Dynamic clinical prediction models for discrete time‐to‐event data with competing risks—A case study on the OUTCOMEREA database

Heyard, Rachel; Timsit, Jean‐François; Essaied, W; Held, Leonhard

doi:10.1002/bimj.201700259

Cited by 9 publications

(16 citation statements)

References 39 publications

(51 reference statements)

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“…Heyard et al. () were interested in the time until a first occurrence of a VAP attributed to PA. However, once ventilator‐assisted patients are extubated or dead they are not at risk for a VAP PA anymore.…”

Section: Case Studymentioning

confidence: 99%

“…Heyard et al. () developed dynamic competing risks models to answer their research question. They further developed a method for CSVS to simplify their models and account for the fact that some variables may not have a direct effect on each outcome.…”

Section: Case Studymentioning

confidence: 99%

“…Heyard et al. () were interested in predicting the probability of a VAP PA event happening at day

t + 2

given that the patient is still at risk at day t . The cause‐specific hazards at

t + 2

as well as the overall hazards at

t + 1

and t are used to predict

\begin{matrix} true \\ right prefixPr false(T = t + 2, R = r false| T \geq t, x_{t} false) & = & left λ_{r} (t + 2 | {boldx}_{t}) \cdot [1 - λ false(t false| x_{t} false)] \cdot [1 - λ false(t + 1 false| x_{t} false)] \\ = & left λ_{r} (t + 2 | {boldx}_{t}) \cdot M (t | {boldx}_{t}) . \end{matrix}

Furthermore, a dynamic prediction model for

λ_{r} false(t + 2 false| x_{t} false)

has been proposed using a landmarking approach which we now want to validate.…”

Section: Case Study Revisitedmentioning

confidence: 99%

“…Heyard, Timsit, Essaied, Held, Heyard et al. () developed dynamic clinical prediction models for discrete time‐to‐event data with competing risks. They extended standard objective Bayesian variable selection methodology to handle discrete‐time competing risks models and identified the most relevant predictors for the timing of ventilator‐associated pneumonia (VAP) caused by a specific organism, Pseudomonas aeruginosa (PA).…”

Section: Introductionmentioning

confidence: 99%

“…The use of discrete time‐to‐event methods (Singer & Willett, ) was a natural choice for Heyard et al. () due to the daily ICU records in the data. These methods are asymptotically equivalent to the Cox regression (with time‐dependent variables) for short time intervals and small event probabilities in these intervals.…”

Section: Introductionmentioning

confidence: 99%

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Validation of discrete time‐to‐event prediction models in the presence of competing risks

2019

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Clinical prediction models play a key role in risk stratification, therapy assignment and many other fields of medical decision making. Before they can enter clinical practice, their usefulness has to be demonstrated using systematic validation. Methods to assess their predictive performance have been proposed for continuous, binary, and time-to-event outcomes, but the literature on validation methods for discrete time-toevent models with competing risks is sparse. The present paper tries to fill this gap and proposes new methodology to quantify discrimination, calibration, and prediction error (PE) for discrete time-to-event outcomes in the presence of competing risks. In our case study, the goal was to predict the risk of ventilator-associated pneumonia (VAP) attributed to Pseudomonas aeruginosa in intensive care units (ICUs). Competing events are extubation, death, and VAP due to other bacteria. The aim of this application is to validate complex prediction models developed in previous work on more recently available validation data. K E Y W O R D Sarea under the curve, calibration slope, competing events, discrete time-to-event model, dynamic prediction models, prediction error, validation INTRODUCTIONClinical prediction models aim to give valid outcome predictions for new patients and to provide a good basis for treatment decisions. Such models need to be systematically validated before entering clinical practice. Assessing the predictive performance in the data set from which the model has been derived will most certainly give an assessment which is too optimistic. To avoid this issue, some kind of cross-validation or external validation is needed. In perfect conditions, the performance of the prediction model is assessed in a second independent data set (Steyerberg, 2009). Such validation data, also referred to as testing data, should incorporate new patients from a different time period or patients from a different center. To quantify how well the prediction model performs, commonly used measures of discrimination and calibration can be computed. A model has satisfactory discrimination if it is able to adequately discriminate between cases and controls. Moreover, a well-calibrated model guarantees good agreement between observed outcomes and predictions. Finally, to evaluate overall performance, quadratic scoring rules like the prediction error (PE) or Brier score (BS) can be calculated to simultaneously assess calibration and discrimination.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Case Studymentioning

