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Research Abstracts - 2007
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Predicting the Risk and Trajectory of Intensive Care Patients Using Survival Models

Caleb W. Hug & Peter Szolovits


With automated systems at most bedsides in the intensive care, the availability of clinical, laboratory and signals data continues to increase. These data, often measured repeatedly over long periods of time, combined with the time sensitivity of intensive care, challenge caregivers to correctly utilize all of the data for optimal patient treatment. But fortunately they also make realistic the possibility of having computers "understand" the evolving condition of a patient. In fact, the volume of these data often precludes meaningful interpretation without such automated assistance. Our research focuses on applying artificial intelligence to patient monitoring systems to provide this assistance. We propose a patient representation that leverages patient outcome prediction models in order to illuminate the current state and the near-term trajectory of a patient as he or she progresses through the ICU.

Related Work

Similar modeling has been done in this field, but its application to patient care has been limited. In the past 20 years, several acuity scores have been proposed including the Simplified Acute Physiology Score (SAPS) [1], the Acute Physiology and Chronic Health Evaluation (APACHE) score [2], and the Mortality Prediction Model (MPM) [3]. These scores have gone through several revisions and can now be used to compare hospital performance, compare the outcomes for different groups of patients, and predict mortality risk for a patient. In general these scores are only available after a patientís first 24 hours in critical care and are calculated using the worst values over that period of time. This model calibration limits the utility of these models as a continuous indictor of patient state during a patientís progression through the ICU.


In our approach, we rely on survival analysis techniques to create outcome models that are applicable for the patientís entire stay. Survival analysis is a relatively new branch of statistics that focuses on modeling time to event data. Such data include cases where, for a variety of reasons, the event is unobserved and marked as censored. While statisticians have suggested numerous approaches to address this problem, the most common methods include parametric accelerated lifetime models and proportional hazards models. In the accelerated lifetime framework, explanatory variables (e.g. systolic blood pressure) scale the expected lifetime. Under the proportional hazards view, the explanatory variables scale the hazard (a subjectís instantaneous risk of death at time t given that they lived until time t). A clever method for estimating the scaling parameters for the proportional hazards model, without first estimating the hazard function, was proposed by Cox in 1972 [4]. We use a time-dependent version of this common semi-parametric survival model and consider the large number of patients who leave the ICU alive as censored cases. While this censoring presumably violates the uninformative censoring assumption of the Cox model, our analysis indicates that the assumption of random uninformative censoring is reasonable.

We have studied patients from retrospective data in a variety of intensive care units at a Boston-area hospital, using data collected in the MIMIC-II project [5]. In this data set, we have identified 3116 patients with 132 characteristics for study. After fitting a Cox proportional hazards model to data from our training set, this model can be used to predict patient survival on the separate validation set. While the baseline for these models differs greatly between individual patients, significant differences exist between the estimations for censored patients and patients who died in the hospital. Another important observation is the relative change in these predictions as patients progress through the intensive care; it is this progression that we are most interested in.


Our preliminary results in this research have shown promise [6]. Many patients demonstrate a healthy recovery, exhibiting a survival prediction that gradually increases until discharge. Other patients show marked deterioration in the survival prediction, ultimately ending in death. Comparing outcome predictions using the survival predictions from our model (the 10-day survival estimate, the cumulative mean 10-day estimate, and the cumulative variance on the 10-day estimate), we have demonstrated results that are slightly better than the SAPS I for predicting patient mortality. More importantly, these predictions are continually available as the patient progresses through the intensive care unit.


[1] J. R. Le Gall, P. Loirat, A. Alperovitch, P. Glaser, C. Granthil, D. Mathieu, P. Mercier, R. Thomas and D. Villers. A simplified acute physiology score for ICU patients. Crit. Care Med., vol. 12, pp. 975-977, Nov. 1984.

[2] W. A. Knaus, J. E. Zimmerman, D. P. Wagner, E. A. Draper and D. E. Lawrence. APACHE-acute physiology and chronic health evaluation: a physiologically based classification system. Crit. Care Med., vol. 9, pp. 591-597, Aug. 1981.

[3] S. Lemeshow, D. Teres, J. S. Avrunin and R. W. Gage. Refining intensive care unit outcome prediction by using changing probabilities of mortality. Crit. Care Med., vol. 16, pp. 470-477, May. 1988.

[4] D. R. Cox. Regression models and life tables (with discussion). Journal of the Royal Statistical Society B, vol. 34, pp. 187-220, 1972.

[5] M. Saeed, C. Lieu, G. Raber and R. G. Mark. MIMIC II: a massive temporal ICU patient database to support research in intelligent patient monitoring. Comput. Cardiol., vol. 29, pp. 641-644, 2002.

[6] C. W. Hug. Predicting the Risk and Trajectory of Intensive Care Patients using Survival Models. S.M. Thesis, MIT. pp. 126 p, 2006.


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