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A. ENDPOINT AND ASCERTAINMENT

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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



                                                 check                                                                                                                                                                                                                                                                                                            value

                 patients with any linked death record                                                                                                                                                                                                                                                                                                      589 of 2468

longest observed interval from surgery to death (days)                                                                                                                                                                                                                                                                                                             4390

                         deaths observed beyond day 90                                                                                                                                                                                                                                                                                                              484

                        deaths observed beyond day 365                                                                                                                                                                                                                                                                                                              397

          explicit end-of-follow-up date in the source                                                                                                                                                                                                                                                                                   not provided by INSPIRE v1.4.2

                                        interpretation Deaths are observed out to several thousand days across the whole cohort, so a 90-day horizon is far inside the linkage window and administrative truncation cannot plausibly affect a meaningful number of patients. Completeness is nonetheless an assumption, not a verified fact, and must be stated as one.



Note the contrast with the renal endpoint: mortality is registry-linked and does not depend on anyone ordering a test, whereas incident AKI is only visible when a creatinine is drawn. The two endpoints are not of equal quality and the manuscript should not treat them as if they were.



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B. 90-DAY MORTALITY BY LACTATE 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

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

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

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

                    age       False continuous (range 20.0-90.0)

    baseline_creatinine       False   continuous (range 0.4-5.5)

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

MODEL: 6 df, 105 events       False                  EPV = 17.50



--- expanded model ---

                    term  empty_cell             non_deaths/deaths

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

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

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

                     age       False  continuous (range 20.0-90.0)

     baseline_creatinine       False    continuous (range 0.4-5.5)

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

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

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

        cpb_duration_min       False continuous (range 15.0-595.0)

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

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/F. BOOTSTRAP VALIDATION (500 subject-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



Incremental value of lactate, bootstrap percentile interval:

       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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G. DECISION CURVE ANALYSIS WITH RESAMPLED UNCERTAINTY

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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



Outputs: <local path>\analysis\results\gate3

