Abstract
We propose new resampling‐based approaches to construct asymptotically valid time‐simultaneous confidence bands for cumulative hazard functions in multistate Cox models. In particular, we exemplify the methodology in detail for the simple Cox model with time‐dependent covariates, where the data may be subject to independent right‐censoring or left‐truncation. We use simulations to investigate their finite sample behavior. Finally, the methods are utilized to analyze two empirical examples with survival and competing risks data.
Highlights
Multiplier resampling has evolved as a state‐of‐the‐art choice for inference on cumulative incidences or hazards in nonparametric and semiparametric survival and multistate models in event history analysis; see Lin et al (1993) and Lin et al (1994) for Cox models and Lin (1997) for competing risks set‐ ups
We propose new resampling‐based approaches to construct asymptotically valid time‐simultaneous confidence bands for cumulative hazard functions in multistate Cox models
We exemplify the methodology in detail for the simple Cox model with time‐dependent covariates, where the data may be subject to independent right‐censoring or left‐truncation
Summary
Multiplier resampling ( known as the wild bootstrap) has evolved as a state‐of‐the‐art choice for inference on cumulative incidences or hazards in nonparametric and semiparametric survival and multistate models in event history analysis; see Lin et al (1993) and Lin et al (1994) for Cox models and Lin (1997) for competing risks set‐ ups. The basic idea is to mimic martingale representations of the estimators by replacing nonobservable martingale residuals with randomly weighted counting processes. It is highly useful to predict survival probabilities based on covariates Such survival functions are typically provided with point‐wise confidence intervals, and this is implemented in all major software packages. When interest is in the survival function as a whole, it is preferable to report it together with uniform confidence intervals These so‐called confidence bands describe the uncertainty of the whole survival function estimation. In the present article we provide such results in Cox models and we investigate various new resampling bands that exhibit a reliable performance even for small sample sizes
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