Pub Date : 2021-03-29DOI: 10.1080/24754269.2021.1905591
Bingkai Wang, Ryoko Susukida, R. Mojtabai, M. Amin-Esmaeili, Michael Rosenblum
We thank the editor for the opportunity to write this commentary on the paper by Jun Shao. The author’s paper gives an excellent review of methods developed for statistical inference when considering covariateadaptive, randomised trial designs. We would like to mention how the results from our paper (Wang et al., 2020) fit into those described by Jun Shao. Our paper focused on stratified permuted block randomisation (Zelen, 1974) and also biased coin randomisation (Efron, 1971), which are categorised as Type 1 randomisation schemes in the author’s paper. According to a survey by Lin et al. (2015) on 224 randomised clinical trials published in leading medical journals in 2014, stratified permuted block randomization was used by 70% of trials. Our goal is to improve precision of statistical inference by combining covariate-adaptive design and covariate adjustment, while providing robustness to model misspecification. In Section 6 of the author’s paper, the same goal was discussed and a linear model of potential outcomes given covariates was considered. Our results generalise those given for linearmodel-based estimators to all M-estimators (under regularity conditions), which covers many estimators used to analyse data from randomised clinical trials. Examples of M-estimators include estimators based on logistic regression (Moore & van der Laan, 2009), inverse probability weighting (Robins et al., 1994), the doubly-robust weighted-least-squares estimator (Robins et al., 2007), the augmented inverse probability weighted estimator (Robins et al., 1994; Scharfstein et al., 1999), and targeted maximum likelihood estimators (TMLE) that converge in 1-step (van der Laan&Gruber, 2012). Our results are able to handle covariate adjustment, various outcome types, repeated measures outcomes and missing outcome data under the missing at random assumption. Using data from three completed trials of substance use disorder treatments, we estimated that the precision gained due to stratified permuted block randomisation and covariate adjustment ranged from 1% to 36%. Another contribution of our paper is to prove the consistency and asymptotic normality of the KaplanMeier estimator under stratified randomization. Its asymptotic variance was also derived. We conjecture that this result can be generalised to cover covariate-adjusted estimators for the survival function, such as estimators by Lu and Tsiatis (2011); Zhang (2015).
我们感谢编辑给邵军的这篇评论文章的机会。作者的论文对在考虑协变量自适应随机试验设计时为统计推断开发的方法进行了极好的综述。我们想提及的是，我们的论文（Wang et al.，2020）的结果如何与邵军描述的结果相吻合。我们的论文集中于分层排列块随机化（Zelen，1974）和有偏硬币随机化（Efron，1971），在作者的论文中被归类为1型随机化方案。根据Lin等人（2015）对2014年发表在主流医学期刊上的224项随机临床试验的调查，70%的试验使用了分层排列块随机化。我们的目标是通过将协变量自适应设计和协变量调整相结合来提高统计推断的精度，同时提供对模型错误指定的鲁棒性。在作者论文的第6节中，讨论了相同的目标，并考虑了给定协变量的潜在结果的线性模型。我们的结果将基于线性模型的估计量推广到所有M-估计量（在正则性条件下），其中包括用于分析随机临床试验数据的许多估计量。M-估计量的例子包括基于逻辑回归的估计量（Moore&van der Laan，2009）、逆概率加权（Robins等人，1994）、双稳健加权最小二乘估计量（Robins et al.，2007）、增强逆概率加权估计量（Robins等人，1994；Scharfstein等人，1999），以及在1步中收敛的目标最大似然估计量（TMLE）（van der Laan&Gruber，2012）。我们的结果能够处理随机缺失假设下的协变量调整、各种结果类型、重复测量结果和缺失结果数据。使用三项已完成的药物使用障碍治疗试验的数据，我们估计，由于分层排列块随机化和协变量调整而获得的精度在1%至36%之间。本文的另一个贡献是证明了KaplanMeier估计量在分层随机化下的一致性和渐近正态性。推导了它的渐近方差。我们猜想这个结果可以推广到覆盖生存函数的协变量调整估计量，例如Lu和Tsiatis（2011）的估计量；张（2015）。
