Dynamic prediction modeling of postoperative mortality among patients undergoing surgical aortic valve replacement in a statewide cohort over a 12-year period

Figures

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  Comparison of 30-day postoperative mortality: Predicted probabilities and observed proportions by risk tertiles and updating strategies.

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  Figure 1. Derivation of the study sample. This figure maps the inclusion and exclusion criteria for the population used for this analysis and also shows how the data were split into the development and validation sets. AVR, Aortic valve replacement; TAVR, transcatheter valve replacement; CABG, coronary artery bypass graft; SAVR, surgical aortic valve replacement.

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  Figure 2. Risk of 30-day postoperative mortality after surgical aortic valve replacement (SAVR) in the patient population. This figure plots the risk of mortality among patients undergoing SAVR over time throughout the study period.

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  Figure 3. Calibration plots of updating strategies. This figure shows the predicted (x-axis) by observed (y-axis) mortality by risk deciles in the validation sample. DLSSM, Dynamic logistic state space model; H-L, Hosmer-Lemeshow χ2 statistic with the corresponding P-value.

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  Figure E1. Overview of model updating strategies. This figure is a visual representation of model updating compared to not updating a clinical prediction model. Panel A (top) depicts the static approach while panel B (bottom) reflects dynamic updating. The initial model is either the least absolute shrinkage and selection operator (LASSO) or the dynamic logistic state space model (DLSSM) model. In the nonupdating scenario (A), the coefficients from the LASSO model are applied to each subsequent year in the validation set starting in 2007. With dynamic updating (B), the initial model is applied to the 2007 cohort (1a) and then updated using the 2007 data. That updated model (2a) is then tested on the 2008 cohort (3a). The model is then updated a second time (4a) based on the 2008 population and is then tested in the 2009 population (5a). The process of testing followed by updating continues yearly in the validation set.

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  Figure E2. Variable selection process of time-varying coefficients for the dynamic logistic state space model (DLSSM). The following plots illustrate the DLSSM variable selection process with corresponding 95% confidence bands (blue). The y-axis is the beta coefficient for each variable throughout the training period when it is not held constant. Any variable in which the 95% confidence bands excluded the initial point estimate would be considered a meaningful change from the time-invariant model and could be used to inform future changes in the testing set.Note that the y-axis varies based on the value of the beta coefficient for age. Due to the limited data and few deaths among those with chronic liver disease, there was not enough information for the model to learn from in the training set. Therefore, we made the assumption that chronic liver disease is a time-invariant coefficient, and the plot is not shown. CKD, Chronic kidney disease.

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  Figure E3. Dynamic logistic state space model (DLSSM) final model coefficients. Illustration of DLSSM model coefficients with corresponding 95% confidence bands. The x-axis is calendar time, with the black vertical line marking the end of the training period (2006) and the beginning of the validation period (2007). The left side of the vertical line is the smoothed coefficient in the training set and the right side represents the k-step ahead (1 year) prediction in the validation set. In this model, only the intercept is time-varying while the 8 coefficients are held constant (except for random error) within the training set. This figure is significant because it demonstrates which variables would be considered as time-varying and which were in-variant DLSSM model used in the analysis. Note that the y-axes vary based on the value of the beta coefficient for the intercept and age plots. CKD, Chronic kidney disease; CLD, chronic liver disease.

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  Figure E4. Yearly calibration plots by updating strategy (2007-2008). This figure shows the predicted (x-axis) by observed (y-axis) mortality by risk deciles in the validation sample within each year of the validation set (2007-2018). Because there are 12 years' data, the plots have been divided into 6 total subsets but collectively make up all the yearly calibration plots. A, 2007 to 2008. B, Yearly calibration plots by updating strategy (2009-2010). C, Yearly calibration plots by updating strategy (2011-2012). D, Yearly calibration plots by updating strategy (2013-2014). E, Yearly calibration plots by updating strategy (2015-2016). F, Yearly calibration plots by updating strategy (2017-2018). DLSSM, Dynamic logistic state space model.

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  Figure E5. Predicted probability of surgical aortic valve replacement (SAVR) 30-day postoperative mortality by strategy over time. The plot shows a comparison of the predicted risk (%) of 30-day postoperative SAVR mortality (y-axis) through the validation years of 2007 to 2018 (x-axis) by the 3 updating strategies. The green line is the static, nonupdating approach. The blue line represents the calibration regression strategy, and the red line is the dynamic logistic state space model (DLSSM) method. The figure is significant because it demonstrates the temporal trends of predicted risk from each updating strategy. The static approach maintains a fixed risk estimate throughout the study period. In contrast, the calibration regression and DLSSM methods incorporate updated information to adapt their risk predictions over time. SAVR, Surgical aortic valve replacement; DLSSM, dynamic logistic state space model.