Maximum Likelihood Estimation Research Articles

A remaining useful life prediction method of aluminum electrolytic capacitor with adaptive degradation model selection

The degradation process of aluminum electrolytic capacitors(AECs) usually exhibits characteristics such as non-linearity and multi-stage. These degradation features lead to the difficulty to accurately predict the remaining useful life(RUL) of the whole degradation process of AECs. To address this, by dividing the capacitor degradation process into two stages, a two-stage RUL prediction method for AECs considering multiple degradation models is proposed in this paper.In the offline parameter estimation phase, the initial degradation model parameters of two stages are estimated using two-step maximum likelihood estimation combined with particle swarm optimization(PSO) algorithm. In the dynamic parameter updating phase, a sequential Bayesian method is used to update the model parameters. To select the optimal degradation model, an evaluation method based on historical RUL similarity is proposed to calculate the fitness of each model. Finally, the effectiveness of the method is verified on NASA’s accelerated degradation data set and several widely used methods are used for comparison. The experimental results show that the proposed method has higher accuracy, which proves the superiority of the method.

Determining the prior mean in Bayesian logistic regression with sparse data: a nonarbitrary approach

Abstract Logistic regression models lead to a bias of the odds ratio (OR) as estimated using the maximum-likelihood (ML) method, when there are few study participants at the binary outcome and factor levels. Although Bayesian methods are frequently applied to reduce this sparse data bias, the specification of the prior distribution for regression coefficients is the most controversial feature. We propose a nonarbitrary and empirical method to determine the prior mean for regression coefficients in Bayesian logistic regression analysis for sparse data. The proposed prior mean is calculated as the difference between the observed log OR and the quasi-expectation of log OR, and is interpreted as a shrinkage statistic of the ML estimate. Further, for easy and fast inference, the proposed method applies to Bayesian logistic regression with the normal prior and the log-F prior via data augmentation. Simulation results indicate that the OR bias based on the proposed method is consistently smaller than that based on the ML method. The OR bias estimated using the proposed method is generally smaller than that based on the mean prior of zero for the regression coefficient. We apply the proposed methods to 2 real data sets.

Modified ridge estimator in the Bell regression model

Abstract The Bell regression model (BRM), a member of the generalized linear models (GLMs), can be used when the dependent variable consists of overdispersed count data. The maximum likelihood estimator (MLE) is generally used to estimate unknown regression coefficients. The major drawback of the MLE is an inflated variance when multicollinearity problems occur. In this study, we proposed a new biased estimator to cope with the multicollinearity in the BRM. The simulation study is conducted to illustrate the performance of the proposed estimator over the MLE and Bell ridge estimator (BRE). Also, we give real data examples to approve the applicability of the proposed estimator in real data problems.

Generalized bivariate Kummer-beta distribution with marginals defined on the unit interval.

In this paper, a generalized bivariate Kummer-beta distribution is proposed. The name derives from the fact that its particular cases include univariate Kummer-beta distributions. This distribution generalizes a number of existing bivariate beta distributions, including Nadarajah's bivariate distributions, Libby and Novick's bivariate beta distribution and a central bivariate Kummer-beta distribution. Various properties associated with this newly introduced distribution are derived. The derived properties include product moments, marginal densities, marginal moments, conditional densities, conditional moments, Rényi entropy and Shannon entropy. Motivated by possible applications in economics, genetics, hydrology, meteorology, nuclear physics, and reliability, we also derive distributions of the product and the ratio of the components following the proposed distribution. Parameter estimation by maximum likelihood method is discussed by deriving expressions for score functions. Inference based on maximum likelihood estimation supposes that the maximum likelihood estimators have zero bias and zero mean squared errors. A simulation study is performed to check this for finite samples.