{"title":"Comment: Inference after covariate-adaptive randomisation: aspects of methodology and theory","authors":"Bingkai Wang, Ryoko Susukida, R. Mojtabai, M. Amin-Esmaeili, Michael Rosenblum","doi":"10.1080/24754269.2021.1905591","DOIUrl":"https://doi.org/10.1080/24754269.2021.1905591","url":null,"abstract":"We thank the editor for the opportunity to write this commentary on the paper by Jun Shao. The author’s paper gives an excellent review of methods developed for statistical inference when considering covariateadaptive, randomised trial designs. We would like to mention how the results from our paper (Wang et al., 2020) fit into those described by Jun Shao. Our paper focused on stratified permuted block randomisation (Zelen, 1974) and also biased coin randomisation (Efron, 1971), which are categorised as Type 1 randomisation schemes in the author’s paper. According to a survey by Lin et al. (2015) on 224 randomised clinical trials published in leading medical journals in 2014, stratified permuted block randomization was used by 70% of trials. Our goal is to improve precision of statistical inference by combining covariate-adaptive design and covariate adjustment, while providing robustness to model misspecification. In Section 6 of the author’s paper, the same goal was discussed and a linear model of potential outcomes given covariates was considered. Our results generalise those given for linearmodel-based estimators to all M-estimators (under regularity conditions), which covers many estimators used to analyse data from randomised clinical trials. Examples of M-estimators include estimators based on logistic regression (Moore & van der Laan, 2009), inverse probability weighting (Robins et al., 1994), the doubly-robust weighted-least-squares estimator (Robins et al., 2007), the augmented inverse probability weighted estimator (Robins et al., 1994; Scharfstein et al., 1999), and targeted maximum likelihood estimators (TMLE) that converge in 1-step (van der Laan&Gruber, 2012). Our results are able to handle covariate adjustment, various outcome types, repeated measures outcomes and missing outcome data under the missing at random assumption. Using data from three completed trials of substance use disorder treatments, we estimated that the precision gained due to stratified permuted block randomisation and covariate adjustment ranged from 1% to 36%. Another contribution of our paper is to prove the consistency and asymptotic normality of the KaplanMeier estimator under stratified randomization. Its asymptotic variance was also derived. We conjecture that this result can be generalised to cover covariate-adjusted estimators for the survival function, such as estimators by Lu and Tsiatis (2011); Zhang (2015).","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"190 - 191"},"PeriodicalIF":0.5,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1905591","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42217844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-26DOI: 10.1080/24754269.2021.1872131
Jiawei Xu, Yincai Tang
Various studies have provided a wide variety of mathematical and statistical models for early epidemic prediction of the COVID-19 outbreaks in Mainland China and other epicentres worldwide. In this paper, we present an integrated modelling framework, which incorporates typical exponential growth models, dynamic systems of compartmental models and statistical approaches, to depict the trends of COVID-19 spreading in 33 most heavily suffering countries. The dynamic system of SIR-X plays the main role for estimation and prediction of the epidemic trajectories showing the effectiveness of containment measures, while the other modelling approaches help determine the infectious period and the basic reproduction number. The modelling framework has reproduced the subexponential scaling law in the growth of confirmed cases and adequate fitting of empirical time-series data has facilitated the efficient forecast of the peak in the case counts of asymptomatic or unidentified infected individuals, the plateau that indicates the saturation at the end of the epidemic growth, as well as the number of daily positive cases for an extended period.
