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Dynamic Risk Prediction via a Joint Frailty-Copula Model and IPD Meta-Analysis: Building Web Applications. ENTROPY 2022; 24:e24050589. [PMID: 35626474 PMCID: PMC9140593 DOI: 10.3390/e24050589] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Revised: 04/11/2022] [Accepted: 04/21/2022] [Indexed: 12/17/2022]
Abstract
Clinical risk prediction formulas for cancer patients can be improved by dynamically updating the formulas by intermediate events, such as tumor progression. The increased accessibility of individual patient data (IPD) from multiple studies has motivated the development of dynamic prediction formulas accounting for between-study heterogeneity. A joint frailty-copula model for overall survival and time to tumor progression has the potential to develop a dynamic prediction formula of death from heterogenous studies. However, the process of developing, validating, and publishing the prediction formula is complex, which has not been sufficiently described in the literature. In this article, we provide a tutorial in order to build a web-based application for dynamic risk prediction for cancer patients on the basis of the R packages joint.Cox and Shiny. We demonstrate the proposed methods using a dataset of breast cancer patients from multiple clinical studies. Following this tutorial, we demonstrate how one can publish web applications available online, which can be manipulated by any user through a smartphone or personal computer. After learning this tutorial, developers acquire the ability to build an online web application using their own datasets.
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Zhou W, Bakoyannis G, Zhang Y, Yiannoutsos CT. Semiparametric marginal regression for clustered competing risks data with missing cause of failure. Biostatistics 2022:6567216. [PMID: 35411923 PMCID: PMC10345995 DOI: 10.1093/biostatistics/kxac012] [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: 07/09/2021] [Revised: 03/22/2022] [Accepted: 03/23/2022] [Indexed: 11/12/2022] Open
Abstract
Clustered competing risks data are commonly encountered in multicenter studies. The analysis of such data is often complicated due to informative cluster size (ICS), a situation where the outcomes under study are associated with the size of the cluster. In addition, the cause of failure is frequently incompletely observed in real-world settings. To the best of our knowledge, there is no methodology for population-averaged analysis with clustered competing risks data with an ICS and missing causes of failure. To address this problem, we consider the semiparametric marginal proportional cause-specific hazards model and propose a maximum partial pseudolikelihood estimator under a missing at random assumption. To make the latter assumption more plausible in practice, we allow for auxiliary variables that may be related to the probability of missingness. The proposed method does not impose assumptions regarding the within-cluster dependence and allows for ICS. The asymptotic properties of the proposed estimators for both regression coefficients and infinite-dimensional parameters, such as the marginal cumulative incidence functions, are rigorously established. Simulation studies show that the proposed method performs well and that methods that ignore the within-cluster dependence and the ICS lead to invalid inferences. The proposed method is applied to competing risks data from a large multicenter HIV study in sub-Saharan Africa where a significant portion of causes of failure is missing.
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Affiliation(s)
- Wenxian Zhou
- Department of Biostatistics and Health Data Science, Indiana University, 410 West 10th Street, Suite 3000, Indianapolis, IN 46202, USA
| | - Giorgos Bakoyannis
- Department of Biostatistics and Health Data Science, Indiana University, 410 West 10th Street, Suite 3000, Indianapolis, IN 46202, USA
| | - Ying Zhang
- Department of Biostatistics, University of Nebraska Medical Center 42nd and Emile, Omaha, NE 68198, USA
| | - Constantin T Yiannoutsos
- Department of Biostatistics and Health Data Science, Indiana University, 410 West 10th Street, Suite 3000, Indianapolis, IN 46202, USA
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Azizi F, Haghighi F, Tabibi Gilani N. Statistical inference for competing risks model under progressive interval censored Weibull data. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2018.1510522] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Fariba Azizi
- School of Mathematics, Statistics and Computer Sciences, College of Science, University of Tehran, Tehran, Iran
| | - Firoozeh Haghighi
- School of Mathematics, Statistics and Computer Sciences, College of Science, University of Tehran, Tehran, Iran
| | - Niloofar Tabibi Gilani
- School of Mathematics, Statistics and Computer Sciences, College of Science, University of Tehran, Tehran, Iran
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Emura T, Shih JH, Ha ID, Wilke RA. Comparison of the marginal hazard model and the sub-distribution hazard model for competing risks under an assumed copula. Stat Methods Med Res 2019; 29:2307-2327. [PMID: 31868107 DOI: 10.1177/0962280219892295] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
For the analysis of competing risks data, three different types of hazard functions have been considered in the literature, namely the cause-specific hazard, the sub-distribution hazard, and the marginal hazard function. Accordingly, medical researchers can fit three different types of the Cox model to estimate the effect of covariates on each of the hazard function. While the relationship between the cause-specific hazard and the sub-distribution hazard has been extensively studied, the relationship to the marginal hazard function has not yet been analyzed due to the difficulties related to non-identifiability. In this paper, we adopt an assumed copula model to deal with the model identifiability issue, making it possible to establish a relationship between the sub-distribution hazard and the marginal hazard function. We then compare the two methods of fitting the Cox model to competing risks data. We also extend our comparative analysis to clustered competing risks data that are frequently used in medical studies. To facilitate the numerical comparison, we implement the computing algorithm for marginal Cox regression with clustered competing risks data in the R joint.Cox package and check its performance via simulations. For illustration, we analyze two survival datasets from lung cancer and bladder cancer patients.
