1
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Tahira A, Danish MY. A generalized Gompertz promotion time cure model and its fitness to cancer data. Heliyon 2024; 10:e32038. [PMID: 38912437 PMCID: PMC11190554 DOI: 10.1016/j.heliyon.2024.e32038] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Revised: 05/27/2024] [Accepted: 05/27/2024] [Indexed: 06/25/2024] Open
Abstract
The cure models based on standard distributions like exponential, Weibull, lognormal, Gompertz, gamma, are often used to analyze survival data from cancer clinical trials with long-term survivors. Sometimes, the data is simple, and the standard cure models fit them very well, however, most often the data are complex and the standard cure models don't fit them reasonably well. In this article, we offer a novel generalized Gompertz promotion time cure model and illustrate its fitness to gastric cancer data by three different methods. The generalized Gompertz distribution is as simple as the generalized Weibull distribution and is not computationally as intensive as the generalized F distribution. One detailed real data application is provided for illustration and comparison purposes.
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Affiliation(s)
- Ayesha Tahira
- Department of Statistics, AIOU, Islamabad, Pin 44000, Pakistan
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2
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Du H, Alacam E, Mena S, Keller BT. Compatibility in imputation specification. Behav Res Methods 2022; 54:2962-2980. [PMID: 35138552 DOI: 10.3758/s13428-021-01749-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/10/2021] [Indexed: 12/16/2022]
Abstract
Missing data such as data missing at random (MAR) are unavoidable in real data and have the potential to undermine the validity of research results. Multiple imputation is one of the most widely used MAR-based methods in education and behavioral science applications. Arbitrarily specifying imputation models can lead to incompatibility and cause biased estimation. Building on the recent developments of model-based imputation and Arnold's compatibility work, this paper systematically summarizes when the traditional fully conditional specification (FCS) is applicable and how to specify a model-based imputation model if needed. We summarize two Compatibility Requirements to help researchers check compatibility more easily and a decision tree to check whether the traditional FCS is applicable in a given scenario. Additionally, we present a clear overview of two types of model-based imputation: the sequential and separate specifications. We illustrate how to specify model-based imputation with examples. Additionally, we provide example code of a free software program, Blimp, for implementing model-based imputation.
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Affiliation(s)
- Han Du
- Department of Psychology, University of California, Pritzker Hall, 502 Portola Plaza, Los Angeles, CA, 90095, USA.
| | - Egamaria Alacam
- Department of Psychology, University of California, Pritzker Hall, 502 Portola Plaza, Los Angeles, CA, 90095, USA
| | - Stefany Mena
- Department of Psychology, University of California, Pritzker Hall, 502 Portola Plaza, Los Angeles, CA, 90095, USA
| | - Brian T Keller
- Department of Educational Psychology, University of Texas at Austin, Austin, TX, 78712, USA
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3
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Balakrishnan N, Barui S, Milienos FS. Piecewise linear approximations of baseline under proportional hazards based COM-Poisson cure models. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2032157] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Affiliation(s)
- N. Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
| | - S. Barui
- Quantitative Methods and Operations Management Area, Indian Institute of Management Kozhikode, Kozhikode, Kerala, India
| | - F. S. Milienos
- Department of Sociology, Panteion University of Social and Political Sciences, Athens, Greece
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4
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Xie Y, Yu Z. Promotion time cure rate model with a neural network estimated nonparametric component. Stat Med 2021; 40:3516-3532. [PMID: 33928665 DOI: 10.1002/sim.8980] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Revised: 03/18/2021] [Accepted: 03/25/2021] [Indexed: 11/07/2022]
Abstract
Promotion time cure rate models (PCM) are often used to model the survival data with a cure fraction. Medical images or biomarkers derived from medical images can be the key predictors in survival models. However, incorporating images in the PCM is challenging using traditional nonparametric methods such as splines. We propose to use neural network to model the nonparametric or unstructured predictors' effect in the PCM context. Expectation-maximization algorithm with neural network for the M-step is used for parameter estimation. Asymptotic properties of the proposed estimates are derived. Simulation studies show good performance in terms of both prediction and estimation. We finally apply our methods to analyze the brain images from open access series of imaging studies data.
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Affiliation(s)
- Yujing Xie
- School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China
| | - Zhangsheng Yu
- School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, China.,Department of Bioinformatics and Biostatistics, SJTU-Yale Joint Center for Biostatistics, Shanghai Jiao Tong University, Shanghai, China
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5
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Vigas MVP, Fatoretto MB, Slanzon GS, Ortega EMM, Demétrio CGB, Bittar CMM. Red propolis effect analysis of dairy calves health based on Weibull regression model with long-term survivors. Res Vet Sci 2021; 136:464-471. [PMID: 33819754 DOI: 10.1016/j.rvsc.2021.03.018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2020] [Revised: 03/11/2021] [Accepted: 03/23/2021] [Indexed: 10/21/2022]
Abstract
Diarrhea is the most common cause of mortality and morbidity in dairy calves during the first weeks of life. It is responsible for the majority of costs related to animal death and treatments, as well as lower productivity due to reduced weight gain. Therefore, studies that focus on strategies to reduce diarrhea incidence and to improve animal welfare are very important for the dairy industry. For that reason, the beneficial effects of red propolis on the health status of preweaned dairy calves was studied. Animal disease data usually present incomplete observations of interest time, so-called censored observations and one of the statistical techniques for this modeling type is the survival analysis, hence it is a set of methods for analyzing data where the response variable is the time until the occurrence of an event of interest. We propose among some methods of survival data analysis, the long-term models. The motivation to study these models is the fact that part of the population is not susceptible to the event of interest during the period of the study, considered as immune or cured. In this paper, we studied the Weibull distribution in a structure of long-term model, including the covariates in the proportion of cured through the logistic link function. Besides, we used the residual analysis to check the assumptions of the model. The reason for the choice of the Weibull distribution was that this model is very flexibility to model a variety of data sets, among them animal science and long-term survival data. We illustrate its application with a case study from an animal experiment, which examined the time till the occurrence of diarrhea in Holstein calves, where a proportion of the animals were not susceptible to this health condition. This experiment aimed to verify the efficiency of red propolis in disease prevention and the influence of that on the proportion of animals that are not susceptible to diarrhea.
