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Estimation of direct effects for survival data by using the Aalen additive hazards model

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Bioinformatics: from nucleotids to networks (N2N)
Abstract
We extend the definition of the controlled direct effect of a point exposure on a survival outcome, other than through some given, time-fixed intermediate variable, to the additive hazard scale. We propose two-stage estimators for this effect when the exposure is dichotomous and randomly assigned and when the association between the intermediate variable and the survival outcome is confounded only by measured factors, which may themselves be affected by the exposure. The first stage of the estimation procedure involves assessing the effect of the intermediate variable on the survival outcome via Aalen's additive regression for the event time, given exposure, intermediate variable and confounders. The second stage involves applying Aalen's additive model, given the exposure alone, to a modified stochastic process (i.e. a modification of the observed counting process based on the first-stage estimates). We give the large sample properties of the estimator proposed and investigate its small sample properties by Monte Carlo simulation. A real data example is provided for illustration.
Keywords
Aalen's additive model, Direct effects, Mediation, Sequential G-estimation, Survival data, Time varying confounding, Time varying effects, MARGINAL STRUCTURAL MODELS, CAUSAL, REGRESSION, INTERVENTIONS, MEDIATION

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Citation

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Chicago
Martinussen, Torben, Stijn Vansteelandt, Mette Gerster, and Jacob von Bornemann Hjelmborg. 2011. “Estimation of Direct Effects for Survival Data by Using the Aalen Additive Hazards Model.” Journal of the Royal Statistical Society Series B-statistical Methodology 73 (5): 773–788.
APA
Martinussen, T., Vansteelandt, S., Gerster, M., & Hjelmborg, J. von B. (2011). Estimation of direct effects for survival data by using the Aalen additive hazards model. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 73(5), 773–788.
Vancouver
1.
Martinussen T, Vansteelandt S, Gerster M, Hjelmborg J von B. Estimation of direct effects for survival data by using the Aalen additive hazards model. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY. 2011;73(5):773–88.
MLA
Martinussen, Torben, Stijn Vansteelandt, Mette Gerster, et al. “Estimation of Direct Effects for Survival Data by Using the Aalen Additive Hazards Model.” JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY 73.5 (2011): 773–788. Print.
@article{1988867,
  abstract     = {We extend the definition of the controlled direct effect of a point exposure on a survival outcome, other than through some given, time-fixed intermediate variable, to the additive hazard scale. We propose two-stage estimators for this effect when the exposure is dichotomous and randomly assigned and when the association between the intermediate variable and the survival outcome is confounded only by measured factors, which may themselves be affected by the exposure. The first stage of the estimation procedure involves assessing the effect of the intermediate variable on the survival outcome via Aalen's additive regression for the event time, given exposure, intermediate variable and confounders. The second stage involves applying Aalen's additive model, given the exposure alone, to a modified stochastic process (i.e. a modification of the observed counting process based on the first-stage estimates). We give the large sample properties of the estimator proposed and investigate its small sample properties by Monte Carlo simulation. A real data example is provided for illustration.},
  author       = {Martinussen, Torben and Vansteelandt, Stijn and Gerster, Mette and Hjelmborg, Jacob von Bornemann},
  issn         = {1369-7412},
  journal      = {JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY},
  keyword      = {Aalen's additive model,Direct effects,Mediation,Sequential G-estimation,Survival data,Time varying confounding,Time varying effects,MARGINAL STRUCTURAL MODELS,CAUSAL,REGRESSION,INTERVENTIONS,MEDIATION},
  language     = {eng},
  number       = {5},
  pages        = {773--788},
  title        = {Estimation of direct effects for survival data by using the Aalen additive hazards model},
  url          = {http://dx.doi.org/10.1111/j.1467-9868.2011.00782.x},
  volume       = {73},
  year         = {2011},
}

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