Modelling Service Times Using Some Beta-Based Compound Distribution

The design of the queueing model involves modelling the arrival and service processes of the system. Conventionally, the arrival process is assumed to follow Poisson while service times are assumed to be exponentially distributed. Other distributions such as Weibull, uniform, lognormal have been used to model service times however, generalized distributions have not been used in this regard. In recent times, attention have been shifted to generalised families of distributions including Beta generalized family of distributions which led to the development of Beta-based distributions. Distributions generated from a mixture of beta random variables are quite numerous in literature with little or no application to service times data. In this study, six Beta-based compound distributions - Beta-Log-logistic distribution (BLlogD), Beta-Weibull distribution (BWeiD), Beta-Lomax distribution (BLomD), Beta-exponential distribution (BExD), Beta-Gompertz distribution (BGomD) and Beta-log-normal distribution (BLnormD) - were compared with the classical service times model on four service times data sets. Maximum likelihood estimator was employed in estimating parameters of the selected models while Akaike Information Criteria (AIC), Consistent Akaike Information Criterion (CAIC), Bayesian Information Criterion (BIC) and Hannan Quin information criterion (HQIC) statistics were employed to select the best model. CDFs, PDFs and PP-plots were used to fit the data of the suggested models. Results from the study shows that Beta-Exponential distribution (BExpD) performed better for the datasets I (AIC=640.3, CAIC=640.5,BIC=648.1 and HQIC=643.4), Beta-weibull distribution (BWeiD) performed better for the data sets II and III (AIC=204.2, 2142.4,CAIC=204.2, 2142.7,BIC=212.8, 2154.9 and HQIC=207.6, 2147.5) while Beta-log-logistic distribution (BLlogD) performed better for the data sets IV (AIC=2275.3,CAIC=2275.5, BIC=2289.3 and HQIC=2280.9). Findings from this study revealed some useful Beta-based compound distributions which performed better than the conventional service time model. From the findings of this study, we recommend researchers to dive deep into queueing theory.

LPI Radar Waveform Recognition Based on Hierarchical Classification Approach and Maximum Likelihood Estimation

The importance of information gathering is emphasized to minimize casualties and economic losses in warfare. Through electronic warfare, which utilizes electromagnetic waves, it is possible to discern the enemy’s intentions and respond accordingly, thereby leading the battle advantageously. Consequently, related research is actively underway. The development of various radar signal modulation techniques has revealed limitations in the existing modulation recognition methods, necessitating the development of distinguishing features to overcome these limitations. This paper proposes and analyzes distinguishing features that can differentiate various modulation schemes. Eleven distinguishing features were employed, and twenty-two types of modulated signals, including analog, digital, and composite modulation, were classified using hierarchical classification approach and maximum likelihood estimation (MLE). The proposed method achieves a recognition performance of 99.76% at an SNR of 20 dB and 98.45% at an SNR of 8 dB.

Determinants of health prevention behaviors in Portugal

Abstract Background One of the main causes of death in developed societies are chronic non-communicable diseases, often originated by risky behaviors as tobacco consumption, poor diet, excessive alcohol consumption and lack of physical activity. Changing lifestyles can thus lead to a reduction in chronic diseases and in their economic costs. The objective of this study is to understand what the main factors associated with health behaviors are. Methods We used the data collected through the Portuguese National Health Surveys from 2014 and 2019. The sample analyzed was composed of individuals aged 15 or more years old living in the national territory at the time the surveys were conducted. Data on demographics, socio-economic variables and health related variables was used. A maximum likelihood estimation was performed using a multivariate probit model, by using health behaviors (weekly exercise, healthy diet, non-smoking, and prudent alcohol consumption) as the outcomes of the analysis. Results The results point to a strong association between social class and health behaviors, particularly between higher income and healthy diet. It is important to highlight that having an appointment with a General Practitioner is positively associated with all healthy behaviors. For all behaviors but healthy diet, the coefficients are statistically significant at a 5% significance level and non-smoking displays the highest one (0.135). Conclusions This study presents the first step to understand the determinants of health prevention behaviors, which is important to design policies targeting lifestyles. One of its main conclusions indicates that social class (income and education) and GP appointments are associated with health behaviors. Further research would be needed to study the underlying mechanisms through which some of these factors impact behaviors. This presentation was supported by National Funds through FCT, I.P., within CINTESIS, R&D Unit (reference UIDB/4255/2020). Key messages • This study is an important step in the formulation of policies targeting lifestyles since it allows us to understand which factors are associated with health behaviors. • From this study one can conclude that social class characteristics, particularly income, and access to GP appointments are associated positively with health behaviors.