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Affiliation(s)
- Ms Valdemiro Piedade Vigas
- Department of Exact Sciences, Luiz de Queiroz College of Agriculture, University of São Paulo, Brazil, Pá dua Dias Avenue, 11, Piracicaba, SP, Brazil; Institute of Mathematics, Federal University of Mato Grosso do Sul, Costa e Silva Avenue, s/n, Bairro Universitário, Campo Grande, MS, Brazil.
| | - Maíra Blumer Fatoretto
- Department of Exact Sciences, Luiz de Queiroz College of Agriculture, University of São Paulo, Brazil, Pá dua Dias Avenue, 11, Piracicaba, SP, Brazil
| | - Giovana Simão Slanzon
- Department of Animal Sciences, Luiz de Queiroz College of Agriculture, University of São Paulo, Brazil, Pá dua Dias Avenue, 11, Piracicaba, SP, Brazil
| | - Edwin Moises Marcos Ortega
- Department of Exact Sciences, Luiz de Queiroz College of Agriculture, University of São Paulo, Brazil, Pá dua Dias Avenue, 11, Piracicaba, SP, Brazil
| | - Clarice Garcia Borges Demétrio
- Department of Exact Sciences, Luiz de Queiroz College of Agriculture, University of São Paulo, Brazil, Pá dua Dias Avenue, 11, Piracicaba, SP, Brazil
| | - Carla Maris Machado Bittar
- Department of Animal Sciences, Luiz de Queiroz College of Agriculture, University of São Paulo, Brazil, Pá dua Dias Avenue, 11, Piracicaba, SP, Brazil
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6
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Guo L, Xiong Y, Joan Hu X. Estimation in the Cox cure model with covariates missing not at random, with application to disease screening/prediction. CAN J STAT 2020. [DOI: 10.1002/cjs.11550] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Lisha Guo
- School of Mathematics and Statistics South‐Central University for Nationalities Wuhan China
| | - Yi Xiong
- Department of Statistics and Actuarial Science Simon Fraser University Burnaby Canada
| | - X. Joan Hu
- Department of Statistics and Actuarial Science Simon Fraser University Burnaby Canada
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7
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Ma Z, Chen G. Bayesian joint analysis using a semiparametric latent variable model with non-ignorable missing covariates for CHNS data. STAT MODEL 2020. [DOI: 10.1177/1471082x19896688] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Motivated by the China Health and Nutrition Survey (CHNS) data, a semiparametric latent variable model with a Dirichlet process (DP) mixtures prior on the latent variable is proposed to jointly analyse mixed binary and continuous responses. Non-ignorable missing covariates are considered through a selection model framework where a missing covariate model and a missing data mechanism model are included. The logarithm of the pseudo-marginal likelihood (LPML) is applied for selecting the priors, and the deviance information criterion measure focusing on the missing data mechanism model only is used for selecting different missing data mechanisms. A Bayesian index of local sensitivity to non-ignorability (ISNI) is extended to explore the local sensitivity of the parameters in our model. A simulation study is carried out to examine the empirical performance of the proposed methodology. Finally, the proposed model and the ISNI index are applied to analyse the CHNS data in the motivating example.
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Affiliation(s)
- Zhihua Ma
- Department of Statistics, School of Economics, Shenzhen University, Shenzhen, Guangdong, China
| | - Guanghui Chen
- Department of Statistics, School of Economics, Jinan University, Guangzhou, Guangdong, China
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8
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Desai M, Montez-Rath ME, Kapphahn K, Joyce VR, Mathur MB, Garcia A, Purington N, Owens DK. Missing data strategies for time-varying confounders in comparative effectiveness studies of non-missing time-varying exposures and right-censored outcomes. Stat Med 2019; 38:3204-3220. [PMID: 31099433 DOI: 10.1002/sim.8174] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2018] [Revised: 03/29/2019] [Accepted: 04/03/2019] [Indexed: 01/12/2023]
Abstract
The treatment of missing data in comparative effectiveness studies with right-censored outcomes and time-varying covariates is challenging because of the multilevel structure of the data. In particular, the performance of an accessible method like multiple imputation (MI) under an imputation model that ignores the multilevel structure is unknown and has not been compared to complete-case (CC) and single imputation methods that are most commonly applied in this context. Through an extensive simulation study, we compared statistical properties among CC analysis, last value carried forward, mean imputation, the use of missing indicators, and MI-based approaches with and without auxiliary variables under an extended Cox model when the interest lies in characterizing relationships between non-missing time-varying exposures and right-censored outcomes. MI demonstrated favorable properties under a moderate missing-at-random condition (absolute bias <0.1) and outperformed CC and single imputation methods, even when the MI method did not account for correlated observations in the imputation model. The performance of MI decreased with increasing complexity such as when the missing data mechanism involved the exposure of interest, but was still preferred over other methods considered and performed well in the presence of strong auxiliary variables. We recommend considering MI that ignores the multilevel structure in the imputation model when data are missing in a time-varying confounder, incorporating variables associated with missingness in the MI models as well as conducting sensitivity analyses across plausible assumptions.