{"title":"An integrated epidemic modelling framework for the real-time forecast of COVID-19 outbreaks in current epicentres","authors":"Jiawei Xu, Yincai Tang","doi":"10.1080/24754269.2021.1872131","DOIUrl":"https://doi.org/10.1080/24754269.2021.1872131","url":null,"abstract":"Various studies have provided a wide variety of mathematical and statistical models for early epidemic prediction of the COVID-19 outbreaks in Mainland China and other epicentres worldwide. In this paper, we present an integrated modelling framework, which incorporates typical exponential growth models, dynamic systems of compartmental models and statistical approaches, to depict the trends of COVID-19 spreading in 33 most heavily suffering countries. The dynamic system of SIR-X plays the main role for estimation and prediction of the epidemic trajectories showing the effectiveness of containment measures, while the other modelling approaches help determine the infectious period and the basic reproduction number. The modelling framework has reproduced the subexponential scaling law in the growth of confirmed cases and adequate fitting of empirical time-series data has facilitated the efficient forecast of the peak in the case counts of asymptomatic or unidentified infected individuals, the plateau that indicates the saturation at the end of the epidemic growth, as well as the number of daily positive cases for an extended period.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"200 - 220"},"PeriodicalIF":0.5,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1872131","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49157511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-26DOI: 10.1080/24754269.2021.1905378
Hanzhong Liu
We congratulate Professor Shao on his exciting and thought-provoking paper and appreciate the Editor’s invitation to discuss it. This paper provided a comprehensive review of the methodology and theory for statistical inference under covariate-adaptive randomisation. Covariate-adaptive randomisation is widely used in the design stage of clinical trials to balance baseline covariates that are most relevant to the outcomes. Researchers often use linear regression or analysis of covariance (ANCOVA) to analyse the experimental results in the analysis stage. However, the validity of the resulting inferences is not crystal clear because the usual modelling assumptions might not be justified by covariate-adaptive randomisation. It is essential to develop a model-assisted methodology and theory for statistical inference under covariate-adaptive randomisation, allowing the working model to be arbitrarily misspecified. Professor Shao’s paper discussed recent developments in this aspect and made recommendations on using valid and efficient inference procedures under covariate-adaptive randomisation. As pointed out by Professor Shao, Ye, Yi, et al. (2020) proposed a model-assisted regression approach and showed that the resulting regression-adjusted average treatment effect estimator is more efficient than (as least as efficient as) the difference-in-means estimator, without any modelling assumptions on the potential outcomes and covariates. In other words, the modelassisted inference is efficient and robust to model misspecification. The efficiency gain and robustness of regression adjustment have been widely investigated under simple randomisation. When there are two treatment arms (treatment and control), Yang and Tsiatis (2001) examined three commonly used regression models for estimating the average treatment effect:
{"title":"Comment on ‘Inference after covariate-adaptive randomisation: aspects of methodology and theory’","authors":"Hanzhong Liu","doi":"10.1080/24754269.2021.1905378","DOIUrl":"https://doi.org/10.1080/24754269.2021.1905378","url":null,"abstract":"We congratulate Professor Shao on his exciting and thought-provoking paper and appreciate the Editor’s invitation to discuss it. This paper provided a comprehensive review of the methodology and theory for statistical inference under covariate-adaptive randomisation. Covariate-adaptive randomisation is widely used in the design stage of clinical trials to balance baseline covariates that are most relevant to the outcomes. Researchers often use linear regression or analysis of covariance (ANCOVA) to analyse the experimental results in the analysis stage. However, the validity of the resulting inferences is not crystal clear because the usual modelling assumptions might not be justified by covariate-adaptive randomisation. It is essential to develop a model-assisted methodology and theory for statistical inference under covariate-adaptive randomisation, allowing the working model to be arbitrarily misspecified. Professor Shao’s paper discussed recent developments in this aspect and made recommendations on using valid and efficient inference procedures under covariate-adaptive randomisation. As pointed out by Professor Shao, Ye, Yi, et al. (2020) proposed a model-assisted regression approach and showed that the resulting regression-adjusted average treatment effect estimator is more efficient than (as least as efficient as) the difference-in-means estimator, without any modelling assumptions on the potential outcomes and covariates. In other words, the modelassisted inference is efficient and robust to model misspecification. The efficiency gain and robustness of regression adjustment have been widely investigated under simple randomisation. When there are two treatment arms (treatment and control), Yang and Tsiatis (2001) examined three commonly used regression models for estimating the average treatment effect:","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"192 - 193"},"PeriodicalIF":0.5,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1905378","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48057966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-26DOI: 10.1080/24754269.2021.1905592
Wei Ma, Li-Xin Zhang, F. Hu
In the past decade, significant progress has been made regarding inference under covariate-adaptive randomisation. We thank Prof. Shao for a timely review of the growing literature about the topic. The paper is focused on the most important and commonly used class of covariate-adaptive randomisation methods, i.e., those balancing discrete covariates. The recent advances in robust inference are emphasised anddiscussed in detail. Several types of outcomes, such as continuous and time-to-event data, are covered. We here provide some additional recent results from the following five perspectives.
