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

A. MORTALITY DATASET — all cohort

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  eligible_operations                   : 2468

  distinct_subjects                     : 2365

  subjects_with_repeat_operations       : 98

  deaths_primary                        : 105

  deaths_from_landmark_horizon          : 105

  deaths_any_time                       : 589



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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

          <=1.9 835      11      1.32    0.66-2.34      1.00   reference

        2.1-3.0 584      18      3.08    1.84-4.83      2.38   1.12-5.08

        3.8-5.9 813      46      5.66    4.17-7.48      4.49   2.31-8.74

     8.6 capped 236      30     12.71   8.74-17.65     10.91  5.38-22.13



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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: 1797/87; 1: 566/18

parsimonious             lac_3.8-5.9       False        0: 1596/59; 1: 767/46

parsimonious          lac_8.6 capped       False        0: 2157/75; 1: 206/30

parsimonious                     age       False continuous (range 20.0-90.0)

parsimonious     baseline_creatinine       False   continuous (range 0.4-5.5)

parsimonious                 asa_ge3       False        0: 772/24; 1: 1591/81

parsimonious MODEL: 6 df, 105 events       False                  EPV = 17.50



--- expanded ---

   model                     term  empty_cell             non_deaths/deaths

expanded              lac_2.1-3.0       False         0: 1797/87; 1: 566/18

expanded              lac_3.8-5.9       False         0: 1596/59; 1: 767/46

expanded           lac_8.6 capped       False         0: 2157/75; 1: 206/30

expanded                      age       False  continuous (range 20.0-90.0)

expanded      baseline_creatinine       False    continuous (range 0.4-5.5)

expanded                  asa_ge3       False         0: 772/24; 1: 1591/81

expanded                   female       False         0: 1446/67; 1: 917/38

expanded                emergency       False         0: 2101/83; 1: 262/22

expanded         cpb_duration_min       False continuous (range 15.0-595.0)

expanded           concurrent_aki       False         0: 1838/60; 1: 525/45

expanded MODEL: 10 df, 105 events       False                   EPV = 10.50



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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         2.58 (1.19-5.58) 1.631951e-02

parsimonious maximum likelihood    lac_3.8-5.9         4.93 (2.50-9.74) 4.309728e-06

parsimonious maximum likelihood lac_8.6 capped       15.71 (7.53-32.78) 2.191361e-13

parsimonious Firth (profile CI)    lac_2.1-3.0         2.52 (1.20-5.54) 1.616854e-02

parsimonious Firth (profile CI)    lac_3.8-5.9         4.74 (2.52-9.68) 4.438712e-06

parsimonious Firth (profile CI) lac_8.6 capped       15.09 (7.53-32.30) 1.518427e-13

parsimonious  ridge (alpha=0.5)    lac_2.1-3.0  2.18 (penalised, no CI)          NaN

parsimonious  ridge (alpha=0.5)    lac_3.8-5.9  4.25 (penalised, no CI)          NaN

parsimonious  ridge (alpha=0.5) lac_8.6 capped 13.38 (penalised, no CI)          NaN

    expanded maximum likelihood    lac_2.1-3.0         2.41 (1.11-5.25) 2.669524e-02

    expanded maximum likelihood    lac_3.8-5.9         3.74 (1.87-7.49) 1.946224e-04

    expanded maximum likelihood lac_8.6 capped        9.01 (4.15-19.56) 2.736062e-08

    expanded Firth (profile CI)    lac_2.1-3.0         2.36 (1.11-5.21) 2.576722e-02

    expanded Firth (profile CI)    lac_3.8-5.9         3.60 (1.88-7.43) 1.927109e-04

    expanded Firth (profile CI) lac_8.6 capped        8.62 (4.12-19.10) 2.211333e-08

    expanded  ridge (alpha=1.0)    lac_2.1-3.0  1.75 (penalised, no CI)          NaN

    expanded  ridge (alpha=1.0)    lac_3.8-5.9  2.83 (penalised, no CI)          NaN

    expanded  ridge (alpha=1.0) lac_8.6 capped  6.66 (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    0.8057    0.0091              0.7966                   500

parsimonious              auc_null    0.7079    0.0063              0.7016                   500

parsimonious             delta_auc    0.0977    0.0028              0.0949                   500

parsimonious     calibration_slope    1.0112    0.0390              0.9722                   500

parsimonious calibration_intercept   -0.0002    0.0831             -0.0833                   500

    expanded              auc_full    0.8336    0.0148              0.8188                   500

    expanded              auc_null    0.8012    0.0130              0.7882                   500

    expanded             delta_auc    0.0324    0.0018              0.0306                   500

    expanded     calibration_slope    1.0143    0.0657              0.9487                   500

    expanded calibration_intercept   -0.0097    0.1427             -0.1524                   500



Out-of-bag incremental discrimination:

       model      quantity  estimate  ci_low  ci_high

parsimonious delta_auc_oob    0.0949  0.0218   0.1516

parsimonious  auc_full_oob    0.7923  0.7316   0.8525

    expanded delta_auc_oob    0.0295 -0.0102   0.0603

    expanded  auc_full_oob    0.8101  0.7592   0.8664



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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          0.03490             0.03398       0.03287   0.00092      -0.00247        0.00281                         0.92

     0.020          0.02924             0.02821       0.02300   0.00103      -0.00347        0.00405                         1.03

     0.030          0.02445             0.02559       0.01293  -0.00114      -0.00342        0.00546                        -1.14

     0.050          0.02081             0.01550      -0.00785   0.00531      -0.00148        0.00921                         5.31

     0.075          0.01547             0.01124      -0.03509   0.00424      -0.00115        0.00884                         4.24

     0.100          0.01153             0.00689      -0.06384   0.00464      -0.00240        0.00845                         4.64

     0.150          0.00708             0.00307      -0.12642   0.00400      -0.00263        0.00699                         4.00

     0.200          0.00314             0.00132      -0.19682   0.00182      -0.00389        0.00569                         1.82



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



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