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Affiliation(s)
- Manisha Desai
- Quantitative Sciences Unit, Department of Medicine, Stanford University, Palo Alto, California
| | - Maria E Montez-Rath
- Division of Nephrology, Department of Medicine, Stanford University, Palo Alto, California
| | - Kristopher Kapphahn
- Quantitative Sciences Unit, Department of Medicine, Stanford University, Palo Alto, California
| | | | - Maya B Mathur
- Department of Biostatistics, Harvard University, Cambridge, Massachusetts
| | - Ariadna Garcia
- Quantitative Sciences Unit, Department of Medicine, Stanford University, Palo Alto, California
| | - Natasha Purington
- Quantitative Sciences Unit, Department of Medicine, Stanford University, Palo Alto, California
| | - Douglas K Owens
- VA Palo Alto Health Care System, Palo Alto, California.,Center for Health Policy/Center for Primary Care and Outcomes Research, Department of Medicine, Stanford University, Stanford, California
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9
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Jacobs R, Lesaffre E, Teunis PFM, Höhle M, van de Kassteele J. Identifying the source of food-borne disease outbreaks: An application of Bayesian variable selection. Stat Methods Med Res 2019; 28:1126-1140. [PMID: 29241399 PMCID: PMC6448052 DOI: 10.1177/0962280217747311] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Early identification of contaminated food products is crucial in reducing health burdens of food-borne disease outbreaks. Analytic case-control studies are primarily used in this identification stage by comparing exposures in cases and controls using logistic regression. Standard epidemiological analysis practice is not formally defined and the combination of currently applied methods is subject to issues such as response misclassification, missing values, multiple testing problems and small sample estimation problems resulting in biased and possibly misleading results. In this paper, we develop a formal Bayesian variable selection method to account for misclassified responses and missing covariates, which are common complications in food-borne outbreak investigations. We illustrate the implementation and performance of our method on a Salmonella Thompson outbreak in the Netherlands in 2012. Our method is shown to perform better than the standard logistic regression approach with respect to earlier identification of contaminated food products. It also allows relatively easy implementation of otherwise complex methodological issues.
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Affiliation(s)
- Rianne Jacobs
- Department of Statistics, Informatics
and Modelling,
RIVM,
Bilthoven, Netherlands
| | | | - Peter FM Teunis
- Centre for Zoonoses and Environmental
Microbiology,
RIVM,
Bilthoven, Netherlands
- Hubert Department of Global Health,
Rollins School of Public Health, Emory University, Atlanta, GA, USA
| | - Michael Höhle
- Department of Mathematics,
Stockholm
University, Stockholm, Sweden
| | - Jan van de Kassteele
- Department of Statistics, Informatics
and Modelling,
RIVM,
Bilthoven, Netherlands
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10
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Affiliation(s)
- Laís H. Loose
- Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil
| | - Dione Maria Valença
- Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal, Brazil
| | - Fábio Mariano Bayer
- Departamento de Estatística and LACESM, Universidade Federal de Santa Maria, Santa Maria, Brazil
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11
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12
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Das K, Rana S, Roy S. Evaluation of Alzheimer's disease progression based on clinical dementia rating scale with missing responses and covariates. J Biopharm Stat 2017; 28:893-908. [PMID: 29173033 DOI: 10.1080/10543406.2017.1402780] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Abstract
In clinical trials, patient's disease severity is usually assessed on a Likert-type scale. Patients, however, may miss one or more follow-up visits (non-monotone missing). The statistical analysis of non-Gaussian longitudinal data with non-monotone missingness is difficult to handle, particularly when both response and time-dependent covariates are subject to such missingness. Even when the number of patients with intermittent missing data is small, ignoring those patients from analysis seems to be unsatisfactory. The focus of the current investigation is to study the progression of Alzheimer's disease by incorporating a non-ignorable missing data mechanism for both response and covariates in a longitudinal setup. Combining the cumulative logit longitudinal model for Alzheimer's disease progression with the bivariate binary model for the missing pattern, we develop a joint likelihood. The parameters are then estimated using the Monte Carlo Newton Raphson Expectation Maximization (MCNREM) method. This approach is quite easy to handle and the convergence of the estimates is attained in a reasonable amount of time. The study reveals that apolipo-protein plays a significant role in assessing a patient's disease severity. A detailed simulation has also been carried out for justifying the performance of our approach.
