Confounder-Adjusted Survival Curves and Cumulative Incidence Functions
adjustedCurves.RdWhat is this package about?
This package aims to unite all available adjustments methods for estimate confounder-adjusted survival curves and cause-specific confounder-adjusted cumulative incidence functions under one consistent framework. We try to make the usage of these methods and the calculation of associated statistics as easy as possible for the user, while still providing substantial functionality.
What exactly are adjusted survival curves / adjusted cumulative incidence functions?
It is well known that confounding is a serious problem when analyzing data from non-randomized studies. This is also true when estimating survival curves or cumulative incidence functions. The aim is to estimate the population averaged survival probability or cumulative incidence for some group \(z\), which would have been observed if every individual would have been assigned to group \(z\). For example, the formal definition for the causal survival curve is:
$$S_{z}(t) = E(I(T_z > t))$$
where \(T_z\) is the survival time that would have been observed if treatment \(z\) was actually administered. See Denz et al. (2023) or Cai and Van der Laan (2020) for more details
What features are included in this package?
This package includes 15 methods to estimate confounder-adjusted survival curves (single event) and 7 methods to estimate confounder adjusted cumulative incidence functions (possibly with multiple competing events). It provides plot functions to easily produce highly customizable and publication-ready graphics. It also allows the user to easily calculate relevant statistics, such as confidence intervals, p-values, and adjusted restricted mean survival time estimates. Multiple Imputation is directly supported.
What does a typical workflow using this package look like?
The design of this package is based on the design of the WeightIt package. It includes two main functions: adjustedsurv and adjustedcif. Every implemented adjustment method has their own documentation page including a small description, code examples, and relevant literature references. The typical workflow using this package is as follows (1) estimate confounder-adjusted curves (survival curves or CIFs) using either adjustedsurv or adjustedcif, (2) plot those using the S3 plot method and sometimes (3) calculate further statistics using adjusted_rmst, adjusted_rmtl or adjusted_curve_test.
When should I use adjustedsurv and when adjustedcif?
With standard time-to-event data where only one type of event is possible both the confounder-adjusted survival curves and the confounder-adjusted cumulative incidence function can be estimated using the adjustedsurv function. While the adjustedsurv function only estimates the survival, the CIF can simply be calculated by \(1 - S(t)\). This transformation from survival curves to CIFs is directly implemented in the plot function (argument cif).
When competing risks are present, the cause-specific confounder-adjusted survival curves can not be estimated in an unbiased way (see for example Satagopan et al. (2004) for an explanation). The cause-specific confounder-adjusted cumulative incidence functions however can be estimated using the adjustedcif function.
What features are missing from this package?
In a former version, this package included two targeted maximum likelihood based methods for the estimation of adjusted survival curves and one for the estimation of adjusted cumulative incidence functions based on discrete-time data. These methods have been removed because the survtmle package has been removed from CRAN and there is currently no other available implementation of these estimators on CRAN. From version 0.10.2 tp 0.11.0 this package then contained an implementation of targeted maximum likelihood estimation for continuous time-to-event data (a wrapper function for the concrete package). This is currently unavailable due to the package being removed from CRAN, but will probably be supported again soon.
This package also currently does not support time-varying treatments or covariates. It also does not support left-censoring, interval-censoring or left-truncation. These features may be added in future releases.
What if the variable of interest is continuous?
All methods in this package are designed strictly for categorical variables of interest. If the variable of interest is continuous the user has to manually categorize the variable and save it as a factor first. This is, however, generally discouraged because artificial categorization may lead to bias or misleading results. To face this issue we have developed the contsurvplot R package which implements multiple plotting methods to visualize the (causal) effect of a continuous variable when analyzing survival data (Denz & Timmesfeld 2023).
Where can I get more information?
The documentation pages contain a lot of information, relevant examples and literature references. Additional examples can be found in the vignette of this package, which can be accessed using vignette(topic="introduction", package="adjustedCurves") or in the main paper associated with this package (Denz et al. 2023). We are also working on a separate article on this package that is going to be published in a peer-reviewed journal.
I want to suggest a new feature / I want to report a bug. Where can I do this?
Bug reports, suggestions and feature requests are highly welcome. Please file an issue on the official github page or contact the author directly using the supplied e-mail address.
References
Robin Denz, Renate Klaaßen-Mielke, and Nina Timmesfeld (2023). "A Comparison of Different Methods to Adjust Survival Curves for Confounders". In: Statistics in Medicine 42.10, pp. 1461-1479.
Robin Denz, Nina Timmesfeld (2023). "Visualizing the (Causal) Effect of a Continuous Variable on a Time-To-Event Outcome". In: Epidemiology 34.5, pp. 652-660.
Weixin Cai and Mark J. van der Laan (2020). "One-Step Targeted Maximum Likelihood Estimation for Time-To-Event Outcomes". In: Biometrics 76, pp. 722-733
J. M. Satagopan, L. Ben-Porat, M. Berwick, M. Robson, D. Kutler, and A. D. Auerbach (2004). "A Note on Competing Risks in Survival Data Analysis". In: British Journal of Cancer 91, pp. 1229-1235.