1
|
Wang Z, Wang C, Wang X. Estimating causal effects in observational studies for survival data with a cure fraction using propensity score adjustment. Biom J 2023; 65:e2100357. [PMID: 37672794 DOI: 10.1002/bimj.202100357] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2021] [Revised: 06/01/2023] [Accepted: 06/15/2023] [Indexed: 09/08/2023]
Abstract
In observational studies, covariates are often confounding factors for treatment assignment. Such covariates need to be adjusted to estimate the causal treatment effect. For observational studies with survival outcomes, it is usually more challenging to adjust for the confounding covariates for causal effect estimation because of censoring. The challenge becomes even thornier when there exists a nonignorable cure fraction in the population. In this paper, we propose a causal effect estimation approach in observational studies for survival data with a cure fraction. We extend the absolute treatment effects on survival outcomes-including the restricted average causal effect and SPCE-to survival outcomes with cure fractions, and construct the corresponding causal effect estimators based on propensity score stratification. We prove the asymptotic properties of the proposed estimators and conduct simulation studies to evaluate their performances. As an illustration, the method is applied to a stomach cancer study.
Collapse
Affiliation(s)
- Ziwen Wang
- School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning, China
| | - Chenguang Wang
- Division of Biostatistics and Bioinformatics, Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University, Baltimore, Maryland, USA
| | - Xiaoguang Wang
- School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning, China
| |
Collapse
|
2
|
Safari WC, López-de-Ullibarri I, Jácome MA. Latency function estimation under the mixture cure model when the cure status is available. LIFETIME DATA ANALYSIS 2023; 29:608-627. [PMID: 36890338 PMCID: PMC9994787 DOI: 10.1007/s10985-023-09591-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/03/2021] [Accepted: 01/26/2023] [Indexed: 06/13/2023]
Abstract
This paper addresses the problem of estimating the conditional survival function of the lifetime of the subjects experiencing the event (latency) in the mixture cure model when the cure status information is partially available. The approach of past work relies on the assumption that long-term survivors are unidentifiable because of right censoring. However, in some cases this assumption is invalid since some subjects are known to be cured, e.g., when a medical test ascertains that a disease has entirely disappeared after treatment. We propose a latency estimator that extends the nonparametric estimator studied in López-Cheda et al. (TEST 26(2):353-376, 2017b) to the case when the cure status is partially available. We establish the asymptotic normality distribution of the estimator, and illustrate its performance in a simulation study. Finally, the estimator is applied to a medical dataset to study the length of hospital stay of COVID-19 patients requiring intensive care.
Collapse
Affiliation(s)
- Wende Clarence Safari
- Inequalities in Cancer Outcomes Network (ICON), Department of Non-Communicable Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, UK.
| | | | - María Amalia Jácome
- Department of Mathematics, Faculty of Science, University of A Coruña, CITIC, A Coruña, Spain
| |
Collapse
|
3
|
Garcia-Vicuña D, López-Cheda A, Jácome MA, Mallor F. Estimation of patient flow in hospitals using up-to-date data. Application to bed demand prediction during pandemic waves. PLoS One 2023; 18:e0282331. [PMID: 36848360 PMCID: PMC9970104 DOI: 10.1371/journal.pone.0282331] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Accepted: 02/13/2023] [Indexed: 03/01/2023] Open
Abstract
Hospital bed demand forecast is a first-order concern for public health action to avoid healthcare systems to be overwhelmed. Predictions are usually performed by estimating patients flow, that is, lengths of stay and branching probabilities. In most approaches in the literature, estimations rely on not updated published information or historical data. This may lead to unreliable estimates and biased forecasts during new or non-stationary situations. In this paper, we introduce a flexible adaptive procedure using only near-real-time information. Such method requires handling censored information from patients still in hospital. This approach allows the efficient estimation of the distributions of lengths of stay and probabilities used to represent the patient pathways. This is very relevant at the first stages of a pandemic, when there is much uncertainty and too few patients have completely observed pathways. Furthermore, the performance of the proposed method is assessed in an extensive simulation study in which the patient flow in a hospital during a pandemic wave is modelled. We further discuss the advantages and limitations of the method, as well as potential extensions.
