Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A flexible control function approach for survival data subject to different types of censoring

Ilias Willems, Sara Rutten, Gilles Crommen, Ingrid Van Keilegom

TL;DR

This paper tackles causal effect estimation of a treatment on a right-censored time-to-event under unobserved confounding and dependent censoring by formulating a flexible transformation-model with a control-function instrumental variable. It jointly models transformed latent event times $T^k$ via $\Lambda_{\theta_k}(T^k)$ with Gaussian errors and a Gaussian copula, enabling identification of causal effects through a two-step estimator and a goodness-of-fit test. The authors establish identifiability and asymptotic theory, develop a parametric bootstrap-based test, and validate performance through extensive simulations, including misspecification analyses. The approach is demonstrated on the JTPA unemployment-duration data, illustrating a positive causal effect of job training programs on unemployment duration and providing practical tools for inference in settings with multiple latent times and various censoring mechanisms.

Abstract

This paper addresses the problem of identifying and estimating the causal effect of a treatment in the presence of unmeasured confounding and various types of right-censoring. Examples of these censoring mechanisms are administrative censoring, competing risks and dependent censoring (e.g. loss to follow-up). Different parametric transformations are applied to each event time, resulting in a regression model with a more additive structure and error terms that are approximately normal and homoscedastic. The transformed event times are modeled using a joint regression framework, assuming multivariate Gaussian error terms with an unspecified covariance matrix. A control function approach is used to deal with unmeasured confounding. The model is shown to be identifiable and a two-step estimation procedure is proposed. This estimator is proven to yield consistent and asymptotically normal estimates. Furthermore, a goodness-of-fit test for the model's validity is developed. Simulations are conducted to examine the finite-sample performance of the proposed estimator under various scenarios. Finally, the methodology is applied to investigate the causal effect of job training programs on unemployment duration using data from the National Job Training Partnership Act (JTPA) study.

A flexible control function approach for survival data subject to different types of censoring

TL;DR

This paper tackles causal effect estimation of a treatment on a right-censored time-to-event under unobserved confounding and dependent censoring by formulating a flexible transformation-model with a control-function instrumental variable. It jointly models transformed latent event times via with Gaussian errors and a Gaussian copula, enabling identification of causal effects through a two-step estimator and a goodness-of-fit test. The authors establish identifiability and asymptotic theory, develop a parametric bootstrap-based test, and validate performance through extensive simulations, including misspecification analyses. The approach is demonstrated on the JTPA unemployment-duration data, illustrating a positive causal effect of job training programs on unemployment duration and providing practical tools for inference in settings with multiple latent times and various censoring mechanisms.

Abstract

This paper addresses the problem of identifying and estimating the causal effect of a treatment in the presence of unmeasured confounding and various types of right-censoring. Examples of these censoring mechanisms are administrative censoring, competing risks and dependent censoring (e.g. loss to follow-up). Different parametric transformations are applied to each event time, resulting in a regression model with a more additive structure and error terms that are approximately normal and homoscedastic. The transformed event times are modeled using a joint regression framework, assuming multivariate Gaussian error terms with an unspecified covariance matrix. A control function approach is used to deal with unmeasured confounding. The model is shown to be identifiable and a two-step estimation procedure is proposed. This estimator is proven to yield consistent and asymptotically normal estimates. Furthermore, a goodness-of-fit test for the model's validity is developed. Simulations are conducted to examine the finite-sample performance of the proposed estimator under various scenarios. Finally, the methodology is applied to investigate the causal effect of job training programs on unemployment duration using data from the National Job Training Partnership Act (JTPA) study.
Paper Structure (19 sections, 3 theorems, 34 equations, 1 figure, 3 tables)

This paper contains 19 sections, 3 theorems, 34 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Related literature
  3. Outline
  4. The model
  5. Model specification
  6. Useful definitions and distributions
  7. Model identification and estimation
  8. Model identification
  9. Estimation of the model parameters
  10. Consistency and asymptotic normality
  11. Asymptotic variance
  12. Goodness-of-fit test
  13. Simulation study
  14. Finite sample performance
  15. Model under misspecification
  16. ...and 4 more sections

Key Result

Theorem 1

Under Assumptions as:A1 to as:A9, suppose that $(T^1_{j}, \ldots, T^K_{j},C_j)$, with $j=1,2$, satisfy model eq:Regression Model rewritten with parameter vectors $(\gamma,\eta_1)$ and $(\gamma,\eta_2)$, respectively. Denote, $Y_j=\min(T^1_{j}, \ldots,T^K_{j},C_j)$ and $\Tilde{\Delta}_j = \bigl(\math for $l_1, \ldots, l_K,l_C \in \{0,1\}$ and for almost every $(w,z)$, it follows that:

Figures (1)

  • Figure 1: Top panel: the estimated survival curves using the two-step estimator with (solid curve) and without (dotted curve) transforming the response. The bottom panels relate to the goodness of fit test. The bottom left panel compares the distributions of $K = \min(T^1, T^2)$ implied by the model and based on the Kaplan-Meier estimator. The bottom right panel shows the bootstrap distribution of the goodness-of-fit test statistic. The vertical red line represents the observed value of the test statistic.

Theorems & Definitions (3)

  • Theorem 1
  • Theorem 2
  • Theorem 3