﻿====================================================================================

A. MORTALITY DATASET — primary cohort

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  eligible_operations                   : 2365

  distinct_subjects                     : 2365

  subjects_with_repeat_operations       : 0

  deaths_primary                        : 90

  deaths_from_landmark_horizon          : 90

  deaths_any_time                       : 561



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B. ABSOLUTE RISK BY STRATUM

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lactate_stratum   n  deaths  risk_pct exact_ci_pct  crude_OR crude_OR_ci

          <=1.9 815      11      1.35    0.68-2.40      1.00   reference

        2.1-3.0 570      17      2.98    1.75-4.73      2.25   1.04-4.83

        3.8-5.9 765      40      5.23    3.76-7.05      4.03   2.05-7.92

     8.6 capped 215      22     10.23   6.52-15.08      8.33  3.97-17.47



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C. SPARSITY AND SEPARATION DIAGNOSTICS

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--- parsimonious ---

       model                   term  empty_cell            non_deaths/deaths

parsimonious            lac_2.1-3.0       False        0: 1722/73; 1: 553/17

parsimonious            lac_3.8-5.9       False        0: 1550/50; 1: 725/40

parsimonious         lac_8.6 capped       False        0: 2082/68; 1: 193/22

parsimonious                    age       False continuous (range 20.0-90.0)

parsimonious    baseline_creatinine       False   continuous (range 0.4-5.5)

parsimonious                asa_ge3       False        0: 751/20; 1: 1524/70

parsimonious MODEL: 6 df, 90 events       False                  EPV = 15.00



--- expanded ---

   model                    term  empty_cell                      non_deaths/deaths

expanded             lac_2.1-3.0       False                  0: 1722/73; 1: 553/17

expanded             lac_3.8-5.9       False                  0: 1550/50; 1: 725/40

expanded          lac_8.6 capped       False                  0: 2082/68; 1: 193/22

expanded                     age       False           continuous (range 20.0-90.0)

expanded     baseline_creatinine       False             continuous (range 0.4-5.5)

expanded                 asa_ge3       False                  0: 751/20; 1: 1524/70

expanded                  female       False                  0: 1393/59; 1: 882/31

expanded               emergency       False                  0: 2040/75; 1: 235/15

expanded        cpb_duration_min       False          continuous (range 20.0-595.0)

expanded          concurrent_aki       False                  0: 1780/54; 1: 495/36

expanded MODEL: 10 df, 90 events        True EPV = 9.00 (below the conventional 10)



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D. MAXIMUM LIKELIHOOD VERSUS FIRTH VERSUS RIDGE

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       model          estimator           term              OR (95% CI)            p

parsimonious maximum likelihood    lac_2.1-3.0         2.46 (1.12-5.39) 2.497079e-02

parsimonious maximum likelihood    lac_3.8-5.9         4.49 (2.24-9.00) 2.351804e-05

parsimonious maximum likelihood lac_8.6 capped       12.69 (5.84-27.55) 1.358569e-10

parsimonious Firth (profile CI)    lac_2.1-3.0         2.41 (1.13-5.34) 2.466429e-02

parsimonious Firth (profile CI)    lac_3.8-5.9         4.32 (2.26-8.93) 2.441804e-05

parsimonious Firth (profile CI) lac_8.6 capped       12.25 (5.84-27.10) 9.729552e-11

parsimonious  ridge (alpha=0.5)    lac_2.1-3.0  2.07 (penalised, no CI)          NaN

parsimonious  ridge (alpha=0.5)    lac_3.8-5.9  3.85 (penalised, no CI)          NaN

parsimonious  ridge (alpha=0.5) lac_8.6 capped 10.70 (penalised, no CI)          NaN

    expanded maximum likelihood    lac_2.1-3.0         2.30 (1.04-5.06) 3.955769e-02

    expanded maximum likelihood    lac_3.8-5.9         3.45 (1.69-7.02) 6.408273e-04

    expanded maximum likelihood lac_8.6 capped        7.64 (3.38-17.29) 1.052046e-06

    expanded Firth (profile CI)    lac_2.1-3.0         2.25 (1.05-5.01) 3.796917e-02

    expanded Firth (profile CI)    lac_3.8-5.9         3.32 (1.71-6.95) 6.334187e-04

    expanded Firth (profile CI) lac_8.6 capped        7.34 (3.35-16.84) 8.400755e-07

    expanded  ridge (alpha=0.5)    lac_2.1-3.0  1.93 (penalised, no CI)          NaN

    expanded  ridge (alpha=0.5)    lac_3.8-5.9  2.97 (penalised, no CI)          NaN

    expanded  ridge (alpha=0.5) lac_8.6 capped  6.46 (penalised, no CI)          NaN



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E. BOOTSTRAP INTERNAL VALIDATION (500 patient-level replicates)

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       model                metric  apparent  optimism  optimism_corrected  bootstrap_replicates

parsimonious              auc_full    0.7984    0.0109              0.7875                   500

parsimonious              auc_null    0.7272    0.0048              0.7224                   500

parsimonious             delta_auc    0.0712    0.0061              0.0651                   500

parsimonious     calibration_slope    1.0117    0.0415              0.9701                   500

parsimonious calibration_intercept   -0.0026    0.0980             -0.1006                   500

    expanded              auc_full    0.8298    0.0178              0.8120                   500

    expanded              auc_null    0.8019    0.0148              0.7871                   500

    expanded             delta_auc    0.0279    0.0030              0.0249                   500

    expanded     calibration_slope    1.0158    0.0742              0.9416                   500

    expanded calibration_intercept   -0.0124    0.1760             -0.1884                   500



Out-of-bag incremental discrimination:

       model      quantity  estimate  ci_low  ci_high

parsimonious delta_auc_oob    0.0653 -0.0083   0.1189

parsimonious  auc_full_oob    0.7833  0.7164   0.8512

    expanded delta_auc_oob    0.0235 -0.0187   0.0571

    expanded  auc_full_oob    0.8017  0.7411   0.8663



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F. DECISION CURVE ANALYSIS, OUT-OF-BAG

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 threshold  nb_with_lactate  nb_without_lactate  nb_treat_all  delta_nb  delta_ci_low  delta_ci_high  net_true_positives_per_1000

     0.010          0.03051             0.02977       0.02834   0.00074      -0.00287        0.00241                         0.74

     0.020          0.02421             0.02381       0.01842   0.00040      -0.00302        0.00369                         0.40

     0.030          0.02105             0.02192       0.00830  -0.00088      -0.00317        0.00580                        -0.88

     0.050          0.01745             0.01182      -0.01257   0.00563      -0.00256        0.00806                         5.63

     0.075          0.01047             0.00871      -0.03994   0.00176      -0.00278        0.00709                         1.76

     0.100          0.01019             0.00705      -0.06883   0.00315      -0.00279        0.00628                         3.15

     0.150          0.00515             0.00368      -0.13170   0.00147      -0.00347        0.00540                         1.47

     0.200          0.00317             0.00211      -0.20243   0.00106      -0.00406        0.00448                         1.06



Every threshold's net-benefit interval includes zero: True



Outputs: <local path>\analysis\results\manuscript_v3

