binary data analysis is a common task in various fields, such as social sciences and epidemiology. Restricted Pseudo Likelihood Estimation (PLE) is a widely used approach for analyzing clustered binary data, providing flexibility in handling complex dependencies within clusters. This study aims to evaluate the efficiency of Restricted Pseudo Likelihood Estimation in balanced and unbalanced clustered binary data models. Using simulated data, we compare the performance of PLE in balanced and unbalanced clustered binary data scenarios. We consider various factors such as the number of clusters, cluster sizes, and intra-cluster correlation. The preferred class of models for clustered binary data is the Hierarchical Generalized Linear Model (HGLM). This article compares the performance of a restricted pseudo-likelihood estimation method of the Hierarchical Generalized Linear Model (HGLM) with equal and unequal cluster sizes. Through comprehensive simulation experiments, we assess the accuracy and precision of PLE estimates in terms of parameter estimation, standard errors, and hypothesis testing. Our findings provide insights into the efficiency of Restricted Pseudo Likelihood Estimation (RPLE) in balanced and unbalanced clustered binary data models. The results highlight the advantages and limitations of PLE in different scenarios, aiding researchers in selecting appropriate modeling approaches for their specific data characteristics. The results can guide researchers in making informed decisions regarding the selection and application of PLE in their own studies, ultimately enhancing the validity and reliability of statistical analyses in the presence of clustered binary data.

Statistical inference of multi-state transition model for longitudinal data with measurement error and heterogeneity

. Multi-state transition model is typically used to analyze longitudinal data in medicine and sociology. Moreover, variables in longitudinal studies usually are error-prone, and random effects are heterogeneous, which will result in biased estimates of the interest parameters. This article is intended to estimate the parameters of the multi-state transition model for longitudinal data with measurement error and heterogeneous random effects and further consider the covariate related to the covariance matrix of random effects is also error-prone when the covariate in the transition model is error-prone. We model the covariance matrix of random effects through the modified Cholesky decomposition and propose a pseudo-likelihood method based on the Monte Carlo expectation-maximization algorithm and the Bayesian method based on Markov Chain Monte Carlo to infer and calculate the whole estimates. Meanwhile, we obtain the asymptotic properties and evaluate the finite sample performance of the proposed method by simulation, which is well in terms of Bias, RMSE, and coverage rate of confidence intervals. In addition, we apply the proposed method to the MFUS data.

Semiparametric pseudo-score and pseudo-likelihood for evaluating correlate of protection in vaccine trials.

In vaccine clinical trials, vaccine efficacy endpoint analysis is usually associated with in high cost or extended study duration, due to the generally low infection rate. Correlate of protection (CoP), which refers to surrogate endpoint, usually immunological response, that can reliably predict the treatment effect, provides a more efficient and less costly approach to evaluate the vaccine. To handle the challenge of the missingness in the unobserved surrogate immune biomarker, the pseudo-score (PS) method, semiparametric method and pseudo-likelihood (PL) method demonstrated their advantages on different aspects. In this article, we propose new methodologies to combine the advantages of PS and PL with semiparametric methods respectively, to achieve higher estimate efficiency, allow continuous baseline predictor variable, and handle multiple surrogate markers. The advantage of our methodologies are demonstrated by a simulation study in different settings and applied to a case study, which eventually can improve the chance of a successful trial.

A pairwise pseudo-likelihood approach for regression analysis of left-truncated failure time data with various types of censoring

BackgroundFailure time data frequently occur in many medical studies and often accompany with various types of censoring. In some applications, left truncation may occur and can induce biased sampling, which makes the practical data analysis become more complicated. The existing analysis methods for left-truncated data have some limitations in that they either focus only on a special type of censored data or fail to flexibly utilize the distribution information of the truncation times for inference. Therefore, it is essential to develop a reliable and efficient method for the analysis of left-truncated failure time data with various types of censoring.MethodThis paper concerns regression analysis of left-truncated failure time data with the proportional hazards model under various types of censoring mechanisms, including right censoring, interval censoring and a mixture of them. The proposed pairwise pseudo-likelihood estimation method is essentially built on a combination of the conditional likelihood and the pairwise likelihood that eliminates the nuisance truncation distribution function or avoids its estimation. To implement the presented method, a flexible EM algorithm is developed by utilizing the idea of self-consistent estimating equation. A main feature of the algorithm is that it involves closed-form estimators of the large-dimensional nuisance parameters and is thus computationally stable and reliable. In addition, an R package LTsurv is developed.ResultsThe numerical results obtained from extensive simulation studies suggest that the proposed pairwise pseudo-likelihood method performs reasonably well in practical situations and is obviously more efficient than the conditional likelihood approach as expected. The analysis results of the MHCPS data with the proposed pairwise pseudo-likelihood method indicate that males have significantly higher risk of losing active life than females. In contrast, the conditional likelihood method recognizes this effect as non-significant, which is because the conditional likelihood method often loses some estimation efficiency compared with the proposed method.ConclusionsThe proposed method provides a general and helpful tool to conduct the Cox’s regression analysis of left-truncated failure time data under various types of censoring.