Collapse
Affiliation(s)
| | - Ana López-Cheda
- Departamento de Matemáticas, Research Group MODES, CITIC, Universidade da Coruña, A Coruña, Spain
| | - María Amalia Jácome
- Departamento de Matemáticas, Research Group MODES, CITIC, Universidade da Coruña, A Coruña, Spain
| | - Fermin Mallor
- Institute of Smart Cities, Public University of Navawordpadrre, Pamplona, Spain
- * E-mail:
| |
Collapse
|
4
|
Safari WC, López-de-Ullibarri I, Jácome MA. Nonparametric kernel estimation of the probability of cure in a mixture cure model when the cure status is partially observed. Stat Methods Med Res 2022; 31:2164-2188. [PMID: 35912505 DOI: 10.1177/09622802221115880] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Cure models are a class of time-to-event models where a proportion of individuals will never experience the event of interest. The lifetimes of these so-called cured individuals are always censored. It is usually assumed that one never knows which censored observation is cured and which is uncured, so the cure status is unknown for censored times. In this paper, we develop a method to estimate the probability of cure in the mixture cure model when some censored individuals are known to be cured. A cure probability estimator that incorporates the cure status information is introduced. This estimator is shown to be strongly consistent and asymptotically normally distributed. Two alternative estimators are also presented. The first one considers a competing risks approach with two types of competing events, the event of interest and the cure. The second alternative estimator is based on the fact that the probability of cure can be written as the conditional mean of the cure status. Hence, nonparametric regression methods can be applied to estimate this conditional mean. However, the cure status remains unknown for some censored individuals. Consequently, the application of regression methods in this context requires handling missing data in the response variable (cure status). Simulations are performed to evaluate the finite sample performance of the estimators, and we apply them to the analysis of two datasets related to survival of breast cancer patients and length of hospital stay of COVID-19 patients requiring intensive care.
Collapse
Affiliation(s)
- Wende Clarence Safari
- Department of Mathematics, Faculty of Computer Science, CITIC, 117349University of A Coruña, A Coruña, Spain
| | - Ignacio López-de-Ullibarri
- Department of Mathematics, 88066Escuela Politécnica de Ingeniería de Ferrol, University of A Coruña, A Coruña, , Spain
| | - María Amalia Jácome
- Department of Mathematics, Faculty of Science, CITIC, 117349University of A Coruña, A Coruña, Spain
| |
Collapse
|
5
|
Xue X, Saeed O, Castagna F, Jorde UP, Agalliu I. The analysis of COVID-19 in-hospital mortality: A competing risk approach or a cure model? Stat Methods Med Res 2022; 31:1976-1991. [PMID: 35711169 PMCID: PMC9207596 DOI: 10.1177/09622802221106300] [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] [Indexed: 11/18/2022]
Abstract
Competing risk analyses have been widely used for the analysis of in-hospital mortality in which hospital discharge is considered as a competing event. The competing risk model assumes that more than one cause of failure is possible, but there is only one outcome of interest and all others serve as competing events. However, hospital discharge and in-hospital death are two outcomes resulting from the same disease process and patients whose disease conditions were stabilized so that inpatient care was no longer needed were discharged. We therefore propose to use cure models, in which hospital discharge is treated as an observed “cure” of the disease. We consider both the mixture cure model and the promotion time cure model and extend the models to allow cure status to be known for those who were discharged from the hospital. An EM algorithm is developed for the mixture cure model. We also show that the competing risk model, which treats hospital discharge as a competing event, is equivalent to a promotion time cure model. Both cure models were examined in simulation studies and were applied to a recent cohort of COVID-19 in-hospital patients with diabetes. The promotion time model shows that statin use improved the overall survival; the mixture cure model shows that while statin use reduced the in-hospital mortality rate among the susceptible, it improved the cure probability only for older but not younger patients. Both cure models show that treatment was more beneficial among older patients.
