1
|
Gazon AB, Milani EA, Mota AL, Louzada F, Tomazella VLD, Calsavara VF. Nonproportional hazards model with a frailty term for modeling subgroups with evidence of long-term survivors: Application to a lung cancer dataset. Biom J 2021; 64:105-130. [PMID: 34569095 DOI: 10.1002/bimj.202000292] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Revised: 06/12/2021] [Accepted: 07/19/2021] [Indexed: 11/09/2022]
Abstract
With advancements in medical treatments for cancer, an increase in the life expectancy of patients undergoing new treatments is expected. Consequently, the field of statistics has evolved to present increasingly flexible models to explain such results better. In this paper, we present a lung cancer dataset with some covariates that exhibit nonproportional hazards (NPHs). Besides, the presence of long-term survivors is observed in subgroups. The proposed modeling is based on the generalized time-dependent logistic model with each subgroup's effect time and a random term effect (frailty). In practice, essential covariates are not observed for several reasons. In this context, frailty models are useful in modeling to quantify the amount of unobservable heterogeneity. The frailty distribution adopted was the weighted Lindley distribution, which has several interesting properties, such as the Laplace transform function on closed form, flexibility in the probability density function, among others. The proposed model allows for NPHs and long-term survivors in subgroups. Parameter estimation was performed using the maximum likelihood method, and Monte Carlo simulation studies were conducted to evaluate the estimators' performance. We exemplify this model's use by applying data of patients diagnosed with lung cancer in the state of São Paulo, Brazil.
Collapse
Affiliation(s)
- Amanda B Gazon
- Department of Statistics, Federal University of São Carlos, São Carlos, São Paulo, Brazil
| | - Eder A Milani
- Institute of Mathematical and Statistics, Federal University of Goiás, Goiânia, Goiás, Brazil.,Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, São Paulo, Brazil
| | - Alex L Mota
- Department of Statistics, Federal University of São Carlos, São Carlos, São Paulo, Brazil.,Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, São Paulo, Brazil
| | - Francisco Louzada
- Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, São Paulo, Brazil
| | - Vera L D Tomazella
- Department of Statistics, Federal University of São Carlos, São Carlos, São Paulo, Brazil
| | - Vinicius F Calsavara
- Department of Epidemiology and Statistics, A.C.Camargo Cancer Center, São Paulo, São Paulo, Brazil.,Samuel Oschin Comprehensive Cancer Institute, Cedars-Sinai Medical Center, Los Angeles, CA, USA
| |
Collapse
|