Estimation of peer pressure in dynamic homogeneous social networks

Social interaction with peer pressure is widely studied in social network analysis. Game theory can be utilized to model dynamic social interaction and one class of game network models assumes that peopleos decision payoff functions hinge on individual covariates and the choices of their friends. However, peer pressure would be misidentified and induce a non-negligible bias when incomplete covariates are involved in the game model. For this reason, we develop a generalized constant peer effects model based on homogeneity structure in dynamic social networks. The new model can effectively avoid bias through homogeneity pursuit and can be applied to a wider range of scenarios. To estimate peer pressure in the model, we first present two algorithms based on the initialize expand merge method and the polynomial-time two-stage method to estimate homogeneity parameters. Then we apply the nested pseudo-likelihood method and obtain consistent estimators of peer pressure. Simulation evaluations show that our proposed methodology can achieve desirable and effective results in terms of the community misclassification rate and parameter estimation error. We also illustrate the advantages of our model in the empirical analysis when compared with a benchmark model.

Inference on semi-parametric transformation model with a pairwise likelihood based on left-truncated and interval-censored data

Semi-parametric transformation models provide a general and flexible class of models for regression analysis of failure time data and many methods have been developed for their estimation. In particular, they include the proportional hazards and proportional odds models as special cases. In this paper, we discuss the situation where one observes left-truncated and interval-censored data, for which it does not seem to exist an established method. For the problem, in contrast to the commonly used conditional approach that may not be efficient, a pairwise pseudo-likelihood method is proposed to recover some missing information in the conditional method. The proposed estimators are proved to be consistent and asymptotically efficient and normal. A simulation study is conducted to assess the empirical performance of the method and suggests that it works well in practical situations. This method is illustrated by using a set of real data arising from an HIV/AIDS cohort study.

A Markov random field model with cumulative logistic functions for spatially dependent ordinal data

This paper presents a class of regression models with cumulative logistic functions that are chiefly designed to analyse spatially dependent ordinal data. In contrast to previous works, the proposed model requires neither the sites to be regularly spaced nor the assumption of an underlying continuous variable. It belongs to a more general class of Markov random field models, and can be considered an extension of the ordinal regression model with the proportional odds link function. Our proposed model allows practitioners to interpret the model parameters using odds ratios. Apart from the theoretical developments, this work also highlights the practical aspects of model fitting, including parameterisation, selection of neighbourhood, and calculation of standard errors. Simulation studies with regularly and irregularly spaced sites were conducted. Modelling strategies including pseudo-likelihood methods were found to be useful in both settings. The proposed model and the non-spatial counterpart were applied to the daily air quality index measured in the United Kingdom. The results indicate the presence of spatial effects and the incorporation of spatial effects led to better model performance in terms of various goodness-of-fit measures.

Bias correction via outcome reassignment for cross-sectional data with binary disease outcome.

Cross-sectionally sampled data with binary disease outcome are commonly analyzed in observational studies to identify the relationship between covariates and disease outcome. A cross-sectional population is defined as a population of living individuals at the sampling or observational time. It is generally understood that binary disease outcome from cross-sectional data contains less information than longitudinally collected time-to-event data, but there is insufficient understanding as to whether bias can possibly exist in cross-sectional data and how the bias is related to the population risk of interest. Wang and Yang (2021) presented the complexity and bias in cross-sectional data with binary disease outcome with detailed analytical explorations into the data structure. As the distribution of the cross-sectional binary outcome is quite different from the population risk distribution, bias can arise when using cross-sectional data analysis to draw inference for population risk. In this paper we argue that the commonly adopted age-specific risk probability is biased for the estimation of population risk and propose an outcome reassignment approach which reassigns a portion of the observed binary outcome, 0 or 1, to the other disease category. A sign test and a semiparametric pseudo-likelihood method are developed for analyzing cross-sectional data using the OR approach. Simulations and an analysis based on Alzheimer's Disease data are presented to illustrate the proposed methods.

Estimation of Zero-Inflated Population Mean with Highly Skewed Nonzero Component: A Bootstrapping Approach

This paper adopts a bootstrap procedure in the maximum pseudo-likelihood method under probability sampling designs. It estimates the mean of a population that is a mixture of excess zero and a nonzero skewed sub-population. Simulations studies show that the bootstrap confidence intervals for zero-inflated log-normal population consistently capture the true mean. The proposed method is applied to a real-life data set.