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Affiliation(s)
- Kalyan Das
- a Department of Statistics , University of Calcutta, Ballygunge Science College , Kolkata , India
| | - Subrata Rana
- a Department of Statistics , University of Calcutta, Ballygunge Science College , Kolkata , India
| | - Surupa Roy
- b Department of Statistics , St. Xavier's College , Kolkata , India
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13
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Vigas VP, Mazucheli J, Louzada F. Application of the Weibull-Poisson long-term survival model. COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS 2017. [DOI: 10.5351/csam.2017.24.4.325] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
| | - Josmar Mazucheli
- Departamento de Estatística, Universidade Estadual de Maringá, Brazil
| | - Francisco Louzada
- Institute of Mathematical Science and Computing, Universidade de São Paulo, Brazil
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14
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Suzuki AK, Barriga GDC, Louzada F, Cancho VG. A general long-term aging model with different underlying activation mechanisms: Modeling, Bayesian estimation, and case influence diagnostics. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2015.1053945] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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15
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Masud A, Tu W, Yu Z. Variable selection for mixture and promotion time cure rate models. Stat Methods Med Res 2016; 27:2185-2199. [DOI: 10.1177/0962280216677748] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Failure-time data with cured patients are common in clinical studies. Data from these studies are typically analyzed with cure rate models. Variable selection methods have not been well developed for cure rate models. In this research, we propose two least absolute shrinkage and selection operators based methods, for variable selection in mixture and promotion time cure models with parametric or nonparametric baseline hazards. We conduct an extensive simulation study to assess the operating characteristics of the proposed methods. We illustrate the use of the methods using data from a study of childhood wheezing.
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Affiliation(s)
- Abdullah Masud
- Department of Biostatistics, Indiana University School of Medicine, Indianapolis, IN, USA
| | - Wanzhu Tu
- Department of Biostatistics, Indiana University School of Medicine, Indianapolis, IN, USA
| | - Zhangsheng Yu
- Department of Bioinformatics and Biostatistics, Shanghai Jiaotong University, Shanghai, China
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16
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de Souza HCC, da Silva Castro Perdoná G, Louzada F, Maris Peria F. On the comparison of risk of death according to different stages of breast cancer via the long-term exponentiated Weibull hazard model. Stat Methods Med Res 2016; 27:2024-2037. [PMID: 29846145 DOI: 10.1177/0962280216673245] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Long-term survivor models have been extensively used for modelling time-to-event data with a significant proportion of patients who do not experience poor outcome. In this paper, we propose a new long-term survivor hazard model, which accommodates comprehensive families of cure rate models as particular cases, including modified Weibull, exponentiated Weibull, Weibull, exponential and Rayleigh distribution, among others. The maximum likelihood estimation procedure is presented. A simulation study evaluates bias and mean square error of the considered estimation procedure as well as the coverage probabilities of the parameters asymptotic and bootstrap confidence intervals. A real Brazilian dataset on breast cancer illustrates the methodology. From the practical point of view, under our modelling, we provide a parameter that works as a metric to quantify and compare the risk between different stages of the disease. We emphasize that, we developed an online platform for oncologists to calculate the probability of survival of patients diagnosed with breast cancer according to the stage of the disease in real time.
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17
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Bernhardt PW. A flexible cure rate model with dependent censoring and a known cure threshold. Stat Med 2016; 35:4607-4623. [DOI: 10.1002/sim.7014] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2015] [Revised: 04/27/2016] [Accepted: 05/11/2016] [Indexed: 12/15/2022]
Affiliation(s)
- Paul W. Bernhardt
- Department of Mathematics and Statistics; Villanova University; Villanova 19085 PA U.S.A
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18
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Rodrigues J, Cordeiro GM, de Castro M, Nadarajah S. A unified class of compound lifetime distributions. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2014.881491] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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19
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Erler NS, Rizopoulos D, Rosmalen JV, Jaddoe VWV, Franco OH, Lesaffre EMEH. Dealing with missing covariates in epidemiologic studies: a comparison between multiple imputation and a full Bayesian approach. Stat Med 2016; 35:2955-74. [PMID: 27042954 DOI: 10.1002/sim.6944] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2015] [Revised: 03/01/2016] [Accepted: 03/02/2016] [Indexed: 12/19/2022]
Abstract
Incomplete data are generally a challenge to the analysis of most large studies. The current gold standard to account for missing data is multiple imputation, and more specifically multiple imputation with chained equations (MICE). Numerous studies have been conducted to illustrate the performance of MICE for missing covariate data. The results show that the method works well in various situations. However, less is known about its performance in more complex models, specifically when the outcome is multivariate as in longitudinal studies. In current practice, the multivariate nature of the longitudinal outcome is often neglected in the imputation procedure, or only the baseline outcome is used to impute missing covariates. In this work, we evaluate the performance of MICE using different strategies to include a longitudinal outcome into the imputation models and compare it with a fully Bayesian approach that jointly imputes missing values and estimates the parameters of the longitudinal model. Results from simulation and a real data example show that MICE requires the analyst to correctly specify which components of the longitudinal process need to be included in the imputation models in order to obtain unbiased results. The full Bayesian approach, on the other hand, does not require the analyst to explicitly specify how the longitudinal outcome enters the imputation models. It performed well under different scenarios. Copyright © 2016 John Wiley & Sons, Ltd.