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Affiliation(s)
- Takeshi Emura
- Graduate Institute of Statistics, National Central University, Taiwan
| | - Jia-Han Shih
- Graduate Institute of Statistics, National Central University, Taiwan
| | - Il Do Ha
- Department of Statistics, Pukyong National University, South Korea
| | - Ralf A Wilke
- Department of Economics, Copenhagen Business School, Denmark
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Tullio A, Magli A, Moretti E, Valent F. Why we should take care of the competing risk bias in survival analysis: A phase II trial on the toxicity profile of radiotherapy for prostate cancer. Rep Pract Oncol Radiother 2019; 24:511-519. [PMID: 31516397 DOI: 10.1016/j.rpor.2019.08.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2018] [Revised: 05/21/2019] [Accepted: 08/11/2019] [Indexed: 11/30/2022] Open
Abstract
Aim The aim of the present study is to evaluate and quantify the bias of competing risks in an Italian oncologic cohort comparing results from different statistical analysis methods. Background Competing risks are very common in randomized clinical trials and observational studies, in particular oncology and radiotherapy ones, and their inappropriate management causes results distortions widely present in clinical scientific articles. Materials and methods This is a single-institution phase II trial including 41 patients affected by prostate cancer and undergoing radiotherapy (IMRT-SIB) at the University Hospital of Udine.Different outcomes were considered: late toxicities, relapse, death.Death in the absence of relapse or late toxicity was considered as a competing event. Results The Kaplan Meier method, compared to cumulative incidence function method, overestimated the probability of the event of interest (toxicity and biochemical relapse) and of the competing event (death without toxicity/relapse) by 9.36%. The log-rank test, compared to Gray's test, overestimated the probability of the event of interest by 5.26%.The Hazard Ratio's and cause specific hazard's Cox regression are not directly comparable to subdistribution hazard's Fine and Gray's modified Cox regression; nonetheless, the FG model, the best choice for prognostic studies with competing risks, found significant associations not emerging with Cox regression. Conclusions This study confirms that using inappropriate statistical methods produces a 10% overestimation in results, as described in the literature, and highlights the importance of taking into account the competing risks bias.
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Affiliation(s)
- Annarita Tullio
- Hygiene and Clinical Epidemiology Unit, "S. Maria della Misericordia" University Hospital of Udine, Udine, Italy
| | - Alessandro Magli
- Department of Radiation Oncology, "S. Maria della Misericordia" University Hospital of Udine, Udine, Italy
| | - Eugenia Moretti
- Department of Medical Physics, "S. Maria della Misericordia" University Hospital of Udine, Udine, Italy
| | - Francesca Valent
- Hygiene and Clinical Epidemiology Unit, "S. Maria della Misericordia" University Hospital of Udine, Udine, Italy
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Yashin AI, Arbeev KG, Arbeeva LS, Wu D, Akushevich I, Kovtun M, Yashkin A, Kulminski A, Culminskaya I, Stallard E, Li M, Ukraintseva SV. How the effects of aging and stresses of life are integrated in mortality rates: insights for genetic studies of human health and longevity. Biogerontology 2015; 17:89-107. [PMID: 26280653 DOI: 10.1007/s10522-015-9594-8] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2015] [Accepted: 07/25/2015] [Indexed: 12/21/2022]
Abstract
Increasing proportions of elderly individuals in developed countries combined with substantial increases in related medical expenditures make the improvement of the health of the elderly a high priority today. If the process of aging by individuals is a major cause of age related health declines then postponing aging could be an efficient strategy for improving the health of the elderly. Implementing this strategy requires a better understanding of genetic and non-genetic connections among aging, health, and longevity. We review progress and problems in research areas whose development may contribute to analyses of such connections. These include genetic studies of human aging and longevity, the heterogeneity of populations with respect to their susceptibility to disease and death, forces that shape age patterns of human mortality, secular trends in mortality decline, and integrative mortality modeling using longitudinal data. The dynamic involvement of genetic factors in (i) morbidity/mortality risks, (ii) responses to stresses of life, (iii) multi-morbidities of many elderly individuals, (iv) trade-offs for diseases, (v) genetic heterogeneity, and (vi) other relevant aging-related health declines, underscores the need for a comprehensive, integrated approach to analyze the genetic connections for all of the above aspects of aging-related changes. The dynamic relationships among aging, health, and longevity traits would be better understood if one linked several research fields within one conceptual framework that allowed for efficient analyses of available longitudinal data using the wealth of available knowledge about aging, health, and longevity already accumulated in the research field.
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Affiliation(s)
- Anatoliy I Yashin
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA. .,The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, 2024 W. Main Street, Room A102E, Durham, NC, 27705, USA.
| | - Konstantin G Arbeev
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA
| | - Liubov S Arbeeva
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA
| | - Deqing Wu
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA
| | - Igor Akushevich
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA
| | - Mikhail Kovtun
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA
| | - Arseniy Yashkin
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA
| | - Alexander Kulminski
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA
| | - Irina Culminskaya
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA
| | - Eric Stallard
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA
| | - Miaozhu Li
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA
| | - Svetlana V Ukraintseva
- The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, Durham, NC, USA.,The Biodemography of Aging Research Unit, Social Science Research Institute, Duke University, 2024 W. Main Street, Room A105, Durham, NC, 27705, USA
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