An advantage of the standard mixture cure model over an usual survival model is how it accounts for the population heterogeneity. It allows a joint estimation for the distribution related to the susceptible and non‐susceptible subjects. The estimation algorithm may provide ±∞$$ pm infty $$ coefficients when the likelihood cannot be maximized. This phenomenon is known as Monotone Likelihood (ML), common in survival and logistic regressions. The ML tends to appear in situations with small sample size, many censored times, many binary or unbalanced covariates. Particularly, it occurs when all uncensored cases correspond to one level of a binary covariate. The existing frequentist solution is an adaptation of the Firth correction, originally proposed to reduce bias of maximum likelihood estimates. It prevents ±∞$$ pm infty $$ estimates by penalizing the likelihood, with the penalty interpreted as the Bayesian Jeffreys prior. In this paper, the penalized likelihood of the standard mixture cure model is considered with different penalties (Bayesian priors). A Monte Carlo simulation study indicates good inference results, especially for balanced data sets. Finally, a real application involving a melanoma data illustrates the approach.
{"title":"Bayesian solution to the monotone likelihood in the standard mixture cure model","authors":"F. M. Almeida, V. D. Mayrink, E. Colosimo","doi":"10.1111/stan.12289","DOIUrl":"https://doi.org/10.1111/stan.12289","url":null,"abstract":"An advantage of the standard mixture cure model over an usual survival model is how it accounts for the population heterogeneity. It allows a joint estimation for the distribution related to the susceptible and non‐susceptible subjects. The estimation algorithm may provide ±∞$$ pm infty $$ coefficients when the likelihood cannot be maximized. This phenomenon is known as Monotone Likelihood (ML), common in survival and logistic regressions. The ML tends to appear in situations with small sample size, many censored times, many binary or unbalanced covariates. Particularly, it occurs when all uncensored cases correspond to one level of a binary covariate. The existing frequentist solution is an adaptation of the Firth correction, originally proposed to reduce bias of maximum likelihood estimates. It prevents ±∞$$ pm infty $$ estimates by penalizing the likelihood, with the penalty interpreted as the Bayesian Jeffreys prior. In this paper, the penalized likelihood of the standard mixture cure model is considered with different penalties (Bayesian priors). A Monte Carlo simulation study indicates good inference results, especially for balanced data sets. Finally, a real application involving a melanoma data illustrates the approach.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73074811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In medical clinical studies, uni‐ and bilateral data naturally occurs if each patient contributes either one or both of paired organ measurements in a stratified design. This paper mainly proposes a common test of risk differences between proportions for stratified uni‐ and bilateral correlated data. Likelihood ratio, score, and Wald‐type test statistics are constructed using global, unconstrained, and constrained maximum likelihood estimations of parameters. Simulation studies are conducted to evaluate the performance of these test procedures in terms of type I error rates and powers. Empirical results show that the likelihood ratio test is more robust and powerful than other statistics. A real example is used to illustrate the proposed methods.
{"title":"Testing the common risk difference of proportions for stratified uni‐ and bilateral correlated data","authors":"Zhiming Li, Changxing Ma, Keyi Mou","doi":"10.1111/stan.12288","DOIUrl":"https://doi.org/10.1111/stan.12288","url":null,"abstract":"In medical clinical studies, uni‐ and bilateral data naturally occurs if each patient contributes either one or both of paired organ measurements in a stratified design. This paper mainly proposes a common test of risk differences between proportions for stratified uni‐ and bilateral correlated data. Likelihood ratio, score, and Wald‐type test statistics are constructed using global, unconstrained, and constrained maximum likelihood estimations of parameters. Simulation studies are conducted to evaluate the performance of these test procedures in terms of type I error rates and powers. Empirical results show that the likelihood ratio test is more robust and powerful than other statistics. A real example is used to illustrate the proposed methods.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78938507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Proportional hazards are often used to model event time data subject to censoring. Samples involving discrete covariates with strong effects can lead to infinite maximum partial likelihood estimates. A methodology is presented for eliminating nuisance parameters estimated at infinity using approximate conditional inference. Of primary interest is testing in cases in which the parameter of primary interest has a finite estimate, but in which other parameters are estimated at infinity.