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Affiliation(s)
- Nicole S Erler
- Department of Biostatistics, Erasmus MC, Wytemaweg 80, Rotterdam, 3015CN, The Netherlands.,Department of Epidemiology, Erasmus MC, Wytemaweg 80, Rotterdam, 3015CN, The Netherlands
| | - Dimitris Rizopoulos
- Department of Biostatistics, Erasmus MC, Wytemaweg 80, Rotterdam, 3015CN, The Netherlands
| | - Joost van Rosmalen
- Department of Biostatistics, Erasmus MC, Wytemaweg 80, Rotterdam, 3015CN, The Netherlands
| | - Vincent W V Jaddoe
- Department of Epidemiology, Erasmus MC, Wytemaweg 80, Rotterdam, 3015CN, The Netherlands.,Department of Pediatrics, Erasmus MC, Wytemaweg 80, Rotterdam, 3015CN, The Netherlands
| | - Oscar H Franco
- Department of Epidemiology, Erasmus MC, Wytemaweg 80, Rotterdam, 3015CN, The Netherlands
| | - Emmanuel M E H Lesaffre
- Department of Biostatistics, Erasmus MC, Wytemaweg 80, Rotterdam, 3015CN, The Netherlands.,L-Biostat, KU Leuven, Kapucijnenvoer 35, Leuven, 3000, Belgium
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20
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Lee MC, Mitra R. Multiply imputing missing values in data sets with mixed measurement scales using a sequence of generalised linear models. Comput Stat Data Anal 2016. [DOI: 10.1016/j.csda.2015.08.004] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
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21
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Zhu H, Ibrahim JG, Chen MH. Diagnostic Measures for the Cox Regression Model with Missing Covariates. Biometrika 2016; 102:907-923. [PMID: 26903666 DOI: 10.1093/biomet/asv047] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
This paper investigates diagnostic measures for assessing the influence of observations and model misspecification in the presence of missing covariate data for the Cox regression model. Our diagnostics include case-deletion measures, conditional martingale residuals, and score residuals. The Q-distance is proposed to examine the effects of deleting individual observations on the estimates of finite-dimensional and infinite-dimensional parameters. Conditional martingale residuals are used to construct goodness of fit statistics for testing possible misspecification of the model assumptions. A resampling method is developed to approximate the p-values of the goodness of fit statistics. Simulation studies are conducted to evaluate our methods, and a real data set is analyzed to illustrate their use.
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Affiliation(s)
- Hongtu Zhu
- Department of Biostatistics, University of North Carolina at Chapel Hill, 3109 McGavran-Greenberg Hall, Campus Box 7420, Chapel Hill, North Carolina 27516, U.S.A.
| | - Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina at Chapel Hill, 3109 McGavran-Greenberg Hall, Campus Box 7420, Chapel Hill, North Carolina 27516, U.S.A.
| | - Ming-Hui Chen
- Department of Statistics, University of Connecticut, 215 Glenbrook Road, U-4120, Storrs, Connecticut 06269, U.S.A.
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22
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Piecewise Linear Approximations for Cure Rate Models and Associated Inferential Issues. Methodol Comput Appl Probab 2016. [DOI: 10.1007/s11009-015-9477-0] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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23
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Ibrahim JG, Chen MH, Lakshminarayanan M, Liu GF, Heyse JF. Bayesian probability of success for clinical trials using historical data. Stat Med 2014; 34:249-64. [PMID: 25339499 DOI: 10.1002/sim.6339] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2014] [Revised: 09/23/2014] [Accepted: 10/03/2014] [Indexed: 11/07/2022]
Abstract
Developing sophisticated statistical methods for go/no-go decisions is crucial for clinical trials, as planning phase III or phase IV trials is costly and time consuming. In this paper, we develop a novel Bayesian methodology for determining the probability of success of a treatment regimen on the basis of the current data of a given trial. We introduce a new criterion for calculating the probability of success that allows for inclusion of covariates as well as allowing for historical data based on the treatment regimen, and patient characteristics. A new class of prior distributions and covariate distributions is developed to achieve this goal. The methodology is quite general and can be used with univariate or multivariate continuous or discrete data, and it generalizes Chuang-Stein's work. This methodology will be invaluable for informing the scientist on the likelihood of success of the compound, while including the information of covariates for patient characteristics in the trial population for planning future pre-market or post-market trials.
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Affiliation(s)
- Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, U.S.A
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Rodrigues J, Balakrishnan N, Cordeiro GM, de Castro M, Cancho VG. Latent cure rate model under repair system and threshold effect. J STAT COMPUT SIM 2014. [DOI: 10.1080/00949655.2014.943223] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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25
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Rodrigues J, Cordeiro GM, de Castro M. Modeling Lifetimes by a Stochastic Process Hitting a Critical Point. COMMUN STAT-THEOR M 2014. [DOI: 10.1080/03610926.2013.844257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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26
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Han G, Schell MJ, Kim J. Improved survival modeling in cancer research using a reduced piecewise exponential approach. Stat Med 2013; 33:59-73. [PMID: 23900779 DOI: 10.1002/sim.5915] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2013] [Accepted: 06/25/2013] [Indexed: 11/05/2022]
Abstract
Statistical models for survival data are typically nonparametric, for example, the Kaplan-Meier curve. Parametric survival modeling, such as exponential modeling, however, can reveal additional insights and be more efficient than nonparametric alternatives. A major constraint of the existing exponential models is the lack of flexibility due to distribution assumptions. A flexible and parsimonious piecewise exponential model is presented to best use the exponential models for arbitrary survival data. This model identifies shifts in the failure rate over time based on an exact likelihood ratio test, a backward elimination procedure, and an optional presumed order restriction on the hazard rate. Such modeling provides a descriptive tool in understanding the patient survival in addition to the Kaplan-Meier curve. This approach is compared with alternative survival models in simulation examples and illustrated in clinical studies.