Estimation in tensor Ising models

AbstractThe $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geqslant 2$. This is a natural generalization of the matrix Ising model that provides a convenient mathematical framework for capturing, not just pairwise, but higher-order dependencies in complex relational data. In this paper, we consider the problem of estimating the natural parameter of the $p$-tensor Ising model given a single sample from the distribution on $N$ nodes. Our estimate is based on the maximum pseudolikelihood (MPL) method, which provides a computationally efficient algorithm for estimating the parameter that avoids computing the intractable partition function. We derive general conditions under which the MPL estimate is $\sqrt N$-consistent, that is, it converges to the true parameter at rate $1/\sqrt N$. Our conditions are robust enough to handle a variety of commonly used tensor Ising models, including spin glass models with random interactions and models where the rate of estimation undergoes a phase transition. In particular, this includes results on $\sqrt N$-consistency of the MPL estimate in the well-known $p$-spin Sherrington–Kirkpatrick model, spin systems on general $p$-uniform hypergraphs and Ising models on the hypergraph stochastic block model (HSBM). In fact, for the HSBM we pin down the exact location of the phase transition threshold, which is determined by the positivity of a certain mean-field variational problem, such that above this threshold the MPL estimate is $\sqrt N$-consistent, whereas below the threshold no estimator is consistent. Finally, we derive the precise fluctuations of the MPL estimate in the special case of the $p$-tensor Curie–Weiss model, which is the Ising model on the complete $p$-uniform hypergraph. An interesting consequence of our results is that the MPL estimate in the Curie–Weiss model saturates the Cramer–Rao lower bound at all points above the estimation threshold, that is, the MPL estimate incurs no loss in asymptotic statistical efficiency in the estimability regime, even though it is obtained by minimizing only an approximation of the true likelihood function for computational tractability.

Robust Bayesian inference for Big Data: Combining sensor-based records with traditional survey data

Big Data often presents as massive nonprobability samples. Not only is the selection mechanism often unknown but larger data volume amplifies the relative contribution of selection bias to total error. Existing bias adjustment approaches assume that the conditional mean structures have been correctly specified for the selection indicator or key substantive measures. In the presence of a reference probability sample, these methods rely on a pseudolikelihood method to account for the sampling weights of the reference sample, which is parametric in nature. Under a Bayesian framework, handling the sampling weights is an even bigger hurdle. To further protect against model misspecification, we expand the idea of double robustness such that more flexible nonparametric methods as well as Bayesian models can be used for prediction. In particular, we employ Bayesian additive regression trees which not only capture nonlinear associations automatically but permit direct quantification of the uncertainty of point estimates through its posterior predictive draws. We apply our method to sensor-based naturalistic driving data from the second Strategic Highway Research Program using the 2017 National Household Travel Survey as a benchmark.

A New Model of Discrete-Continuous Bivariate Distribution with Applications to Medical Data.

The bivariate Poisson exponential-exponential distribution is an important lifetime distribution in medical data analysis. In this article, the conditionals, probability mass function (pmf), Poisson exponential and probability density function (pdf), and exponential distribution are used for creating bivariate distribution which is called bivariate Poisson exponential-exponential conditional (BPEEC) distribution. Some properties of the BPEEC model are obtained such as the normalized constant, conditional densities, regression functions, and product moment. Moreover, the maximum likelihood and pseudolikelihood methods are used to estimate the BPEEC parameters based on complete data. Finally, two data sets of real bivariate data are analyzed to compare the methods of estimation. In addition, a comparison between the BPEEC model with the bivariate exponential conditionals (BEC) and bivariate Poisson exponential conditionals (BPEC) is considered.

Trade Continuity and Global Production Sharing in Emerging Economies: Evidence from Panel Gravity Analysis

ABSTRACT This article examines the effect of trade continuity, measured by the lagged imports of intermediate goods, on global production sharing in emerging economies. We estimate an augmented gravity model using the Poisson pseudo maximum likelihood method with a panel dataset of bilateral exports of 29 emerging economies from 2004 to 2017. Our results show that trade continuity positively affects global production sharing. We provide new empirical evidence that trade continuity is process-specific and may vary between parts and components and final assembly stages. Our findings have policy implications on the process-specific nature of global production sharing.

Fitting three-dimensional Laguerre tessellations by hierarchical marked point process models

We present a general statistical methodology for analysing a Laguerre tessellation data set viewed as a realization of a marked point process model. In the first step, for the points, we use a nested sequence of multiscale processes which constitute a flexible parametric class of pairwise interaction point process models. In the second step, for the marks/radii conditioned on the points, we consider various exponential family models where the canonical sufficient statistic is based on tessellation characteristics. For each step, parameter estimation based on maximum pseudolikelihood methods is tractable. For model selection, we consider maximized log pseudolikelihood functions for models of the radii conditioned on the points. Model checking is performed using global envelopes and corresponding tests in both steps and moreover by comparing observed and simulated tessellation characteristics in the second step. We apply our methodology for a 3D Laguerre tessellation data set representing the microstructure of a polycrystalline metallic material, where simulations under a fitted model may substitute expensive laboratory experiments.