confidence: 99%

Section: Case Studymentioning

confidence: 99%

“…Heyard et al. () were interested in predicting the probability of a VAP PA event happening at day

t + 2

given that the patient is still at risk at day t . The cause‐specific hazards at

t + 2

as well as the overall hazards at

t + 1

and t are used to predict

\begin{matrix} true \\ right prefixPr false(T = t + 2, R = r false| T \geq t, x_{t} false) & = & left λ_{r} (t + 2 | {boldx}_{t}) \cdot [1 - λ false(t false| x_{t} false)] \cdot [1 - λ false(t + 1 false| x_{t} false)] \\ = & left λ_{r} (t + 2 | {boldx}_{t}) \cdot M (t | {boldx}_{t}) . \end{matrix}

Furthermore, a dynamic prediction model for

λ_{r} false(t + 2 false| x_{t} false)

has been proposed using a landmarking approach which we now want to validate.…”

Section: Case Study Revisitedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Validation of discrete time‐to‐event prediction models in the presence of competing risks

2019

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Dynamic prediction: A challenge for biostatisticians, but greatly needed by patients, physicians and the public

et al. 2019

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Prognosis is usually expressed in terms of the probability that a patient will or will not have experienced an event of interest t years after diagnosis of a disease. This quantity, however, is of little informative value for a patient who is still event-free after a number of years. Such a patient would be much more interested in the conditional probability of being event-free in the upcoming years, given that he/she did not experience the event in the s years after diagnosis, called "conditional survival." It is the simplest form of a dynamic prediction and can be dealt with using straightforward extensions of standard time-to-event analyses in clinical cohort studies. For a healthy individual, a related problem with further complications is the so-called "ageconditional probability of developing cancer" in the next t years. Here, the competing risk of dying from other diseases has to be taken into account. For both situations, the hazard function provides the central dynamic concept, which can be further extended in a natural way to build dynamic prediction models that incorporate both baseline and time-dependent characteristics. Such models are able to exploit the most current information accumulating over time in order to accurately predict the further course or development of a disease. In this article, the biostatistical challenges as well as the relevance and importance of dynamic prediction are illustrated using studies of multiple myeloma, a hematologic malignancy with a formerly rather poor prognosis which has improved over the last few years. K E Y W O R D Sage-conditional probability of developing cancer, conditional survival, dynamic prognosis, landmark regression models, time-dependent bias 822In doing so, we consider only absolute CS since this is the quantity of major interest in a clinical context. From a public health or epidemiologic perspective, however, relative CS, defined as the ratio of survival probabilities with the denominator derived from an age-adjusted normal population, may also be a highly relevant quantity (Shack, Braynt, Lockwood, & Ellison, 2013), which is sometimes also used for a statistical definition of cure (Baade, Youlden, & Chambers, 2011).On the other hand, for a healthy individual it might be of interest to know the probability of developing a certain disease, for example, a specific type of cancer. Quantities that are regularly published are age-specific incidence rates. These, however, cannot be directly translated into probabilities since death from other causes, for example, cardiovascular death, constitutes a competing event. Thus, the framework of multistate competing risks models has to be used to account for this fact. In a similar way as argued for CS, the resulting probabilities are of little value for an individual who is still alive and healthy at some age . Here, age-conditional probabilities of developing or dying from cancer are of interest for healthy individuals and today these are frequently reported by tumor registers and/or national statistical offi...

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Competing risks analysis for discrete time‐to‐event data

Schmid

Berger

2020

WIREs Computational Stats

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This article presents an overview of statistical methods for the analysis of discrete failure times with competing events. We describe the most commonly used modeling approaches for this type of data, including discrete versions of the cause‐specific hazards model and the subdistribution hazard model. In addition to discussing the characteristics of these methods, we present approaches to nonparametric estimation and model validation. Our literature review suggests that discrete competing‐risks analysis has gained substantial interest in the research community and is used regularly in econometrics, biostatistics, and educational research.This article is categorized under: Statistical Models > Survival Models Statistical Models > Semiparametric Models Statistical Models > Generalized Linear Models

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Dynamic clinical prediction models for discrete time‐to‐event data with competing risks—A case study on the OUTCOMEREA database

Cited by 9 publications

References 39 publications

Validation of discrete time‐to‐event prediction models in the presence of competing risks

Validation of discrete time‐to‐event prediction models in the presence of competing risks

Dynamic prediction: A challenge for biostatisticians, but greatly needed by patients, physicians and the public

Competing risks analysis for discrete time‐to‐event data

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