Joint modeling approach for semicompeting risks data with missing nonterminal event status

Hu, Chen; Tsodikov, Alex

doi:10.1007/s10985-013-9288-y

Cited by 8 publications

(8 citation statements)

References 33 publications

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“…Define derivatives of

γ_{i}

with respect to

H

and

boldβ

{\overset{γ}{true}}_{i, H} (H (t); boldβ) = \frac{\partial γ_{i} (H (t); boldβ)}{\partial italicdH false(t false)}

{\overset{γ}{true}}_{i, β} (H (t); boldβ) = \frac{\partial γ_{i} (H (t); boldβ)}{\partial β},

respectively. For a functional

J false(f false), : f = f false(x false)

, the functional derivative in is defined as

\frac{\partial J false(f false)}{\partial italicdf false(s false)} = {(|, \frac{\partial J false(f + ε g false)}{\partial ε})}_{ε = 0, g = 1 false(x > s false)}

(see Hu and Tsodikov, , Section ) and corresponds to taking the derivative with respect to a jump in

H

at time t when

H

is a step function. For a linear functional of the form

J false(f false) = \int_{0}^{t} ϕ false(x false) italicdf false(x false)

, the functional derivative is

\begin{matrix} right \frac{\partial J}{\partial} \end{matrix}

…”

Section: Nonparametric Maximum Likelihood Estimationmentioning

confidence: 99%

See 1 more Smart Citation

Semiparametric Time-to-Event Modeling in the Presence of a Latent Progression Event

Rice

Tsodikov

2016

Biometrics

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Summary In cancer research, interest frequently centers on factors influencing a latent event that must precede a terminal event. In practice it is often impossible to observe the latent event precisely, making inference about this process difficult. To address this problem, we propose a joint model for the unobserved time to the latent and terminal events, with the two events linked by the baseline hazard. Covariates enter the model parametrically as linear combinations that multiply, respectively, the hazard for the latent event and the hazard for the terminal event conditional on the latent one. We derive the partial likelihood estimators for this problem assuming the latent event is observed, and propose a profile likelihood–based method for estimation when the latent event is unobserved. The baseline hazard in this case is estimated nonparametrically using the EM algorithm, which allows for closed-form Breslow-type estimators at each iteration, bringing improved computational efficiency and stability compared with maximizing the marginal likelihood directly. We present simulation studies to illustrate the finite-sample properties of the method; its use in practice is demonstrated in the analysis of a prostate cancer data set.

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“…Define derivatives of

γ_{i}

with respect to

H

and

boldβ

{\overset{γ}{true}}_{i, H} (H (t); boldβ) = \frac{\partial γ_{i} (H (t); boldβ)}{\partial italicdH false(t false)}

{\overset{γ}{true}}_{i, β} (H (t); boldβ) = \frac{\partial γ_{i} (H (t); boldβ)}{\partial β},

respectively. For a functional

J false(f false), : f = f false(x false)

, the functional derivative in is defined as

\frac{\partial J false(f false)}{\partial italicdf false(s false)} = {(|, \frac{\partial J false(f + ε g false)}{\partial ε})}_{ε = 0, g = 1 false(x > s false)}

(see Hu and Tsodikov, , Section ) and corresponds to taking the derivative with respect to a jump in

H

at time t when

H

is a step function. For a linear functional of the form

J false(f false) = \int_{0}^{t} ϕ false(x false) italicdf false(x false)

, the functional derivative is

\begin{matrix} right \frac{\partial J}{\partial} \end{matrix}

…”

Section: Nonparametric Maximum Likelihood Estimationmentioning

confidence: 99%

“…(see Hu and Tsodikov, 2014a, Section 3.2) and corresponds to taking the derivative with respect to a jump in H at time t when H is a step function. For a linear functional of the form…”

Section: Functional Derivative and Score Equationsmentioning

confidence: 99%

Semiparametric Time-to-Event Modeling in the Presence of a Latent Progression Event

Rice

Tsodikov

2016

Biometrics

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“…Zeng et al 20 estimated treatment effects in consideration of treatment switching. Hu and Tsodikov 21 considered missing nonterminal event status under a joint modeling approach.…”

Section: Introductionmentioning

confidence: 99%

On shared gamma‐frailty conditional Markov model for semicompeting risks data

Zhang

Bakoyannis

et al. 2020

Statistics in Medicine

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Semicompeting risks data are a mixture of competing risks data and progressive state data. This type of data occurs when a nonterminal event is subject to truncation by a well‐defined terminal event, but not vice versa. The shared gamma‐frailty conditional Markov model (GFCMM) has been used to analyze semicompeting risks data because of its flexibility. There are two versions of this model: the restricted and the unrestricted model. Maximum likelihood estimation methodology has been proposed in the literature. However, we found through numerical experiments that the unrestricted model sometimes yields nonparametrically biased estimation. In this article, we provide a practical guideline for using the GFCMM in the analysis of semicompeting risk data that includes: (a) a score test to assess if the restricted model, which does not exhibit estimation problems, is reasonable under a proportional hazards assumption, and (b) a graphical illustration to justify whether the unrestricted model yields nonparametric estimation with substantial bias for cases where the test provides a statistical significant result against the restricted model. This guideline was applied to the Indianapolis‐Ibadan Dementia Project data as an illustration to explore how dementia occurrence changes mortality risk.

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“…Semicompeting risks (Fig. 1, middle) have been proposed for the case where death may precede progression (Hu and Tsodikov, 2014). Xu et al (2010) observe that semicompeting risks essentially amount to the progressive illness-death model (Fix and Neyman, 1951;Fig.…”

Section: Introductionmentioning

confidence: 99%

Sieve estimation in a Markov illness-death process under dual censoring

Boruvka

Cook

2016

Biostatistics

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Semiparametric methods are well-established for the analysis of a progressive Markov illness-death process observed up to a noninformative right censoring time. However often the intermediate and terminal events are censored in different ways, leading to a dual censoring scheme. In such settings unbiased estimation of the cumulative transition intensity functions cannot be achieved without some degree of smoothing. To overcome this problem we develop a sieve maximum likelihood approach for inference on the hazard ratio. A simulation study shows that the sieve estimator offers improved finite-sample performance over common imputation-based alternatives and is robust to some forms of dependent censoring. The proposed method is illustrated using data from cancer trials.

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Joint modeling approach for semicompeting risks data with missing nonterminal event status

Cited by 8 publications

References 33 publications

Semiparametric Time-to-Event Modeling in the Presence of a Latent Progression Event

Semiparametric Time-to-Event Modeling in the Presence of a Latent Progression Event

On shared gamma‐frailty conditional Markov model for semicompeting risks data

Sieve estimation in a Markov illness-death process under dual censoring

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