{"title":"Comment on ‘Inference after covariate-adaptive randomisation: aspects of methodology and theory’","authors":"Wei Ma, Li-Xin Zhang, F. Hu","doi":"10.1080/24754269.2021.1905592","DOIUrl":"https://doi.org/10.1080/24754269.2021.1905592","url":null,"abstract":"In the past decade, significant progress has been made regarding inference under covariate-adaptive randomisation. We thank Prof. Shao for a timely review of the growing literature about the topic. The paper is focused on the most important and commonly used class of covariate-adaptive randomisation methods, i.e., those balancing discrete covariates. The recent advances in robust inference are emphasised anddiscussed in detail. Several types of outcomes, such as continuous and time-to-event data, are covered. We here provide some additional recent results from the following five perspectives.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"187 - 189"},"PeriodicalIF":0.5,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1905592","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44414007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-24DOI: 10.1080/24754269.2021.1905357
J. Shao
I would like to thank all discussants for their insightful discussions on the topic of statistical inference after covariate-adaptive randomisation, especially for including reviews of some new results and references that are not in my review written more than a year ago. I hope these discussions together with my review will stimulate further studies in this important area having many applications particularly in clinical trials. My rejoinder focuses on somemain points from four separate groups of discussants.
{"title":"Rejoinder on ‘Inference after covariate-adaptive randomization: aspects of methodology and theory’","authors":"J. Shao","doi":"10.1080/24754269.2021.1905357","DOIUrl":"https://doi.org/10.1080/24754269.2021.1905357","url":null,"abstract":"I would like to thank all discussants for their insightful discussions on the topic of statistical inference after covariate-adaptive randomisation, especially for including reviews of some new results and references that are not in my review written more than a year ago. I hope these discussions together with my review will stimulate further studies in this important area having many applications particularly in clinical trials. My rejoinder focuses on somemain points from four separate groups of discussants.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"196 - 199"},"PeriodicalIF":0.5,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1905357","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48872041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-22DOI: 10.1080/24754269.2021.1905377
T. Ye, Yanyao Yi
We first want to commend (Shao, 2021) for a timely paper that reviews the methodological and theoretical advances in statistical inference after covariateadaptive randomisation in the last decade. The paper clearly presents the important considerations and pragmatic recommendations when analysing data obtained from covariate-adaptive randomisation, which provides principled guidelines for the practice. The aim of our remaining comments is to extend the discussion on the invariance property in Shao (2021). That is, the asymptotic distribution of an estimator remains the same under different covariate-adaptive randomisation schemes. For ease of reading, we follow the notation in Shao (2021) whenever possible and focus on the case of two treatment arms (i.e., k = 2). The ideas can be extended to the case of multiple treatment arms. For continuous or binary outcomes, Shao (2021) describes three post-stratified estimators for the population mean difference θ0 = E(Y(2) − Y(1)):
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Pub Date : 2021-03-19DOI: 10.1080/24754269.2021.1898181
Zhigao Wang, Xianyi Wu, Chunjuan Qiu
For stochastic loss reserving, we propose an individual information model (IIM) which accommodates not only individual/micro data consisting of incurring times, reporting developments, settlement developments as well as payments of individual claims but also heterogeneity among policies. We give over-dispersed Poisson assumption about the moments of reporting developments and payments of every individual claims. Model estimation is conducted under quasi-likelihood theory. Analytic expressions are derived for the expectation and variance of outstanding liabilities, given historical observations. We utilise conditional mean square error of prediction (MSEP) to measure the accuracy of loss reserving and also theoretically prove that when risk portfolio size is large enough, IIM shows a higher prediction accuracy than individual/micro data model (IDM) in predicting the outstanding liabilities, if the heterogeneity indeed influences claims developments and otherwise IIM is asymptotically equivalent to IDM. Some simulations are conducted to investigate the conditional MSEPs for IIM and IDM. A real data analysis is performed basing on real observations in health insurance.
{"title":"Stochastic loss reserving using individual information model with over-dispersed Poisson","authors":"Zhigao Wang, Xianyi Wu, Chunjuan Qiu","doi":"10.1080/24754269.2021.1898181","DOIUrl":"https://doi.org/10.1080/24754269.2021.1898181","url":null,"abstract":"For stochastic loss reserving, we propose an individual information model (IIM) which accommodates not only individual/micro data consisting of incurring times, reporting developments, settlement developments as well as payments of individual claims but also heterogeneity among policies. We give over-dispersed Poisson assumption about the moments of reporting developments and payments of every individual claims. Model estimation is conducted under quasi-likelihood theory. Analytic expressions are derived for the expectation and variance of outstanding liabilities, given historical observations. We utilise conditional mean square error of prediction (MSEP) to measure the accuracy of loss reserving and also theoretically prove that when risk portfolio size is large enough, IIM shows a higher prediction accuracy than individual/micro data model (IDM) in predicting the outstanding liabilities, if the heterogeneity indeed influences claims developments and otherwise IIM is asymptotically equivalent to IDM. Some simulations are conducted to investigate the conditional MSEPs for IIM and IDM. A real data analysis is performed basing on real observations in health insurance.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"114 - 128"},"PeriodicalIF":0.5,"publicationDate":"2021-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1898181","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44012300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-08DOI: 10.1080/24754269.2021.1894402
Yiying Zhang
This paper carries out stochastic comparisons on the total capacity of weighted k-out-of-n systems with heterogeneous components. The expectation order, the increasing convex/concave order and the usual stochastic order are employed to investigate stochastic behaviours of system capacity. Sufficient conditions are established in terms of majorisation-type orders between the vectors of component lifetime distribution parameters and the vectors of weights. Some examples are also provided as illustrations.