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Affiliation(s)
- Gang Han
- Department of Biostatistics, Yale University School of Public Health, 60 College Street, New Haven, CT 06520, U.S.A
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Escarela G, Ruiz-de-Chavez J, Castillo-Morales A. Addressing missing covariates for the regression analysis of competing risks: Prognostic modelling for triaging patients diagnosed with prostate cancer. Stat Methods Med Res 2013; 25:1579-95. [PMID: 23804968 DOI: 10.1177/0962280213492406] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Competing risks arise in medical research when subjects are exposed to various types or causes of death. Data from large cohort studies usually exhibit subsets of regressors that are missing for some study subjects. Furthermore, such studies often give rise to censored data. In this article, a carefully formulated likelihood-based technique for the regression analysis of right-censored competing risks data when two of the covariates are discrete and partially missing is developed. The approach envisaged here comprises two models: one describes the covariate effects on both long-term incidence and conditional latencies for each cause of death, whilst the other deals with the observation process by which the covariates are missing. The former is formulated with a well-established mixture model and the latter is characterised by copula-based bivariate probability functions for both the missing covariates and the missing data mechanism. The resulting formulation lends itself to the empirical assessment of non-ignorability by performing sensitivity analyses using models with and without a non-ignorable component. The methods are illustrated on a 20-year follow-up involving a prostate cancer cohort from the National Cancer Institutes Surveillance, Epidemiology, and End Results program.
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Affiliation(s)
- Gabriel Escarela
- Departamento de Matemáticas, Universidad Autónoma Metropolitana - Iztapalapa, Mexico City, Mexico
| | - Juan Ruiz-de-Chavez
- Departamento de Matemáticas, Universidad Autónoma Metropolitana - Iztapalapa, Mexico City, Mexico
| | - Alberto Castillo-Morales
- Departamento de Matemáticas, Universidad Autónoma Metropolitana - Iztapalapa, Mexico City, Mexico
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28
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Fonseca RS, Valença DM, Bolfarine H. Cure rate survival models with missing covariates: a simulation study. J STAT COMPUT SIM 2013. [DOI: 10.1080/00949655.2011.613396] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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29
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Mahabadi SE, Ganjali M. An index of local sensitivity to non-ignorability for parametric survival models with potential non-random missing covariate: an application to the SEER cancer registry data. J Appl Stat 2012. [DOI: 10.1080/02664763.2012.710196] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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30
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Louzada F, Cancho VG, Roman M, Leite JG. A new long-term lifetime distribution induced by a latent complementary risk framework. J Appl Stat 2012. [DOI: 10.1080/02664763.2012.706264] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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31
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Demarqui FN, Loschi RH, Dey DK, Colosimo EA. A class of dynamic piecewise exponential models with random time grid. J Stat Plan Inference 2012. [DOI: 10.1016/j.jspi.2011.09.006] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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32
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Rodrigues J, Balakrishnan N, Cordeiro GM, de Castro M. A unified view on lifetime distributions arising from selection mechanisms. Comput Stat Data Anal 2011. [DOI: 10.1016/j.csda.2011.06.018] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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33
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Kim S, Chen MH, Dey DK. A new threshold regression model for survival data with a cure fraction. LIFETIME DATA ANALYSIS 2011; 17:101-122. [PMID: 20414804 PMCID: PMC7829617 DOI: 10.1007/s10985-010-9166-9] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2009] [Accepted: 04/10/2010] [Indexed: 05/29/2023]
Abstract
Due to the fact that certain fraction of the population suffering a particular type of disease get cured because of advanced medical treatment and health care system, we develop a general class of models to incorporate a cure fraction by introducing the latent number N of metastatic-competent tumor cells or infected cells caused by bacteria or viral infection and the latent antibody level R of immune system. Various properties of the proposed models are carefully examined and a Markov chain Monte Carlo sampling algorithm is developed for carrying out Bayesian computation for model fitting and comparison. A real data set from a prostate cancer clinical trial is analyzed in detail to demonstrate the proposed methodology.
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Affiliation(s)
- Sungduk Kim
- Division of Epidemiology, Statistics and Prevention Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, NIH, Rockville, MD 20852, USA.
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34
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Perdoná GC, Louzada-Neto F. A general hazard model for lifetime data in the presence of cure rate. J Appl Stat 2010. [DOI: 10.1080/02664763.2010.505948] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Gleici Castro Perdoná
- a DMS-FMRP and FAEPA-RP, Universidade de São Paulo , 14049-900, Ribeirão Preto, SP, Brazil
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35
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de Castro M, Cancho VG, Rodrigues J. A hands-on approach for fitting long-term survival models under the GAMLSS framework. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2010; 97:168-177. [PMID: 19758722 DOI: 10.1016/j.cmpb.2009.08.002] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2008] [Revised: 08/05/2009] [Accepted: 08/11/2009] [Indexed: 05/28/2023]
Abstract
In many data sets from clinical studies there are patients insusceptible to the occurrence of the event of interest. Survival models which ignore this fact are generally inadequate. The main goal of this paper is to describe an application of the generalized additive models for location, scale, and shape (GAMLSS) framework to the fitting of long-term survival models. In this work the number of competing causes of the event of interest follows the negative binomial distribution. In this way, some well known models found in the literature are characterized as particular cases of our proposal. The model is conveniently parameterized in terms of the cured fraction, which is then linked to covariates. We explore the use of the gamlss package in R as a powerful tool for inference in long-term survival models. The procedure is illustrated with a numerical example.
