scholarly journals Estimating Survival Functions after Stcox with Time-varying Coefficients

2016 ◽  
Vol 16 (4) ◽  
pp. 867-879 ◽  
Author(s):  
Constantin Ruhe
Keyword(s):  
Proportional Hazards ◽  
Cox Model ◽  
Survival Function ◽  
Time Dependent ◽  
Time Varying ◽  
Survival Functions ◽  
Nonproportional Hazards ◽  
Varying Coefficients ◽  
Proportional Hazards Assumption ◽  
Time Varying Coefficients

In many applications of the Cox model, the proportional-hazards assumption is implausible. In these cases, the solution to nonproportional hazards usually consists of modeling the effect of the variable of interest and its interaction effect with some function of time. Although Stata provides a command to implement this interaction in stcox, it does not allow the typical visualizations using stcurve if stcox was estimated with the tvc() option. In this article, I provide a short workaround that estimates the survival function after stcox with time-dependent coefficients. I introduce and describe the scurve_tvc command, which automates this procedure and allows users to easily visualize survival functions for models with time-varying effects.

Bootstrap pointwise confidence intervals for covariate-adjusted survivor functions in the Cox model

2019 ◽  
Vol 19 (1) ◽  
pp. 185-199
Author(s):  
Constantin Ruhe
Keyword(s):  
Confidence Intervals ◽  
Proportional Hazards ◽  
Cox Model ◽  
Survival Functions ◽  
Bootstrap Confidence Intervals ◽  
Cox Models ◽  
Varying Coefficients ◽  
Asymptotic Confidence Intervals ◽  
Time Varying Coefficients ◽  
Additional Option

Survival functions are a common visualization of predictions from the Cox model. However, neither Stata’s stcurve command nor the communitycontributed scurve tvc command allows one to estimate confidence intervals. In this article, I discuss how bootstrap confidence intervals can be formed for covariate-adjusted survival functions in the Cox model. The new bsurvci command automates this procedure and allows users to visualize the results. bsurvci enables one to estimate uncertainty around survival functions estimated from Cox models with time-varying coefficients, a capability that was not previously available in Stata. Furthermore, it provides Stata users with an additional option for survival estimates from Cox models with proportional hazards by allowing them to choose between bootstrap confidence intervals using bsurvci and asymptotic confidence intervals from an existing community-contributed command, survci. Because asymptotic confidence intervals make distributional assumptions when constructing confidence intervals, the bootstrap procedure proposed in this article provides a nonparametric alternative.

The Identifiability of the Mixed Proportional Hazards Model with Time-Varying Coefficients

1996 ◽  
Vol 12 (4) ◽  
pp. 733-738 ◽  
Author(s):  
Brian P. McCall
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Time Varying ◽  
Varying Coefficients ◽  
Hazards Model ◽  
Time Varying Coefficients ◽  
Mixed Proportional Hazards

This paper establishes conditions for the nonparametric identifiability of the mixed proportional hazards model with time-varying coefficients. Unlike the mixed proportional hazards model, a regressor with two distinct values is not sufficient to identify this model. An unbounded regressor, however, is sufficient for identification.

scholarly journals Climatic responses to systematic time variations of parameters: a dynamical approach

2018 ◽  
Vol 25 (3) ◽  
pp. 649-658 ◽  
Author(s):  
Catherine Nicolis
Keyword(s):  
Evolution Equations ◽  
Time Dependent ◽  
Time Varying ◽  
Climatic Response ◽  
Varying Coefficients ◽  
Classical Stability ◽  
Theoretical Predictions ◽  
Time Variations ◽  
Time Varying Coefficients ◽  
Climatic Responses

Abstract. The climatic response to time-dependent parameters is revisited from a nonlinear dynamics perspective. Some general trends are identified, based on a generalized stability criterion extending classical stability analysis to account for the presence of time-varying coefficients in the evolution equations of the system's variables. Theoretical predictions are validated by the results of numerical integration of the evolution equations of prototypical systems of relevance in atmospheric and climatic dynamics.

scholarly journals Hypothesis testing for an extended cox model with time-varying coefficients

Biometrics ◽  
2014 ◽  
Vol 70 (3) ◽  
pp. 619-628 ◽  
Author(s):  
Takumi Saegusa ◽  
Chongzhi Di ◽  
Ying Qing Chen
Keyword(s):  
Hypothesis Testing ◽  
Cox Model ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Varying Coefficients ◽  
Extended Cox Model

scholarly journals Climatic responses to systematic time variations of parameters: A dynamical approach

2018 ◽  
Author(s):  
Catherine Nicolis
Keyword(s):  
Evolution Equations ◽  
Time Dependent ◽  
Time Varying ◽  
Climatic Response ◽  
Varying Coefficients ◽  
Classical Stability ◽  
Theoretical Predictions ◽  
Time Variations ◽  
Time Varying Coefficients ◽  
Climatic Responses

Abstract. The climatic response to time-dependent parameters is revisited from a nonlinear dynamics perspective. Some general trends are identified, based on a generalised stability criterion extending classical stability analysis to account for the presence of time-varying coefficients in the evolution equations of the system's variables. Theoretical predictions are validated by the results of numerical integration of the evolution equations of prototypical systems of relevance in atmospheric and climatic dynamics.

Quantifying Change Over Time: Interpreting Time-varying Effects In Duration Analyses

2018 ◽  
Vol 26 (1) ◽  
pp. 90-111 ◽  
Author(s):  
Constantin Ruhe
Keyword(s):  
Interstate Conflict ◽  
Event History ◽  
Time Varying ◽  
Correct Interpretation ◽  
Nonproportional Hazards ◽  
Varying Coefficients ◽  
Hazard Ratios ◽  
Time Varying Coefficients ◽  
Over Time ◽  
Survivor Functions

Duration analyses in political science often model nonproportional hazards through interactions with analysis time. To facilitate their interpretation, methodologists have proposed methods to visualize time-varying coefficients or hazard ratios. While these techniques are a useful, initial postestimation step, I argue that they are insufficient to identify the overall impact of a time-varying effect and may lead to faulty inference when a coefficient changes its sign. I show how even significant changes of a coefficient’s sign do not imply that the overall effect is reversed over time. In order to enable a correct interpretation of time-varying effects in this context, researchers should visualize their results with survivor functions. I outline how survivor functions are calculated for models with time-varying effects and demonstrate the need for such a nuanced interpretation using the prominent finding of a time-varying effect of mediation on interstate conflict. The reanalysis of the data using the proposed visualization methods indicates that the conclusions of earlier mediation research are misleading. The example highlights how survivor functions are an essential tool to clarify the ambiguity inherent in time-varying coefficients in event history models.

Sign in / Sign up

Export Citation Format

Share Document