Use of dynamic microsimulation to predict disease progression in patients with pneumonia-related sepsis

Abstract

Introduction: Sepsis is the leading cause of death in critically ill patients and often affects individuals with community-acquired pneumonia. To overcome the limitations of earlier mathematical models used to describe sepsis and predict outcomes, we designed an empirically based Monte Carlo model that simulates the progression of sepsis in hospitalized patients over a 30-day period.

Methods: The model simulates changing health over time, as represented by the Sepsis-related Organ Failure Assessment (SOFA) score, as a function of a patient's previous health state and length of hospital stay. We used data from patients enrolled in the GenIMS (Genetic and Inflammatory Markers of Sepsis) study to calibrate the model, and tested the model's ability to predict deaths, discharges, and daily SOFA scores over time using different algorithms to estimate the natural history of sepsis. We evaluated the stability of the methods using bootstrap sampling techniques.

Results: Of the 1,888 patients originally enrolled, most were elderly (mean age 67.77 years) and white (80.72%). About half (47.98%) were female. Most were relatively ill, with a mean Acute Physiology and Chronic Health Evaluation III score of 56 and Pneumonia Severity Index score of 73.5. The model's estimates of the daily pattern of deaths, discharges, and SOFA scores over time were not statistically different from the actual pattern when information about how long patients had been ill was included in the model (P = 0.91 to 0.98 for discharges; P = 0.26 to 0.68 for deaths). However, model estimates of these patterns were different from the actual pattern when the model did not include data on the duration of illness (P < 0.001 for discharges; P = 0.001 to 0.040 for deaths). Model results were stable to bootstrap validation.

Conclusion: An empiric simulation model of sepsis can predict complex longitudinal patterns in the progression of sepsis, most accurately by models that contain data representing both organ-system levels of and duration of illness. This work supports the incorporation into mathematical models of disease of the clinical intuition that the history of disease in an individual matters, and represents an advance over several prior simulation models that assume a constant rate of disease progression.

Figure 1

Basic structure of the simulation model. In the model, a patient with static and dynamic characteristics enters the hospital ward or intensive care unit (ICU). The patient could remain in the same location, move between the ward and ICU, die, or be discharged from the hospital. CNS, central nervous system; SOFA, Sepsis-related Organ Failure Assessment.

Figure 2

Empiric method for updating the patient's health. To update a model-generated patient's SOFA scores from one time to the next (from t - 0 to t + 1), the model searches for a patient with similar characteristics at t - 0. The model finds the 'similar' patient's t + 1 scores and uses them to represent the generated patient's t + 1 scores. CNS, central nervous system; SOFA, Sepsis-related Organ Failure Assessment.

Figure 3

Predicted and actual (observed) numbers of discharges and deaths per day during hospitalization. The similarity criteria used for the predictions are least restrictive at the top of the figure (not matching on both duration in the hospital and direction of illness progression) and most restrictive at the bottom (matching on duration in the hospital and direction of illness progression). Simulated values are the average of 100 replications of the simulation. SOFA, Sepsis-related Organ Failure Assessment.

Figure 4

Predicted and actual (observed) daily average total SOFA score of patients in the hospital. The similarity criteria used for the predictions are least restrictive at the top of the figure (not matching on both duration in the hospital and direction of illness progression) and most restrictive at the bottom (matching on duration in the hospital and direction of illness progression). Simulated values are the average of 100 replications of the simulation. SOFA, Sepsis-related Organ Failure Assessment.

Figure 5

Bootstrap validation of the model results. The model was re-evaluated on 100 bootstrapped samples of 50 replications under each of the similarity criteria shown in Figure 3. Only results of the simulations using component SOFA scores are shown. Empiric 95% confidence limits around the predicted number of discharges or deaths each day are constructed from the distribution of simulated discharges or deaths on each day of the simulation. The results indicate that the model results are relatively stable to random fluctuations in the data that were used to calibrate it, and confirm the finding that duration of disease is more important in predicting overall outcome than the instantaneous direction of progression of disease.