Cox's Periodic Regression Model

Pons, Odile; Turckheim, Élisabeth de

doi:10.1214/aos/1176350828

Cited by 16 publications

(18 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Lemma 1 can be strengthened to obtain the uniform convergence of

S_{n}^{false(k false)}

in β , using arguments similar to those in the proof of Lemma 2.3 in Pons & de Turckheim (1988).…”

Section: Definitions and Model Assumptionsmentioning

confidence: 99%

“…With Ω( β 0 ) = − ∂ 2 ( β 0 )/ ∂β∂β T being a positive-definite matrix by Condition A3, we see that ( β ) is concave and maximized at β = β 0 . The consistency of β̂ n is proved using a classic convex analysis theorem; see, e.g., Andersen & Gill (1982), Pons & de Turckheim (1988) or Lin et al (2000). …”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Another theoretical approach originates from Pons & de Turckheim (1988), who studied Cox's model with periodic baseline intensity using a single realization under certain ergodicity conditions. Similar ideas could be applied to the modulated renewal model (1), with ergodicity conditions assumed such that unpredictable processes converge uniformly to deterministic limits which can be substituted in the estimating equation.…”

Section: Introductionmentioning

confidence: 99%

“…Similarly to Lin & Fine (2009), we posit certain conditions on the dependence structure of the process. However, as shown in § 3·1, the theoretical developments and resulting inferences are much more challenging than in Oakes & Cui (1994), Pons & de Turckheim (1988) and Lin & Fine (2009), owing to the lack of either an independence property or a martingale approximation for the estimating function.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust analysis of semiparametric renewal process models

Lin¹,

Truong²,

Fine³

2013

Biometrika

View full text Add to dashboard Cite

Summary A rate model is proposed for a modulated renewal process comprising a single long sequence, where the covariate process may not capture the dependencies in the sequence as in standard intensity models. We consider partial likelihood-based inferences under a semiparametric multiplicative rate model, which has been widely studied in the context of independent and identical data. Under an intensity model, gap times in a single long sequence may be used naively in the partial likelihood with variance estimation utilizing the observed information matrix. Under a rate model, the gap times cannot be treated as independent and studying the partial likelihood is much more challenging. We employ a mixing condition in the application of limit theory for stationary sequences to obtain consistency and asymptotic normality. The estimator's variance is quite complicated owing to the unknown gap times dependence structure. We adapt block bootstrapping and cluster variance estimators to the partial likelihood. Simulation studies and an analysis of a semiparametric extension of a popular model for neural spike train data demonstrate the practical utility of the rate approach in comparison with the intensity approach.

show abstract

“…Lemma 1 can be strengthened to obtain the uniform convergence of

S_{n}^{false(k false)}

in β , using arguments similar to those in the proof of Lemma 2.3 in Pons & de Turckheim (1988).…”

Section: Definitions and Model Assumptionsmentioning

confidence: 99%

Section: Proof Of Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust analysis of semiparametric renewal process models

Lin¹,

Truong²,

Fine³

2013

Biometrika

View full text Add to dashboard Cite

show abstract

“…We define a profile likelihood for the parameters β jj and p jj , related to non-parametric estimation of the functions |jj , and we estimate the parameters by maximization. Similar methods were used in Breslow (1972) and for other models in Pons and Turckheim (1988), Pons and Visser (2000) and Pons (2000). In the next section, we introduce the notations and define more precisely the estimators of the parameters β jj , p jj and the cumulative hazard function.…”

Section: Introductionmentioning

confidence: 99%

Estimation in a model for a semi-Markov process with covariates under right-censoring

Pons¹

2004

Statistics

View full text Add to dashboard Cite

A semi-Markov model with covariates is proposed for a multi-state process with a finite number of states such that the transition probabilities between the states and the distribution functions of the duration times between the occurrence of two states depend on a discrete covariate. The hazard rates for the time elapsed between two successive states depend on the covariate through a proportional hazards model involving a set of regression parameters, while the transition probabilities depend on the covariate in an unspecified way. We propose estimators for these parameters and for the cumulative hazard functions of the sojourn times. A difficulty comes from the fact that when a sojourn time in a state is right-censored, the next state is unknown. We prove that our estimators are consistent and asymptotically Gaussian under the model constraints.

show abstract

Cox Regression Model

Sasieni

2005

Encyclopedia of Biostatistics

View full text Add to dashboard Cite

In 1972, D.R. Cox proposed the semiparametric model for the hazard at time t for an individual with covariates z . Here, the hazard is the instantaneous conditional probability of failure at t given that failure has not happened before t . The Cox model has had enormous influence in the theory and practice of biostatistics, and this article surveys its definition, history, basic use, estimators and algorithms, asymptotic properties, use of time‐dependent covariates, model checking, and alternatives and extensions.

show abstract

Cox's Periodic Regression Model

Cited by 16 publications

References 13 publications

Robust analysis of semiparametric renewal process models

Robust analysis of semiparametric renewal process models

Estimation in a model for a semi-Markov process with covariates under right-censoring

Cox Regression Model

Contact Info

Product

Resources

About