Collapse
Affiliation(s)
- Xiaonan Xue
- Department of Epidemiology & Population Health, Albert Einstein College of Medicine, New York, NY 10461, USA
| | - Omar Saeed
- Department of Medicine, Division of Cardiology, 2013Montefiore Medical Center, Albert Einstein College of Medicine, New York, NY 10461, USA
| | - Francesco Castagna
- Department of Medicine, Division of Cardiology, 2013Montefiore Medical Center, Albert Einstein College of Medicine, New York, NY 10461, USA
| | - Ulrich P Jorde
- Department of Medicine, Division of Cardiology, 2013Montefiore Medical Center, Albert Einstein College of Medicine, New York, NY 10461, USA
| | - Ilir Agalliu
- Department of Epidemiology & Population Health, Albert Einstein College of Medicine, New York, NY 10461, USA
| |
Collapse
|
6
|
Safari WC, López-de-Ullibarri I, Jácome MA. A product-limit estimator of the conditional survival function when cure status is partially known. Biom J 2021; 63:984-1005. [PMID: 33646606 DOI: 10.1002/bimj.202000173] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2020] [Revised: 11/07/2020] [Accepted: 11/21/2020] [Indexed: 01/18/2023]
Abstract
We introduce a nonparametric estimator of the conditional survival function in the mixture cure model for right-censored data when cure status is partially known. The estimator is developed for the setting of a single continuous covariate but it can be extended to multiple covariates. It extends the estimator of Beran, which ignores cure status information. We obtain an almost sure representation, from which the strong consistency and asymptotic normality of the estimator are derived. Asymptotic expressions of the bias and variance demonstrate a reduction in the variance with respect to Beran's estimator. A simulation study shows that, if the bandwidth parameter is suitably chosen, our estimator performs better than others for an ample range of covariate values. A bootstrap bandwidth selector is proposed. Finally, the proposed estimator is applied to a real dataset studying survival of sarcoma patients.
Collapse
Affiliation(s)
- Wende Clarence Safari
- Faculty of Computer Science, Department of Mathematics, University of A Coruña, CITIC, A Coruña, Spain
| | | | - María Amalia Jácome
- Faculty of Science, Department of Mathematics, University of A Coruña, CITIC, A Coruña, Spain
| |
Collapse
|
7
|
Tawiah R, McLachlan GJ, Ng SK. A bivariate joint frailty model with mixture framework for survival analysis of recurrent events with dependent censoring and cure fraction. Biometrics 2020; 76:753-766. [PMID: 31863594 DOI: 10.1111/biom.13202] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Revised: 12/02/2019] [Accepted: 12/04/2019] [Indexed: 12/31/2022]
Abstract
In the study of multiple failure time data with recurrent clinical endpoints, the classical independent censoring assumption in survival analysis can be violated when the evolution of the recurrent events is correlated with a censoring mechanism such as death. Moreover, in some situations, a cure fraction appears in the data because a tangible proportion of the study population benefits from treatment and becomes recurrence free and insusceptible to death related to the disease. A bivariate joint frailty mixture cure model is proposed to allow for dependent censoring and cure fraction in recurrent event data. The latency part of the model consists of two intensity functions for the hazard rates of recurrent events and death, wherein a bivariate frailty is introduced by means of the generalized linear mixed model methodology to adjust for dependent censoring. The model allows covariates and frailties in both the incidence and the latency parts, and it further accounts for the possibility of cure after each recurrence. It includes the joint frailty model and other related models as special cases. An expectation-maximization (EM)-type algorithm is developed to provide residual maximum likelihood estimation of model parameters. Through simulation studies, the performance of the model is investigated under different magnitudes of dependent censoring and cure rate. The model is applied to data sets from two colorectal cancer studies to illustrate its practical value.
Collapse
Affiliation(s)
- Richard Tawiah
- School of Medicine and Menzies Health Institute Queensland, Griffith University, Nathan, Australia.,School of Psychology, University of New South Wales, Sydney, Australia
| | | | - Shu Kay Ng
- School of Medicine and Menzies Health Institute Queensland, Griffith University, Nathan, Australia
| |
Collapse
|
8
|
Lin L, Huang L. Connections between cure rates and survival probabilities in proportional hazards models. Stat (Int Stat Inst) 2019. [DOI: 10.1002/sta4.255] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Li‐Hsiang Lin
- School of Industrial and Systems EngineeringGeorgia Institute of Technology Georgia 30332 USA
| | - Li‐Shan Huang
- Institute of StatisticsNational Tsing Hua University Hsinchu Taiwan
| |
Collapse
|