Age, Sex, and Waist-to-Height Ratio Approach the Discrimination of Fifty-Four Model Inputs for Prevalent Hypertension: An Explainable Machine Learning Analysis of the Chilean National Health Survey

Figures

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  Figure 1. Receiver operating characteristic curves on the held-out partition (n = 1412; 524 events) for three models: the full XGBoost model, the full penalised logistic model, and the parsimonious XGBoost model containing age, sex and waist-to-height ratio. The vertical axis is sensitivity, and the horizontal axis is one minus specificity. The dotted diagonal denotes the line of no discrimination (area under the curve 0.5). Shaded regions are 95% bootstrap bands obtained by resampling the 271 held-out census segments, so their width reflects between-segment rather than between-participant variability. The near-coincidence of the parsimonious and full curves across the operating range is the graphical form of the difference of 0.0084 AUC reported in Table 5.

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  Figure 2. Calibration of the same three models as Figure 1 on the held-out partition. Predicted probabilities are grouped into deciles; the horizontal axis is the mean predicted probability within each decile and the vertical axis the observed proportion of hypertensive participants, with 95% binomial intervals. The diagonal denotes perfect agreement between predicted and observed risk, and points below it indicates over-prediction. Expected calibration error (ECE) is the mean absolute deviation between the two across deciles and is reported as a point estimate only, for the reason given in the note to Table 4. The held-out values are 0.030 for the full XGBoost model, 0.010 for the full penalised logistic model, and 0.025 for the parsimonious XGBoost model. The first two are the values reported in Table 4; the third belongs to the parsimonious specification of Table 5, which is not among the models in Table 4, whose third model is CatBoost.

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  Figure 3. Held-out discrimination of the full XGBoost model within strata, with 95% bootstrap intervals obtained by resampling census segments. The dashed vertical line marks the overall held-out estimate. No pairwise contrast reached significance.

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  Figure 4. Distribution and direction of individual contributions to the output of the full XGBoost model for the fifteen highest-ranked inputs on the held-out partition. Each point is one participant; horizontal position is the SHAP value on the log-odds scale, and colour encodes the percentile of the input value. This figure is generated from the same single attribution computation as Table 8 and Figure 5, Figure 6 and Figure 7.

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  Figure 5. Mean absolute SHAP contribution of the fifteen highest-ranked model inputs to the output of the full XGBoost model, on the log-odds scale. Bars are annotated with the 2.5th-to-97.5th-percentile rank interval obtained from 25 refits on segment-level bootstrap resamples of the development data. Fifteen inputs are displayed for visual context; the twelve for which attribution is tabulated appear in Table 8. Only the first eight positions are reliably ordered; beyond that, rank intervals overlap so extensively that the displayed ordering should not be read as a ranking.

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  Figure 6. Dependence of individual SHAP contributions on input value for six model inputs, with a smoothed conditional mean overlaid; blue points are individual participant contributions, the orange line is the smoothed conditional mean and the dotted horizontal line marks zero contribution. The vertical axis is the SHAP contribution on the log-odds scale, where zero denotes no departure from the model base value of −0.4604; the horizontal axis is the input value, truncated at the 1st and 99th percentiles so that extreme values do not compress the informative range. Units are years for age, mL/min/1.73 m2 for estimated glomerular filtration rate (eGFR), mg/dL for glucose and LDL cholesterol, and dimensionless for the waist-to-height ratio. The urinary sodium-to-creatinine ratio is the native survey variable (Supplementary Table S1a, input 41), distinct from the derived sodium-to-potassium ratio (input 43) and is reported in the units supplied by the survey, which the official documentation does not specify; it is displayed for illustration and ranks thirteenth in Supplementary Table S5, below the eighth position beyond which we interpret no attribution. The step-like appearance reflects…

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  Figure 7. Contributions to the predicted risk of two representative participants, one at the 95th and one at the 5th percentile of predicted probability, showing the ten largest contributions with input values, the predicted probability, and the observed outcome. Positive contributions are shown in orange-red and negative in blue.

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  Figure 8. Net benefit across threshold probabilities for the three principal models on the held-out partition. This is a hypothetical mathematical illustration of threshold behaviour in this dataset and does not correspond to any real clinical decision, because blood pressure would necessarily be available wherever these models could be applied.