Nonparametric Inference for Markov Processes with Missing Absorbing State

Bakoyannis, Giorgos; Zhang, Ying; Yiannoutsos, Constantin T.

doi:10.5705/ss.202017.0175

Cited by 14 publications

(37 citation statements)

References 7 publications

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“…Compared to the previous work by Bluhmki et al (2018), which used counting process theory arguments in their derivations, we justify the properties of the proposed tests through the use of modern empirical process theory (Van Der Vaart and Wellner, 1996;Kosorok, 2008). As it will be argued later in the text, the practical advantage of our derivations lies on the fact that our proposed tests can be straightforwardly adapted to more complex settings such as cases with incompletely observed absorbing states (Bakoyannis et al, 2019). This can be done by replacing the influence function of the standard Aalen-Johansen estimator with the influence function of any other well-behaved and asymptotically linear estimator of the transition probabilities in our proposed testing procedures.…”

Section: Introductionmentioning

confidence: 80%

“…A special case of this is the issue of missing causes of death in biomedical applications. In such cases, a complete case analysis, which discards cases with a missing cause of death, is well known to lead to biased estimates (Gao and Tsiatis, 2005;Lu and Liang, 2008;Bakoyannis et al, 2019). In general, more complicated cases require extensions of the standard Aalen-Johansen estimator, denoted byP n,hj (s, t), to consistently estimate the transition probabilities of interest over a compact interval H ⊂ [0, τ ].…”

Section: Extensions To More Complex Settingsmentioning

confidence: 99%

“…Therefore, conditions D1-D3 are expected to have been established in works extending the standard Aalen-Johansen estimator to more complex settings. This is the case, for example, for the nonparametric estimator of the transition probability matrix with incompletely observed absorbing states (Bakoyannis et al, 2019).…”

Section: Extensions To More Complex Settingsmentioning

confidence: 99%

“…In many settings one can observe that a process has arrived at some absorbing state, but the actual absorbing state is unobserved for some study participants, such as in cases with missing causes of death. For such situations, Bakoyannis et al (2019) proposed a nonparametric maximum pseudolikelihood estimator (NPMPLE) under a missing at random assumption.…”

Section: Missing Absorbing Statesmentioning

confidence: 99%

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Nonparametric tests for transition probabilities in nonhomogeneous Markov processes

Bakoyannis

2019

Journal of Nonparametric Statistics

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This paper proposes nonparametric two-sample tests for the direct comparison of the probabilities of a particular transition between states of a continuous time nonhomogeneous Markov process with a finite state space. The proposed tests are a linear nonparametric test, an L 2 -norm-based test and a Kolmogorov-Smirnov-type test. Significance level assessment is based on rigorous procedures, which are justified through the use of modern empirical process theory. Moreover, the L 2 -norm and the Kolmogorov-Smirnov-type tests are shown to be consistent for every fixed alternative hypothesis. The proposed tests are also extended to more complex situations such as cases with incompletely observed absorbing states and non-Markov processes. Simulation studies show that the test statistics perform well even with small sample sizes. Finally, the proposed tests are applied to data on the treatment of early breast cancer from the European Organization for Research and Treatment of Cancer (EORTC) trial 10854, under an illness-death model.

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Section: Introductionmentioning

confidence: 80%

Section: Extensions To More Complex Settingsmentioning

confidence: 99%

Section: Extensions To More Complex Settingsmentioning

confidence: 99%

Section: Missing Absorbing Statesmentioning

confidence: 99%

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Nonparametric tests for transition probabilities in nonhomogeneous Markov processes

Bakoyannis

2019

Journal of Nonparametric Statistics

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“…When an internal validation sample is available, the problem reduces to the problem of missing cause of failure in the competing risks model and the analysis can be performed using methods for missing data, such as multiple imputation . More recent proposals for the analysis of misclassified competing risks data and more general Markov processes with interval validation samples are based on maximum nonparametric pseudolikelihood estimation . In settings without internal validation data, Bakoyannis and Yiannoutsos explored the extent of bias in cumulative incidence functions due to nondifferential misclassification of event type and proposed a simple uniformly consistent estimator to correct for such missclassification when the misclassification probabilities are known.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric estimation of the cumulative incidence function under outcome misclassification using external validation data

Edwards

Bakoyannis

Yiannoutsos

et al. 2019

Statistics in Medicine

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Misclassification of outcomes or event types is common in health sciences research and can lead to serious bias when estimating the cumulative incidence functions in settings with competing risks. Recent work has shown how to estimate nonparametric cumulative incidence functions in the presence of nondifferential outcome misclassification when the misclassification probabilities are known. Here, we extend this approach to account for misclassification that is differential with respect to important predictors of the outcome using misclassification probabilities estimated from external validation data. Moreover, we propose a bootstrap approach in which the observations from both the main study data and the external validation study are resampled to allow the uncertainty in the misclassification probabilities to propagate through the analysis into the final confidence intervals, ensuring appropriate confidence interval coverage probabilities. The proposed estimator is shown to be uniformly consistent and simulation studies indicate that both the estimator and the standard error estimation approach perform well in finite samples. The methodology is applied to estimate the cumulative incidence of death and disengagement from HIV care in a large cohort of HIV infected individuals in sub‐Saharan Africa, where a significant death underreporting issue leads to outcome misclassification. This analysis uses external validation data from a separate study conducted in the same country.

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A pseudo‐likelihood method for estimating misclassification probabilities in competing‐risks settings when true‐event data are partially observed

et al. 2020

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Nonparametric Inference for Markov Processes with Missing Absorbing State

Cited by 14 publications

References 7 publications

Nonparametric tests for transition probabilities in nonhomogeneous Markov processes

Nonparametric tests for transition probabilities in nonhomogeneous Markov processes

Nonparametric estimation of the cumulative incidence function under outcome misclassification using external validation data

A pseudo‐likelihood method for estimating misclassification probabilities in competing‐risks settings when true‐event data are partially observed

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