Real-time exposure to negative news media and suicidal ideation intensity among LGBTQ young adults in a high-stigma US state

Abstract Background With a recent surge in anti-LGBTQ policies and associated news/media coverage worldwide, there is a crucial need to study the role of LGBTQ negative news/media on proximal risk for suicide among LGBTQ youth, especially in high-stigma contexts. Methods Using a smartphone-based protocol, participants responded to brief self-report surveys 3x per day for 28 consecutive days. LGBTQ young adults (ages 18-24 years old) residing in Tennessee with recent suicidal ideation were recruited. At each assessment, participants reported real-time exposure to negative news/media, whether the news/media was related to LGBTQ topics, expectations of anti-LGBTQ rejection, and current intensity of passive suicidal ideation, active suicidal ideation, and self-harm ideation. Statistical analyses employed multilevel path analyses with restricted maximum likelihood estimation. Results 31 participants completed 2189 assessments (90.5% median compliance). Within-person effects showed that real-time exposure to LGBTQ - but not general - negative news/media was positively associated with suicidal ideation intensity. Significant indirect effects were present from exposure to LGBTQ negative news/media to higher suicidal ideation intensity through expectations of rejection. Mediation through expectations of rejection accounted for 25% and 39% of the total effect for active and passive suicidal ideation, respectively. Conclusions Findings have important public health implications related to media reporting, policy, and clinical intervention. Interventions targeting media organizations should promote responsible reporting practices and increase awareness of the potential suicidogenic impact of negative LGBTQ news coverage. This study joins numerous others in documenting the potential mental health harms of policies that restrict LGBTQ visibility and rights. Mental health professionals play a vital role in promoting coping in the face of exposure to LGBTQ negative news/media content.

The effects of hypothetical psychological interventions on alcohol use in European young adults

Abstract Background Low psychosocial well-being (PWB) and high emotion-driven impulsiveness (EDI) are associated with alcohol. Yet, it is unclear whether a hypothetical intervention targeting one or the other in adolescence might be more effective in reducing alcohol consumption (AC) in young adulthood. Therefore, we aimed to compare the separate causal effects of PWB and EDI in adolescence on AC in young adulthood. Methods We included 505 European young adults from the IDEFICS/I.Family cohort (mean age: 20.2 years; age range: 18.2-23.5 years) who did not drink alcohol at study entry. AC was operationalized as the amount of weekly consumed alcoholic beverages (mean: 4.2 drinks per week; range: 0.3-70 drinks per week). EDI was assessed using the negative urgency subscale from the UPPS-P Impulsive Behaviour Scale. PWB was assessed using the KINDLR Health-Related Quality of Life Questionnaire. Following the principles of target trial emulation, we estimated, separately, the average causal effects of PWB and EDI on AC accounting for relevant confounders and applying a semi-parametric doubly robust method (targeted maximum likelihood estimation). We stratified the results by sex and parental education. Results If all adolescents, hypothetically, had high levels of PWB, compared to low levels, we estimated a decrease in the average amount of alcoholic beverages in young adulthood by 0.1 drinks per week [95%-confidence interval: -2.3; 2.1]. Furthermore, if all adolescents had low levels of EDI, compared to high levels, we estimated an increase in alcoholic beverages in young adulthood by 1.5 drinks per week [0.1; 2.9]. Different effects for sex and parental education groups were found. Conclusions Hypothetical interventions targeting PWB in adolescents were not found to have effects on reducing AC in young adulthood. Interventions targeting EDI, however, would lead to an increase in AC. This may be due to unmeasured confounding and the missing distinction between drinking motives. Key messages • We demonstrate that causal inference methods, compared to traditional ones, improve the robustness of estimated effect measures and address important sources of bias in European cohort data. • To inform public health interventions on reducing alcohol consumption, future research should investigate different drinking motives, e.g. alleviating negative emotions or enhancing positive emotions.