{"title":"Inference in the presence of likelihood monotonicity for proportional hazards regression","authors":"J. Kolassa, Juan Zhang","doi":"10.1111/stan.12287","DOIUrl":"https://doi.org/10.1111/stan.12287","url":null,"abstract":"Proportional hazards are often used to model event time data subject to censoring. Samples involving discrete covariates with strong effects can lead to infinite maximum partial likelihood estimates. A methodology is presented for eliminating nuisance parameters estimated at infinity using approximate conditional inference. Of primary interest is testing in cases in which the parameter of primary interest has a finite estimate, but in which other parameters are estimated at infinity.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77308751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, new statistical algorithms for accurate peak detection in the metabolomic data are proposed. Specifically, liquid chromatograph‐mass spectrometry data are analyzed. The discretized skew‐t mixture model for peak detection is proposed. It shows great flexibility and capability in fitting skewed or heavy‐tailed peaks. The methodology is further extended to cross‐sample peak alignment for identifying the true peaks. A measure of peak credibility is provided through the assessment of misclassification probabilities between two cross‐sample peaks. The proposed algorithms are applied to spike‐in data with promising results.
{"title":"Discretized skew‐t mixture model for deconvoluting liquid chromatograph mass spectrometry data","authors":"Xuwen Zhu, Xiang Zhang","doi":"10.1111/stan.12285","DOIUrl":"https://doi.org/10.1111/stan.12285","url":null,"abstract":"In this paper, new statistical algorithms for accurate peak detection in the metabolomic data are proposed. Specifically, liquid chromatograph‐mass spectrometry data are analyzed. The discretized skew‐t mixture model for peak detection is proposed. It shows great flexibility and capability in fitting skewed or heavy‐tailed peaks. The methodology is further extended to cross‐sample peak alignment for identifying the true peaks. A measure of peak credibility is provided through the assessment of misclassification probabilities between two cross‐sample peaks. The proposed algorithms are applied to spike‐in data with promising results.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78459194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Serge-Hippolyte Arnaud Kanga, O. Hili, S. Dabo‐Niang, Assi N'Guessan
The purpose of this work is to nonparametrically estimate the conditional quantile for a locally stationary multivariate spatial process. The new kernel quantile estimate derived from the one of conditional distribution function (CDF). The originality in the paper is based on the ability to take into account some local spatial dependency in estimate CDF form. Consistency and asymptotic normality of the estimates are obtained under α$$ alpha $$ ‐mixing condition. Numerical study and application to real data are given in order to illustrate the performance of our methodology.
{"title":"Asymptotic properties of nonparametric quantile estimation with spatial dependency","authors":"Serge-Hippolyte Arnaud Kanga, O. Hili, S. Dabo‐Niang, Assi N'Guessan","doi":"10.1111/stan.12284","DOIUrl":"https://doi.org/10.1111/stan.12284","url":null,"abstract":"The purpose of this work is to nonparametrically estimate the conditional quantile for a locally stationary multivariate spatial process. The new kernel quantile estimate derived from the one of conditional distribution function (CDF). The originality in the paper is based on the ability to take into account some local spatial dependency in estimate CDF form. Consistency and asymptotic normality of the estimates are obtained under α$$ alpha $$ ‐mixing condition. Numerical study and application to real data are given in order to illustrate the performance of our methodology.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88768370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The problem of finding Effective Sample Size (ESS) in Phase II clinical trials where toxicity and efficacy are the two components of the treatment response vector is considered. In particular, one of the components is assumed to be binary and the other is assumed to be continuous. The case of binary safety and continuous efficacy is studied for different prior distributions under different set up. Theoretical expressions are obtained in various situations. The methods are evaluated and compared by simulation studies. The proposed method is then illustrated by using some real life data on a phase II vaccine trial for Covid‐19.
{"title":"Prior effective sample size in phase II clinical trials with mixed binary and continuous responses","authors":"Meghna Bose, J. Angers, A. Biswas","doi":"10.1111/stan.12283","DOIUrl":"https://doi.org/10.1111/stan.12283","url":null,"abstract":"The problem of finding Effective Sample Size (ESS) in Phase II clinical trials where toxicity and efficacy are the two components of the treatment response vector is considered. In particular, one of the components is assumed to be binary and the other is assumed to be continuous. The case of binary safety and continuous efficacy is studied for different prior distributions under different set up. Theoretical expressions are obtained in various situations. The methods are evaluated and compared by simulation studies. The proposed method is then illustrated by using some real life data on a phase II vaccine trial for Covid‐19.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91225677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we present statistical inference of unknown lifetime parameters based on a progressive Type‐I interval censored dataset in presence of independent competing risks. A progressive Type‐I interval censoring scheme is a generalization of an interval censoring scheme, allowing intermediate withdrawals of test units at the inspection points. We assume that the lifetime distribution corresponding to a failure mode belongs to a log‐location‐scale family of distributions. Subsequently, we present the maximum likelihood analysis for unknown model parameters. We observe that the numerical computation of the maximum likelihood estimates can be significantly eased by developing an expectation‐maximization algorithm. We demonstrate the same for three popular choices of the log‐location‐scale family of distributions. We then provide Bayesian inference of the unknown lifetime parameters via Gibbs Sampling and a related data augmentation scheme. We compare the performance of the maximum likelihood estimators and Bayesian estimators using a detailed simulation study. We also illustrate the developed methods using a progressive Type‐I interval censored dataset.