{"title":"Stochastic comparisons on total capacity of weighted k-out-of-n systems with heterogeneous components","authors":"Yiying Zhang","doi":"10.1080/24754269.2021.1894402","DOIUrl":"https://doi.org/10.1080/24754269.2021.1894402","url":null,"abstract":"This paper carries out stochastic comparisons on the total capacity of weighted k-out-of-n systems with heterogeneous components. The expectation order, the increasing convex/concave order and the usual stochastic order are employed to investigate stochastic behaviours of system capacity. Sufficient conditions are established in terms of majorisation-type orders between the vectors of component lifetime distribution parameters and the vectors of weights. Some examples are also provided as illustrations.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"72 - 80"},"PeriodicalIF":0.5,"publicationDate":"2021-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1894402","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41996341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-21DOI: 10.1080/24754269.2021.1877960
M. Wüthrich
In estimation and prediction theory, considerable attention is paid to the question of having unbiased estimators on a global population level. Recent developments in neural network modelling have mainly focused on accuracy on a granular sample level, and the question of unbiasedness on the population level has almost completely been neglected by that community. We discuss this question within neural network regression models, and we provide methods of receiving unbiased estimators for these models on the global population level.
{"title":"The balance property in neural network modelling","authors":"M. Wüthrich","doi":"10.1080/24754269.2021.1877960","DOIUrl":"https://doi.org/10.1080/24754269.2021.1877960","url":null,"abstract":"In estimation and prediction theory, considerable attention is paid to the question of having unbiased estimators on a global population level. Recent developments in neural network modelling have mainly focused on accuracy on a granular sample level, and the question of unbiasedness on the population level has almost completely been neglected by that community. We discuss this question within neural network regression models, and we provide methods of receiving unbiased estimators for these models on the global population level.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"6 1","pages":"1 - 9"},"PeriodicalIF":0.5,"publicationDate":"2021-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1877960","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43750558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-12DOI: 10.1080/24754269.2021.1884444
Hongyan Jiang, R. Yue
The main purpose of this paper is to investigate D-optimal population designs in multi-response linear mixed models for longitudinal data. Observations of each response variable within subjects are assumed to have a first-order autoregressive structure, possibly with observation error. The equivalence theorems are provided to characterise the D-optimal population designs for the estimation of fixed effects in the model. The semi-Bayesian D-optimal design which is robust against the serial correlation coefficient is also considered. Simulation studies show that the correlation between multi-response variables has tiny effects on the optimal design, while the experimental costs are important factors in the optimal designs.
{"title":"D-optimal population designs in linear mixed effects models for multiple longitudinal data","authors":"Hongyan Jiang, R. Yue","doi":"10.1080/24754269.2021.1884444","DOIUrl":"https://doi.org/10.1080/24754269.2021.1884444","url":null,"abstract":"The main purpose of this paper is to investigate D-optimal population designs in multi-response linear mixed models for longitudinal data. Observations of each response variable within subjects are assumed to have a first-order autoregressive structure, possibly with observation error. The equivalence theorems are provided to characterise the D-optimal population designs for the estimation of fixed effects in the model. The semi-Bayesian D-optimal design which is robust against the serial correlation coefficient is also considered. Simulation studies show that the correlation between multi-response variables has tiny effects on the optimal design, while the experimental costs are important factors in the optimal designs.","PeriodicalId":22070,"journal":{"name":"Statistical Theory and Related Fields","volume":"5 1","pages":"88 - 94"},"PeriodicalIF":0.5,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/24754269.2021.1884444","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48448725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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