Adherence to the ABC pathway improves prognosis in patients with AF: preliminary findings from an updated meta-analysis of 360,000 patients

Abstract Background With the increasing complexity of patients with Atrial Fibrillation (AF), the ‘Atrial Fibrillation Better Care’ (ABC) pathway was proposed to streamline a holistic approach for the comprehensive management of patients with AF. The ABC pathway is based on three main pillars: ‘A’ Avoid stroke (through optimal anticoagulant use); ‘B’ Better symptom control; and ‘C’ Cardiovascular and Comorbidity management optimization. Such a holistic and integrated approach is currently recommended by international guidelines, including the ones from the European Society of Cardiology (ESC); a previous meta-analysis showed sub-optimal adherence to such approach in real-world cohorts, with an overall reduction in the risk of major outcomes in patients treated according to the ABC pathway. We hereby performed an updated systematic review and meta-analysis of the current evidence on the implementation of the ABC pathway in patients with AF. Methods We performed a systematic review and meta-analysis according to PRISMA Guidelines. MEDLINE and EMBASE were searched for all studies reporting data on the prevalence of ABC pathway adherent management in patients with AF, and/or the association between ABC pathway management and the incidence of major outcomes, including all-cause death, cardiovascular death, thromboembolism, and major bleeding. Data on the prevalence of ABC pathway management were pooled using a generalized linear mixed model; number of events and total number of patients were pooled using a random-effect model. Pooled estimates were reported as odds ratios (OR) and 95% Confidence Intervals (95%CI); heterogeneity was estimated using the restricted maximum-likelihood estimator, and the Inconsistency index (I2) was also reported. Results 4,059 articles were retrieved from the literature search; after duplicates removal, title and abstract screening and full-text evaluation, 16 studies were included, for a total of more than 360,000 patients. Pooled prevalence of adherence to the ABC pathway was 28.5% (95%CI: 21.1-37.3%, I2=100%; Figure 1). Adherence to the ABC pathway was associated with a significant lower risk of all-cause death (pooled OR: 0.47, 95%CI: 0.40-0.56, I2=97%), cardiovascular death (pooled OR: 0.43, 95%CI: 0.33-0.56, I2=95%) and stroke (pooled OR: 0.61, 95%CI: 0.47-0.79, I2=91%; Figure 1). Patients treated adherent to the ABC pathway also showed a lower risk of major bleeding (pooled OR: 0.77, 95%CI: 0.66-0.90, I2=85%). Conclusions In this updated systematic review and meta-analysis, adherence to the ABC pathway was found in less than one-third of patients with AF. Implementation of the ABC pathway was associated with lower risk of all major adverse events in patients with AF, including all-cause death, and thromboembolic and bleeding events. These data further reinforce the need for routine implementation of the ABC pathway for the management of AF in clinical practice.Figure 1

A convexity-constrained parameterization of the random effects generalized partial credit model.

An alternative closed-form expression for the marginal joint probability distribution of item scores under the random effects generalized partial credit model is presented. The closed-form expression involves a cumulant generating function and is therefore subjected to convexity constraints. As a consequence, complicated moment inequalities are taken into account in maximum likelihood estimation of the parameters of the model, so that the estimation solution is always proper. Another important favorable consequence is that the likelihood function has a single local extreme point, the global maximum. Furthermore, attention is paid to expected a posteriori person parameter estimation, generalizations of the model, and testing the goodness-of-fit of the model. Procedures proposed are demonstrated in an illustrative example.