{"title":"Inference for log‐location‐scale family of distributions under competing risks with progressive type‐I interval censored data","authors":"Soumya Roy, B. Pradhan","doi":"10.1111/stan.12282","DOIUrl":"https://doi.org/10.1111/stan.12282","url":null,"abstract":"In this article, we present statistical inference of unknown lifetime parameters based on a progressive Type‐I interval censored dataset in presence of independent competing risks. A progressive Type‐I interval censoring scheme is a generalization of an interval censoring scheme, allowing intermediate withdrawals of test units at the inspection points. We assume that the lifetime distribution corresponding to a failure mode belongs to a log‐location‐scale family of distributions. Subsequently, we present the maximum likelihood analysis for unknown model parameters. We observe that the numerical computation of the maximum likelihood estimates can be significantly eased by developing an expectation‐maximization algorithm. We demonstrate the same for three popular choices of the log‐location‐scale family of distributions. We then provide Bayesian inference of the unknown lifetime parameters via Gibbs Sampling and a related data augmentation scheme. We compare the performance of the maximum likelihood estimators and Bayesian estimators using a detailed simulation study. We also illustrate the developed methods using a progressive Type‐I interval censored dataset.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73790831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kai Yang, Qingqing Zhang, Xinyang Yu, Xiaogang Dong
This paper considers a mixture double autoregressive model with two components, which can flexibly capture the features usually exhibited by many financial returns such as heteroscedasticity, large kurtosis and multimodal marginals. Bayesian method based on modern Markov Chain Monte Carlo (MCMC) technology is used to estimate the model parameters. The heteroscedasticity test problem for the underlying process is also addressed by means of Bayes factor. The performances of the proposed methods are evaluated via some simulations. It is shown that the MCMC algorithm is an effective tool to deal with the mixture model. Finally, the proposed model is applied to the S&P500 index data.set.
{"title":"Bayesian inference for a mixture double autoregressive model","authors":"Kai Yang, Qingqing Zhang, Xinyang Yu, Xiaogang Dong","doi":"10.1111/stan.12281","DOIUrl":"https://doi.org/10.1111/stan.12281","url":null,"abstract":"This paper considers a mixture double autoregressive model with two components, which can flexibly capture the features usually exhibited by many financial returns such as heteroscedasticity, large kurtosis and multimodal marginals. Bayesian method based on modern Markov Chain Monte Carlo (MCMC) technology is used to estimate the model parameters. The heteroscedasticity test problem for the underlying process is also addressed by means of Bayes factor. The performances of the proposed methods are evaluated via some simulations. It is shown that the MCMC algorithm is an effective tool to deal with the mixture model. Finally, the proposed model is applied to the S&P500 index data.set.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77185832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Editorial Statistics","authors":"M. Ristić, M. Duijn, Nan Geloven","doi":"10.1111/stan.12279","DOIUrl":"https://doi.org/10.1111/stan.12279","url":null,"abstract":"","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90696401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We model the incidence of the COVID-19 disease during the first wave of the epidemic in Castilla-Leon (Spain). Within-province dynamics may be governed by a generalized logistic map, but this lacks of spatial structure. To couple the provinces, we relate the daily new infections through a density-independent parameter that entails positive spatial correlation. Pointwise values of the input parameters are fitted by an optimization procedure. To accommodate the significant variability in the daily data, with abruptly increasing and decreasing magnitudes, a random noise is incorporated into the model, whose parameters are calibrated by maximum likelihood estimation. The calculated paths of the stochastic response and the probabilistic regions are in good agreement with the data.
{"title":"A phenomenological model for COVID-19 data taking into account neighboring-provinces effect and random noise.","authors":"Julia Calatayud, Marc Jornet, Jorge Mateu","doi":"10.1111/stan.12278","DOIUrl":"10.1111/stan.12278","url":null,"abstract":"<p><p>We model the incidence of the COVID-19 disease during the first wave of the epidemic in Castilla-Leon (Spain). Within-province dynamics may be governed by a generalized logistic map, but this lacks of spatial structure. To couple the provinces, we relate the daily new infections through a density-independent parameter that entails positive spatial correlation. Pointwise values of the input parameters are fitted by an optimization procedure. To accommodate the significant variability in the daily data, with abruptly increasing and decreasing magnitudes, a random noise is incorporated into the model, whose parameters are calibrated by maximum likelihood estimation. The calculated paths of the stochastic response and the probabilistic regions are in good agreement with the data.</p>","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9538456/pdf/STAN-9999-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33514323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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