Promote sign consistency in cure rate model with Weibull lifetime

Chenlu Zheng; Jianping Zhu; Chenlu Zheng; Jianping Zhu

doi:10.3934/math.2022176

AIMS Mathematics

2022, Volume 7, Issue 2: 3186-3202. doi: 10.3934/math.2022176

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Research article

Promote sign consistency in cure rate model with Weibull lifetime

Chenlu Zheng ^1,2,
Jianping Zhu ^{1,2
,
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1.
School of Management, Xiamen University, Xiamen, China
2.
Data Mining Research Center, Xiamen University, Xiamen, China

Received: 27 October 2021 Accepted: 22 November 2021 Published: 25 November 2021
MSC : 62N01, 62N02

In survival analysis, the cure rate model is widely adopted when a proportion of subjects have long-term survivors. The cure rate model is composed of two parts: the first part is the incident part which describes the probability of cure (infinity survival), and the second part is the latency part which describes the conditional survival of the uncured subjects (finite survival). In the standard cure rate model, there are no constraints on the relations between the coefficients in the two model parts. However, in practical applications, the two model parts are quite related. It is desirable that there may be some relations between the two sets of the coefficients corresponding to the same covariates. Existing works have considered incorporating a joint distribution or structural effect, which is too restrictive. In this paper, we consider a more flexible model that allows the two sets of covariates can be in different distributions and magnitudes. In many practical cases, it is hard to interpret the results when the two sets of the coefficients of the same covariates have conflicting signs. Therefore, we proposed a sign consistency cure rate model with a sign-based penalty to improve interpretability. To accommodate high-dimensional data, we adopt a group lasso penalty for variable selection. Simulations and a real data analysis demonstrate that the proposed method has competitive performance compared with alternative methods.
- sign consistency,
- cure rate model,
- survival analysis,
- regularization,
- Weibull distribution
Citation: Chenlu Zheng, Jianping Zhu. Promote sign consistency in cure rate model with Weibull lifetime[J]. AIMS Mathematics, 2022, 7(2): 3186-3202. doi: 10.3934/math.2022176

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Abstract

In survival analysis, the cure rate model is widely adopted when a proportion of subjects have long-term survivors. The cure rate model is composed of two parts: the first part is the incident part which describes the probability of cure (infinity survival), and the second part is the latency part which describes the conditional survival of the uncured subjects (finite survival). In the standard cure rate model, there are no constraints on the relations between the coefficients in the two model parts. However, in practical applications, the two model parts are quite related. It is desirable that there may be some relations between the two sets of the coefficients corresponding to the same covariates. Existing works have considered incorporating a joint distribution or structural effect, which is too restrictive. In this paper, we consider a more flexible model that allows the two sets of covariates can be in different distributions and magnitudes. In many practical cases, it is hard to interpret the results when the two sets of the coefficients of the same covariates have conflicting signs. Therefore, we proposed a sign consistency cure rate model with a sign-based penalty to improve interpretability. To accommodate high-dimensional data, we adopt a group lasso penalty for variable selection. Simulations and a real data analysis demonstrate that the proposed method has competitive performance compared with alternative methods.

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