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1 Dichotomization of ICU length of stay based on model calibration Marion Verduijn, Niels Peek, Frans Voorbraak, Evert de Jonge, Bas de Mol

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2 ICU length of stay (LOS) Important outcome after cardiac surgery Predictive models for identification of high risk patients case load planning and resource allocation

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3 Main objective Development of a predictive model to estimate the risk of long ICU LOS using the method of class probability trees

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4 Data 2063 patients (Academic Medical Center, Amsterdam, 1997-2001) - preoperative (e.g., age, gender) - operative (e.g., surgery type, duration) - first 24h ICU stay (e.g., blood pressure, temperature) (122 patients died: 5.2%)

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5 Problem of outcome definition How should we define the outcome ‘long ICU LOS’? Literature: outcome dichotomized based on threshold values of 2-10 days without motivation or based on simple statistics

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6 Objective of this study Selection of the threshold value to dichotomize ICU LOS in a structured fashion based on data analysis

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7 Approach 1.Development of tree models for outcomes defined with different threshold values 2.Calculation of the model performance 3.Selection of the best model

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8 First results thresholdproportion events† Brier score‡ class probability tree 2 days0.5480.475 3 days0.3900.418 4 days0.2920.348 5 days0.2450.293 6 days0.2070.280 7 days0.1820.274 8 days0.1670.242 9 days0.1560.230 10 days0.1410.232 12 days0.1290.216 † patients with ICU LOS higher than the threshold value of death ‡ determined using 10-fold cross-validation

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9 Distances between probabilities I PxPx MxMx d RelEr d AbsEr d SqEr d KL 0.10.150.6660.050.00250.0122 0.010.0150.6660.0050.0000250.00109 0.0010.00150.6660.00050.000000250.000108

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10 Distances between probabilities I PxPx MxMx d RelEr d AbsEr d SqEr d KL 0.10.150.6660.050.00250.0122 0.010.0150.6660.0050.0000250.00109 0.0010.00150.6660.00050.000000250.000108

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11 Distances between probabilities I PxPx MxMx d RelEr d AbsEr d SqEr d KL 0.10.150.6660.050.00250.0122 0.010.0150.6660.0050.0000250.00109 0.0010.00150.6660.00050.000000250.000108

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12 ALOR distance Distance between two probabilities for a given x Absolute Log-Odds Ratio

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13 Property of ALOR: approximate proportional equivalence PxPx MxMx d RelEr d AbsEr d SqEr d KL d ALOR 0.10.150.6660.050.00250.01220.4626 0.010.0150.6660.0050.0000250.001090.4105 0.0010.00150.6660.00050.000000250.0001080.4060 Distances between probabilities II

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14 MALOR statistic Distance measure for all elements in F Mean value of the Absolute Log-Odds Ratio (MALOR) quantifies model calibration

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15 Procedure of threshold selection 1) define a set of possible threshold values T 2) for all threshold values t in T do a) define the dichotomized outcome Y t using threshold t b) build a predictive model M t for outcome Y t c) compute D MALOR (M t, P t ) 3) select threshold value with minimal MALOR statistic

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16 Additional results thresholdproportion events† Brier score‡MALOR class probability tree tree ensemble 2 days0.5480.4750.4150.492 3 days0.3900.4180.3660.490 4 days0.2920.3480.3120.516 5 days0.2450.2930.2800.468 6 days0.2070.2800.2510.534 7 days0.1820.2740.2320.575 8 days0.1670.2420.2120.618 9 days0.1560.2300.2060.616 10 days0.1410.2320.1930.765 12 days0.1290.2160.1810.709 † patients with ICU LOS higher than the threshold value of death ‡ determined using 10-fold cross-validation

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17 Tree model for ‘ICU LOS>5 days or death’

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18 Discussion and conclusions Class probability trees to identify high risk groups Performance measure should be insensitive to class unbalance when comparing models for different prediction problems

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19 Marion Verduijn m.verduijn@amc.uva.nl

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