Multi-state model for studying an intermediate event using time-dependent covariates: application to breast cancer

Abstract Purpose To extend the functionality of the existing INFLUENCE nomogram for locoregional recurrence (LRR) of breast cancer toward the prediction of secondary primary tumors (SP) and distant metastases (DM) using updated follow-up data and the best suitable statistical approaches. Methods Data on women diagnosed with non-metastatic invasive breast cancer were derived from the Netherlands Cancer Registry (n = 13,494). To provide flexible time-dependent individual risk predictions for LRR, SP, and DM, three statistical approaches were assessed; a Cox proportional hazard approach (COX), a parametric spline approach (PAR), and a random survival forest (RSF). These approaches were evaluated on their discrimination using the Area Under the Curve (AUC) statistic and on calibration using the Integrated Calibration Index (ICI). To correct for optimism, the performance measures were assessed by drawing 200 bootstrap samples. Results Age, tumor grade, pT, pN, multifocality, type of surgery, hormonal receptor status, HER2-status, and adjuvant therapy were included as predictors. While all three approaches showed adequate calibration, the RSF approach offers the best optimism-corrected 5-year AUC for LRR (0.75, 95%CI: 0.74–0.76) and SP (0.67, 95%CI: 0.65–0.68). For the prediction of DM, all three approaches showed equivalent discrimination (5-year AUC: 0.77–0.78), while COX seems to have an advantage concerning calibration (ICI < 0.01). Finally, an online calculator of INFLUENCE 2.0 was created. Conclusions INFLUENCE 2.0 is a flexible model to predict time-dependent individual risks of LRR, SP and DM at a 5-year scale; it can support clinical decision-making regarding personalized follow-up strategies for curatively treated non-metastatic breast cancer patients.

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Marginal quantile regression for longitudinal data analysis in the presence of time-dependent covariates

The International Journal of Biostatistics ◽

10.1515/ijb-2020-0010 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

I-Chen Chen ◽

Philip M. Westgate

Keyword(s):

Parameter Estimation ◽

Longitudinal Data ◽

Quantile Regression ◽

Mean Squared Error ◽

Time Dependent ◽

Regression Methods ◽

Squared Error ◽

Highly Correlated ◽

Time Dependent Covariates ◽

Independence Structure

AbstractWhen observations are correlated, modeling the within-subject correlation structure using quantile regression for longitudinal data can be difficult unless a working independence structure is utilized. Although this approach ensures consistent estimators of the regression coefficients, it may result in less efficient regression parameter estimation when data are highly correlated. Therefore, several marginal quantile regression methods have been proposed to improve parameter estimation. In a longitudinal study some of the covariates may change their values over time, and the topic of time-dependent covariate has not been explored in the marginal quantile literature. As a result, we propose an approach for marginal quantile regression in the presence of time-dependent covariates, which includes a strategy to select a working type of time-dependency. In this manuscript, we demonstrate that our proposed method has the potential to improve power relative to the independence estimating equations approach due to the reduction of mean squared error.

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