Matrix Factorization and Prediction for High-Dimensional Co-Occurrence Count Data via Shared Parameter Alternating Zero Inflated Gamma Model

High-dimensional sparse matrix data frequently arise in various applications. A notable example is the weighted word–word co-occurrence count data, which summarizes the weighted frequency of word pairs appearing within the same context window. This type of data typically contains highly skewed non-negative values with an abundance of zeros. Another example is the co-occurrence of item–item or user–item pairs in e-commerce, which also generates high-dimensional data. The objective is to utilize these data to predict the relevance between items or users. In this paper, we assume that items or users can be represented by unknown dense vectors. The model treats the co-occurrence counts as arising from zero-inflated Gamma random variables and employs cosine similarity between the unknown vectors to summarize item–item relevance. The unknown values are estimated using the shared parameter alternating zero-inflated Gamma regression models (SA-ZIG). Both canonical link and log link models are considered. Two parameter updating schemes are proposed, along with an algorithm to estimate the unknown parameters. Convergence analysis is presented analytically. Numerical studies demonstrate that the SA-ZIG using Fisher scoring without learning rate adjustment may fail to find the maximum likelihood estimate. However, the SA-ZIG with learning rate adjustment performs satisfactorily in our simulation studies.

Quantitative evidence of the community of shared future for mankind as a driver of sustainable development in human society

In an era marked by global economic challenges, an increasing array of non-traditional security threats, and a proliferation of conflicts and issues, China has put forth the building of a community of shared future for mankind as a way to address this question of the times. The theory of the community of shared future for mankind offers a framework to address contemporary issues by promoting equality, mutual benefit, security, justice, openness, innovation, multicultural exchange, and green development. This paper innovatively quantifies the five core principles of the theory of the community of shared future for mankind using the entropy method. It calculates the proxy variable for sustainable development, green total factor productivity, using the super-efficiency Slack-Based Measure model in Data Envelopment Analysis. Baseline regression is conducted on this basis. The Principal Component Analysis method and another Data Envelopment Analysis method, the Malmquist index, are utilized to recalculate the indicators, followed by another round of regression analysis. The results are consistent with the baseline regression. Additionally, Ordinary Least Squares, Partial Least Squares, Maximum Likelihood Estimation, Ridge regression, and Lasso regression are employed to ensure the robustness of the results. The findings indicate a significant positive relationship between the community of a shared future for mankind and the sustainable development of human society, with consistent conclusions drawn from different calculation methods and regression techniques. Through value recognition, international cooperation based on benefit-sharing and mutual reciprocity can guide humanity towards a harmonious coexistence with nature, irrespective of regional and economic disparities. This study provides quantitative evidence of the impact of the community of a shared future for mankind on the sustainable development of human society, filling a gap in existing research. Based on these findings, feasible policy recommendations are proposed to promote sustainable development in human society.

Statistical inference and data analysis for inverted Kumaraswamy distribution based on maximum ranked set sampling with unequal samples

A very useful modification to ranked set sampling (RSS) that allows a larger set size without significantly increasing ranking errors is the maximum ranked set sampling with unequal samples (MRSSU) approach. This article covers the parameter estimation of the inverted Kumaraswamy distribution using MRSSU and RSS designs. The maximum likelihood and Bayesian estimation techniques are considered. The regarded Bayesian estimation technique is determined in the case of non-informative and informative priors represented by Jeffreys and gamma priors, respectively. Squared error and minimum expected are the two loss functions that are employed. We presented a simulation study to evaluate the performance of the recommended estimations using root mean squared error and relative bias. The Bayes point estimates were computed using the Metropolis–Hastings algorithm. Additional conclusions have been made based on actual geological data regarding the intervals between Kiama Blowhole’s 64 consecutive eruptions. Based on the same number of measured units, the results of simulation and real data analysis showed that MRSSU estimators performed much better than their RSS counterparts.