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Affiliation(s)
- Mário de Castro
- Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Caixa Postal 668, 13560-970, São Carlos-SP, Brazil.
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36
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Maximum Likelihood Inference for the Cox Regression Model with Applications to Missing Covariates. J MULTIVARIATE ANAL 2009; 100:2018-2030. [PMID: 19802375 DOI: 10.1016/j.jmva.2009.03.013] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
In this paper, we carry out an in-depth theoretical investigation for existence of maximum likelihood estimates for the Cox model (Cox, 1972, 1975) both in the full data setting as well as in the presence of missing covariate data. The main motivation for this work arises from missing data problems, where models can easily become difficult to estimate with certain missing data configurations or large missing data fractions. We establish necessary and sufficient conditions for existence of the maximum partial likelihood estimate (MPLE) for completely observed data (i.e., no missing data) settings as well as sufficient conditions for existence of the maximum likelihood estimate (MLE) for survival data with missing covariates via a profile likelihood method. Several theorems are given to establish these conditions. A real dataset from a cancer clinical trial is presented to further illustrate the proposed methodology.
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37
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Abstract
Incomplete data are quite common in biomedical and other types of research, especially in longitudinal studies. During the last three decades, a vast amount of work has been done in the area. This has led, on the one hand, to a rich taxonomy of missing-data concepts, issues, and methods and, on the other hand, to a variety of data-analytic tools. Elements of taxonomy include: missing data patterns, mechanisms, and modeling frameworks; inferential paradigms; and sensitivity analysis frameworks. These are described in detail. A variety of concrete modeling devices is presented. To make matters concrete, two case studies are considered. The first one concerns quality of life among breast cancer patients, while the second one examines data from the Muscatine children's obesity study.
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Affiliation(s)
- Joseph G. Ibrahim
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, USA
| | - Geert Molenberghs
- Center for Statistics à International Institute for Biostatistic and Statistical Bioinformatics, Hasselt University and Catholic University Leuven, Agoralaan 1, 3590 Diepenbeek, Belgium
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38
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Demarqui FN, Loschi RH, Colosimo EA. Estimating the grid of time-points for the piecewise exponential model. LIFETIME DATA ANALYSIS 2008; 14:333-356. [PMID: 18463801 DOI: 10.1007/s10985-008-9086-0] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2006] [Accepted: 04/15/2008] [Indexed: 05/26/2023]
Abstract
One of the greatest challenges related to the use of piecewise exponential models (PEMs) is to find an adequate grid of time-points needed in its construction. In general, the number of intervals in such a grid and the position of their endpoints are ad-hoc choices. We extend previous works by introducing a full Bayesian approach for the piecewise exponential model in which the grid of time-points (and, consequently, the endpoints and the number of intervals) is random. We estimate the failure rates using the proposed procedure and compare the results with the non-parametric piecewise exponential estimates. Estimates for the survival function using the most probable partition are compared with the Kaplan-Meier estimators (KMEs). A sensitivity analysis for the proposed model is provided considering different prior specifications for the failure rates and for the grid. We also evaluate the effect of different percentage of censoring observations in the estimates. An application to a real data set is also provided. We notice that the posteriors are strongly influenced by prior specifications, mainly for the failure rates parameters. Thus, the priors must be fairly built, say, really disclosing the expert prior opinion.
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Affiliation(s)
- Fabio N Demarqui
- Departamento de Estatistica, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6.627, Pampulha, 31270-010, Belo Horizonte, MG, Brazil
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39
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Abstract
We consider a class of semiparametric models for the covariate distribution and missing data mechanism for missing covariate and/or response data for general classes of regression models including generalized linear models and generalized linear mixed models. Ignorable and nonignorable missing covariate and/or response data are considered. The proposed semiparametric model can be viewed as a sensitivity analysis for model misspecification of the missing covariate distribution and/or missing data mechanism. The semiparametric model consists of a generalized additive model (GAM) for the covariate distribution and/or missing data mechanism. Penalized regression splines are used to express the GAMs as a generalized linear mixed effects model, in which the variance of the corresponding random effects provides an intuitive index for choosing between the semiparametric and parametric model. Maximum likelihood estimates are then obtained via the EM algorithm. Simulations are given to demonstrate the methodology, and a real data set from a melanoma cancer clinical trial is analyzed using the proposed methods.
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Affiliation(s)
- Qingxia Chen
- Department of Biostatistics, Vanderbilt University, Nashville, Tennessee 37232, USA.
