scholarly journals Semiparametric estimation of structural failure time models in continuous-time processes

Biometrika ◽  
2019 ◽  
Author(s):  
S Yang ◽  
K Pieper ◽  
F Cools
Keyword(s):  
Continuous Time ◽  
Failure Time ◽  
Dependent Censoring ◽  
Model Parameters ◽  
Structural Failure ◽  
Time Model ◽  
Efficiency Theory ◽  
Doubly Robust ◽  
Continuous Time Processes ◽  
Artificial Censoring

Summary Structural failure time models are causal models for estimating the effect of time-varying treatments on a survival outcome. G-estimation and artificial censoring have been proposed for estimating the model parameters in the presence of time-dependent confounding and administrative censoring. However, most existing methods require manually pre-processing data into regularly spaced data, which may invalidate the subsequent causal analysis. Moreover, the computation and inference are challenging due to the nonsmoothness of artificial censoring. We propose a class of continuous-time structural failure time models that respects the continuous-time nature of the underlying data processes. Under a martingale condition of no unmeasured confounding, we show that the model parameters are identifiable from a potentially infinite number of estimating equations. Using the semiparametric efficiency theory, we derive the first semiparametric doubly robust estimators, which are consistent if the model for the treatment process or the failure time model, but not necessarily both, is correctly specified. Moreover, we propose using inverse probability of censoring weighting to deal with dependent censoring. In contrast to artificial censoring, our weighting strategy does not introduce nonsmoothness in estimation and ensures that resampling methods can be used for inference.

Estimating the effect of zidovudine on Kaposi's sarcoma from observational data using a rank preserving structural failure-time model

1998 ◽  
Vol 17 (10) ◽  
pp. 1073-1102 ◽  
Author(s):  
Marshall M. Joffe ◽  
Donald R. Hoover ◽  
Lisa P. Jacobson ◽  
Lawrence Kingsley ◽  
Joan S. Chmiel ◽  
...  
Keyword(s):  
Observational Data ◽  
Kaposi's Sarcoma ◽  
Failure Time ◽  
Kaposi’S Sarcoma ◽  
Structural Failure ◽  
Time Model ◽  
Failure Time Model

scholarly journals Gaussian process regression for survival time prediction with genome-wide gene expression

Biostatistics ◽  
2019 ◽  
Author(s):  
Aaron J Molstad ◽  
Li Hsu ◽  
Wei Sun
Keyword(s):  
Gene Expression ◽  
Gaussian Process ◽  
Survival Time ◽  
Failure Time ◽  
Real Data ◽  
Accelerated Failure Time Model ◽  
Model Parameters ◽  
Time Model ◽  
Genome Wide ◽  
Genome Wide Gene Expression

SummaryPredicting the survival time of a cancer patient based on his/her genome-wide gene expression remains a challenging problem. For certain types of cancer, the effects of gene expression on survival are both weak and abundant, so identifying non-zero effects with reasonable accuracy is difficult. As an alternative to methods that use variable selection, we propose a Gaussian process accelerated failure time model to predict survival time using genome-wide or pathway-wide gene expression data. Using a Monte Carlo expectation–maximization algorithm, we jointly impute censored log-survival time and estimate model parameters. We demonstrate the performance of our method and its advantage over existing methods in both simulations and real data analysis. The real data that we analyze were collected from 513 patients with kidney renal clear cell carcinoma and include survival time, demographic/clinical variables, and expression of more than 20 000 genes. In addition to the right-censored survival time, our method can also accommodate left-censored or interval-censored outcomes; and it provides a natural way to combine multiple types of high-dimensional -omics data. An R package implementing our method is available in the Supplementary material available at Biostatistics online.

Limiting distribution for a simple model of order book dynamics

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Łukasz Kruk
Keyword(s):  
Continuous Time ◽  
Limit Order Book ◽  
Limiting Distribution ◽  
Model Parameters ◽  
Order Book ◽  
Continuous Time Model ◽  
Time Model ◽  
Limiting Behavior ◽  
Bid Ask Spread ◽  
Limit Orders

AbstractA continuous-time model for the limit order book dynamics is considered. The set of outstanding limit orders is modeled as a pair of random counting measures and the limiting distribution of this pair of measure-valued processes is obtained under suitable conditions on the model parameters. The limiting behavior of the bid-ask spread and the midpoint of the bid-ask interval are also characterized.

Discretization of deflated bond prices

2000 ◽  
Vol 32 (2) ◽  
pp. 540-563 ◽  
Author(s):  
Paul Glasserman ◽  
Hui Wang
Keyword(s):  
Interest Rates ◽  
Term Structure ◽  
Discrete Time ◽  
Continuous Time ◽  
Unit Interval ◽  
Continuous Time Model ◽  
Time Model ◽  
Numerical Work ◽  
Continuous Time Process ◽  
Continuous Time Processes

This paper proposes and analyzes discrete-time approximations to a class of diffusions, with an emphasis on preserving certain important features of the continuous-time processes in the approximations. We start with multivariate diffusions having three features in particular: they are martingales, each of their components evolves within the unit interval, and the components are almost surely ordered. In the models of the term structure of interest rates that motivate our investigation, these properties have the important implications that the model is arbitrage-free and that interest rates remain positive. In practice, numerical work with such models often requires Monte Carlo simulation and thus entails replacing the original continuous-time model with a discrete-time approximation. It is desirable that the approximating processes preserve the three features of the original model just noted, though standard discretization methods do not. We introduce new discretizations based on first applying nonlinear transformations from the unit interval to the real line (in particular, the inverse normal and inverse logit), then using an Euler discretization, and finally applying a small adjustment to the drift in the Euler scheme. We verify that these methods enforce important features in the discretization with no loss in the order of convergence (weak or strong). Numerical results suggest that these methods can also yield a better approximation to the law of the continuous-time process than does a more standard discretization.

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