Handling missing data in variational autoencoder based item response theory.

Recently Variational Autoencoders (VAEs) have been proposed as a method to estimate high dimensional Item Response Theory (IRT) models on large datasets. Although these improve the efficiency of estimation drastically compared to traditional methods, they have no natural way to deal with missing values. In this paper, we adapt three existing methods from the VAE literature to the IRT setting and propose one new method. We compare the performance of the different VAE-based methods to each other and to marginal maximum likelihood estimation for increasing levels of missing data in a simulation study for both three- and ten-dimensional IRT models. Additionally, we demonstrate the use of the VAE-based models on an existing algebra test dataset. Results confirm that VAE-based methods are a time-efficient alternative to marginal maximum likelihood, but that a larger number of importance-weighted samples are needed when the proportion of missing values is large.

Model-based estimates of age-structured SARS-CoV-2 epidemiology in households

BackgroundUnderstanding how infectious disease transmission varies from person to person, including associations with age and contact behavior, can help design effective control strategies. Within households, transmission may be highly variable because of differing transmission risks by age, household size, and individual contagiousness. Our aim was to disentangle those factors by fitting mathematical models to SARS-CoV-2 household survey and serologic data.MethodsWe surveyed members of 3,381 Utah households from January-April 2021 and performed SARS-CoV-2 antibody testing on all available members. We paired these data with a probabilistic model of household importation and transmission composed of a novel combination of transmission variability and age- and size-structured heterogeneity. We calculated maximum likelihood estimates of mean and variability of household transmission probability between household members in different age groups and different household sizes, simultaneously with importation probability and probabilities of false negative and false positive test results.Results12.8% of individual participants, residing in 17.4% of the participating households, showed serologic evidence of prior infection or reported a prior positive test on the survey. Serologically positive individuals in younger age groups were less likely than older adults to have tested positive during their infection according to our survey results. Our model results suggested that adolescents and young adults (ages 13–24) acquired SARS-CoV-2 infection outside the household at a rate substantially higher than younger children and older adults. Our estimate of the household secondary attack rate (HSAR) among adults aged 45 and older exceeded HSARs to and/or from younger age groups at a given household size. We found lower HSAR in households with more members, independent of age differences. The age-specific HSAR patterns we found could not be explained by age-dependent biological susceptibility and transmissibility alone, suggesting that age groups contacted each other at different rates within households.ConclusionsWe disentangled several factors contributing to age-specific infection risk, including non-household exposure, within-household exposure to specific age groups, and household size. Within-household contact rate differences played a significant role in driving household transmission epidemiology. These findings provide nuanced insights for understanding community outbreak patterns and mechanisms of differential infection risk.

Capital structure of special-purpose governments

PurposeThe paper examines whether special purpose governments follow the pecking order model when raising capital, replacing firm equity in the original model with local intergovernmental revenues. Special purpose governments are a relatively underexamined component of state and local governments, and their capital structure choices have important implications for America’s aggregate fiscal health. This paper seeks to illuminate special purpose governments’ choices among available forms of capital.Design/methodology/approachTo address our research inquiry regarding whether special-purpose governments adhere to the pecking order theory, we narrow our focus to a specific group of transit entities. Our investigation utilizes data sourced from two distinct repositories: the United States Census of Governments and the National Transit Database. To facilitate integration of these disparate datasets, we establish a correspondence between them using the Federal Information Processing Standard and the transit identification number. Initially, our analysis employs maximum likelihood estimation, comparing these estimates to those generated by a naïve model. Subsequently, we derive parameter estimates through the application of a bivariate probit model.FindingsThe paper supports the pecking order hypothesis where internal funds are consumed first, debt is consumed next and IGR is consumed last. The results are robust and are not influenced by simultaneity bias.Research limitations/implicationsThe paper uses transit special purpose governments as the special purpose government of interest. These transit special purpose governments have high fixed costs that may inform their capital structure decisions relative to non-transit special purpose governments. Additionally, transit special purpose governments often have a profit-maximizing objective that may not uniformly apply to other special purpose governments, such as school districts, who lack such an incentive.Practical implicationsOur research should grab the attention of state and local politicians, voters, policy experts and scholars. Special-purpose governments, a key part of our governmental system, are on the rise. Understanding them better can guide decision-making on how to allocate resources, set policies and plan strategically. This knowledge boosts financial reporting quality, transparency, accountability and public confidence. Journalists can leverage our findings to ensure accurate and thorough reporting, fostering accountability and trust. Additionally, debt markets and analysts can factor this information into their risk assessments.Originality/valueThe paper enhances our understanding of how special purpose governments interact with existing models of corporate finance when making capital structure decisions.