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40
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Chen MH, Ibrahim JG, Shao QM. Propriety of the Posterior Distribution and Existence of the MLE for Regression Models With Covariates Missing at Random. J Am Stat Assoc 2004. [DOI: 10.1198/016214504000000368] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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41
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Brown ER, Ibrahim JG. Bayesian approaches to joint cure-rate and longitudinal models with applications to cancer vaccine trials. Biometrics 2004; 59:686-93. [PMID: 14601770 DOI: 10.1111/1541-0420.00079] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Complex issues arise when investigating the association between longitudinal immunologic measures and time to an event, such as time to relapse, in cancer vaccine trials. Unlike many clinical trials, we may encounter patients who are cured and no longer susceptible to the time-to-event endpoint. If there are cured patients in the population, there is a plateau in the survival function, S(t), after sufficient follow-up. If we want to determine the association between the longitudinal measure and the time-to-event in the presence of cure, existing methods for jointly modeling longitudinal and survival data would be inappropriate, since they do not account for the plateau in the survival function. The nature of the longitudinal data in cancer vaccine trials is also unique, as many patients may not exhibit an immune response to vaccination at varying time points throughout the trial. We present a new joint model for longitudinal and survival data that accounts both for the possibility that a subject is cured and for the unique nature of the longitudinal data. An example is presented from a cancer vaccine clinical trial.
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Affiliation(s)
- Elizabeth R Brown
- Department of Biostatistics, University of Washington, Seattle, Washington 98105, USA.
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42
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Tsodikov AD, Ibrahim JG, Yakovlev AY. Estimating Cure Rates From Survival Data: An Alternative to Two-Component Mixture Models. J Am Stat Assoc 2003; 98:1063-1078. [PMID: 21151838 PMCID: PMC2998771 DOI: 10.1198/01622145030000001007] [Citation(s) in RCA: 235] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
This article considers the utility of the bounded cumulative hazard model in cure rate estimation, which is an appealing alternative to the widely used two-component mixture model. This approach has the following distinct advantages: (1) It allows for a natural way to extend the proportional hazards regression model, leading to a wide class of extended hazard regression models. (2) In some settings the model can be interpreted in terms of biologically meaningful parameters. (3) The model structure is particularly suitable for semiparametric and Bayesian methods of statistical inference. Notwithstanding the fact that the model has been around for less than a decade, a large body of theoretical results and applications has been reported to date. This review article is intended to give a big picture of these modeling techniques and associated statistical problems. These issues are discussed in the context of survival data in cancer.
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Affiliation(s)
| | - J. G. Ibrahim
- Department of Biostatistics, University of North Carolina, McGavran-Greenberg Hall, Chapel Hill, NC 27599
| | - A. Y. Yakovlev
- Department of Statistics and Computational Biology, University of Rochester, 601 Elmwood Avenue, Box 630, Rochester, NY 14642
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43
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Hanson T, Bedrick EJ, Johnson WO, Thurmond MC. A mixture model for bovine abortion and foetal survival. Stat Med 2003; 22:1725-39. [PMID: 12720307 DOI: 10.1002/sim.1376] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
The effect of spontaneous abortion on the dairy industry is substantial, costing the industry on the order of US dollars 200 million per year in California alone. We analyse data from a cohort study of nine dairy herds in Central California. A key feature of the analysis is the observation that only a relatively small proportion of cows will abort (around 10;15 per cent), so that it is inappropriate to analyse the time-to-abortion (TTA) data as if it were standard censored survival data, with cows that fail to abort by the end of the study treated as censored observations. We thus broaden the scope to consider the analysis of foetal lifetime distribution (FLD) data for the cows, with the dual goals of characterizing the effects of various risk factors on (i). the likelihood of abortion and, conditional on abortion status, on (ii). the risk of early versus late abortion. A single model is developed to accomplish both goals with two sets of specific herd effects modelled as random effects. Because multimodal foetal hazard functions are expected for the TTA data, both a parametric mixture model and a non-parametric model are developed. Furthermore, the two sets of analyses are linked because of anticipated dependence between the random herd effects. All modelling and inferences are accomplished using modern Bayesian methods.
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Affiliation(s)
- Timothy Hanson
- Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA
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44
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Morbiducci M, Nardi A, Rossi C. Classification of “cured” individuals in survival analysis: the mixture approach to the diagnostic–prognostic problem. Comput Stat Data Anal 2003. [DOI: 10.1016/s0167-9473(02)00185-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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45
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Gagnon DR, Glickman ME, Myers RH, Cupples LA. The analysis of survival data with a non-susceptible fraction and dual censoring mechanisms. Stat Med 2003; 22:3249-62. [PMID: 14518026 DOI: 10.1002/sim.1568] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
It is known that the ages of onset of many diseases are determined by both a genetic predisposition to disease as well as environmental risk factors that are capable of either triggering or hastening the onset of disease. Difficulties in modelling onset ages arise when a large fraction fail to inherit the disease-causing gene, and multiple reasons for censoring result in unobserved onset ages. We present a parametric Bayesian model that includes subjects with missing age information, non-susceptible subjects and allows for regression on risk factor information. The model is fit using Markov chain Monte Carlo simulation from the posterior distribution, and allows the simultaneous estimation of the proportion of the population at risk of disease, the mean onset age of disease, survival after disease onset, and the association of risk factors with susceptibility, onset age and survival after onset. An example employing Huntington's disease data is presented.
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Affiliation(s)
- David R Gagnon
- Boston University School of Public Health, Boston 02118, U.S.A.
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46
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Ibrahim JG, Chen MH, Lipsitz SR. Bayesian methods for generalized linear models with covariates missing at random. CAN J STAT 2002. [DOI: 10.2307/3315865] [Citation(s) in RCA: 74] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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