Some Improvements of the Bootstrap over the Delta Method Probability Errors for Whittle Estimators

The purpose of this paper is to compare the coverage probability errors of the parametric bootstrap with that of the delta method for the covariance parameters of a regression model with auto-regressive fractionally integrated moving average (ARFIMA) errors. We consider the coverage probability errors of both confidence intervals (CIs) and tests based on the the plug-in Whittle maximum likelihood (PWML) estimators. We first show that, under some sets of conditions on the regression coefficients, the spectral density function, and the parameter values, the bounds on the coverage probability errors of the two-sided delta method and parametric bootstrap confidence intervals on the plug-in Whittle likelihood estimator or the covariance parameter are shown to be $O(n^{-1})$ and $o(n^{-3/2}\ln{n})$, respectively, where n is the sample size. Next, we show that those of the one-sided parametric bootstrap confidence intervals are shown to be $O(n^{-1/2})$ and $o(n^{-1}\ln{n})$, respectively. These results show that for both one-sided and two-sided confidence intervals and tests, the bootstrap provides a significant improvement over that of the delta method.

Two-stage pseudo maximum likelihood estimation of semiparametric copula-based regression models for semi-competing risks data.

We propose a two-stage estimation procedure for a copula-based model with semi-competing risks data, where the non-terminal event is subject to dependent censoring by the terminal event, and both events are subject to independent censoring. With a copula-based model, the marginal survival functions of individual event times are specified by semiparametric transformation models, and the dependence between the bivariate event times is specified by a parametric copula function. For the estimation procedure, in the first stage, the parameters associated with the marginal of the terminal event are estimated using only the corresponding observed outcomes, and in the second stage, the marginal parameters for the non-terminal event time and the copula parameter are estimated together via maximizing a pseudo-likelihood function based on the joint distribution of the bivariate event times. We derived the asymptotic properties of the proposed estimator and provided an analytic variance estimator for inference. Through simulation studies, we showed that our approach leads to consistent estimates with less computational cost and more robustness than the one-stage procedure developed in Chen YH (Lifetime Data Anal 18:36-57, 2012), where all parameters were estimated simultaneously. In addition, our approach demonstrates more desirable finite-sample performances over another existing two-stage estimation method proposed in Zhu H et al., (Commu Statistics-Theory Methods 51(22):7830-7845, 2021) . An R package PMLE4SCR is developed to implement our proposed method.

Uniformization and bounded Taylor series in Newton-Raphsonmethod improves computational performance for a multistate transition model estimation and inference.

Multistate transition models (MSTMs) are valuable tools depicting disease progression. However, due to the complexity of MSTMs, larger sample size and longer follow-up time in real-world data, the computation of statistical estimation and inference for MSTMs becomes challenging. A bounded Taylor series in Newton-Raphson procedure is proposed which leverages the uniformization technique to derive maximum likelihood estimates and corresponding covariance matrix. The proposed method, namely uniformization Taylor-bounded Newton-Raphson, is validated in three simulation studies, which demonstrate the accuracy in parameter estimation, the efficiency in computation time and robustness in terms of different situations. This method is also illustrated using a large electronic medical record data related to statin-induced side effects and discontinuation.