﻿[note] 3 patients contribute no post-landmark follow-up time and are excluded from the time-to-event analysis.

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

A. PERSON-TIME AND EVENT ACCOUNTING (clock starts at the landmark)

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

lactate_stratum   n  aki_events  competing_deaths  censored  person_days  median_followup_days  rate_per_100_person_days

          <=1.9 727          63                 1       663       3274.7                  5.45                     1.924

        2.1-3.0 486          50                 1       435       2165.4                  5.47                     2.309

        3.8-5.9 573          77                 5       491       2450.6                  4.87                     3.142

     8.6 capped 109          17                 1        91        465.2                  5.40                     3.654



maximum follow-up after the landmark: 5.00 days

total censored before day-6 coverage : 732



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

B. AALEN-JOHANSEN CUMULATIVE INCIDENCE (death as a competing event)

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

lactate_stratum        event   n  horizon_days  at_risk_at_horizon  at_risk_pct  cif_pct  ci_low_pct  ci_high_pct

          <=1.9 incident AKI 727           1.0                 678         93.3     5.52        3.86         7.19

          <=1.9 incident AKI 727           2.0                 634         87.2     7.08        5.21         8.96

          <=1.9 incident AKI 727           3.0                 608         83.6     7.68        5.73         9.63

          <=1.9 incident AKI 727           4.0                 460         63.3     8.54        6.47        10.62

          <=1.9 incident AKI 727           5.0                 373         51.3     8.78        6.66        10.90

        2.1-3.0 incident AKI 486           1.0                 444         91.4     6.62        4.40         8.84

        2.1-3.0 incident AKI 486           2.0                 417         85.8     8.11        5.67        10.55

        2.1-3.0 incident AKI 486           3.0                 386         79.4     9.01        6.44        11.58

        2.1-3.0 incident AKI 486           4.0                 318         65.4     9.27        6.66        11.88

        2.1-3.0 incident AKI 486           5.0                 252         51.9     9.87        7.14        12.60

        3.8-5.9 incident AKI 573           1.0                 505         88.1     9.28        6.90        11.67

        3.8-5.9 incident AKI 573           2.0                 471         82.2    10.73        8.19        13.28

        3.8-5.9 incident AKI 573           3.0                 437         76.3    11.31        8.70        13.93

        3.8-5.9 incident AKI 573           4.0                 367         64.0    12.15        9.43        14.86

        3.8-5.9 incident AKI 573           5.0                 278         48.5    12.91       10.08        15.73

     8.6 capped incident AKI 109           1.0                  92         84.4    13.81        7.32        20.30

     8.6 capped incident AKI 109           2.0                  87         79.8    15.68        8.83        22.53

     8.6 capped incident AKI 109           3.0                  82         75.2    15.68        8.83        22.53

     8.6 capped incident AKI 109           4.0                  72         66.1    15.68        8.83        22.53

     8.6 capped incident AKI 109           5.0                  58         53.2    15.68        8.83        22.53



[stability] 877 of 1895 patients (46.3%) lose renal follow-up in the last 12 hours before the 7-day window closes. The risk set is nearly exhausted there, so the day-6 CIF is driven by a handful of late events and should not be reported as the endpoint estimate. Day 5 is the last horizon with an adequate risk set in every stratum.



Fine-Gray score test at beta=0 (Gray's-test analogue): chi2 = 10.727 on 3 df, p = 0.0133

Cause-specific multivariate log-rank test: chi2 = 10.835 on 3 df, p = 0.0127



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

C. CAUSE-SPECIFIC COX AND FINE-GRAY SUBDISTRIBUTION MODELS

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

--- cause-specific hazard (death censors) ---

         model    n  events   lr_stat  lr_df     lr_p  HR[lac_2.1-3.0]  HR[lac_3.8-5.9]  HR[lac_8.6 capped] HR[lac_2.1-3.0]_ci HR[lac_3.8-5.9]_ci HR[lac_8.6 capped]_ci  p[lac_2.1-3.0]  p[lac_3.8-5.9]  p[lac_8.6 capped]  HR[lactate_score] HR[lactate_score]_ci  p[lactate_score]

         crude 1895     207 10.486222      3 0.014855         1.196681         1.604178            1.918748          0.83-1.73          1.15-2.24             1.12-3.28        0.343198        0.005442           0.017124                NaN                  NaN               NaN

   crude trend 1895     207 10.344574      1 0.001299              NaN              NaN                 NaN                NaN                NaN                   NaN             NaN             NaN                NaN           1.259642            1.10-1.45          0.001224

      adjusted 1895     207  9.709347      3 0.021205         1.156237         1.537056            2.043141          0.80-1.68          1.09-2.16             1.18-3.53        0.447053        0.013212           0.010496                NaN                  NaN               NaN

adjusted trend 1895     207  9.453196      1 0.002108              NaN              NaN                 NaN                NaN                NaN                   NaN             NaN             NaN                NaN           1.258206            1.09-1.46          0.002017



--- Fine-Gray subdistribution hazard ---

         model    n  events  competing  wald_stat  wald_df   wald_p  sHR[lac_2.1-3.0] sHR[lac_2.1-3.0]_ci  p[lac_2.1-3.0]  sHR[lac_3.8-5.9] sHR[lac_3.8-5.9]_ci  p[lac_3.8-5.9]  sHR[lac_8.6 capped] sHR[lac_8.6 capped]_ci  p[lac_8.6 capped]  sHR[lactate_score] sHR[lactate_score]_ci  p[lactate_score]

         crude 1895     207          8  10.524344        3 0.014597          1.196561           0.83-1.73        0.343465          1.600825           1.15-2.23        0.005652             1.912766              1.12-3.27           0.017663                 NaN                   NaN               NaN

   crude trend 1895     207          8  10.356369        1 0.001290               NaN                 NaN             NaN               NaN                 NaN             NaN                  NaN                    NaN                NaN            1.258256             1.09-1.45          0.001290

      adjusted 1895     207          8   9.849415        3 0.019891          1.155312           0.79-1.68        0.449553          1.532400           1.09-2.15        0.013876             2.025697              1.17-3.50           0.011439                 NaN                   NaN               NaN

adjusted trend 1895     207          8   9.365245        1 0.002211               NaN                 NaN             NaN               NaN                 NaN             NaN                  NaN                    NaN                NaN            1.255491             1.09-1.45          0.002211



------------------------------------------------------------------------------

Proportional-hazards check on the cause-specific model

------------------------------------------------------------------------------

         index  test_statistic      p  -log2(p)

   lac_2.1-3.0          0.2131 0.6443    0.6342

   lac_3.8-5.9          2.7494 0.0973    3.3616

lac_8.6 capped          5.5745 0.0182    5.7781



When does the AKI actually happen?

lactate_stratum   n  aki_events  events_within_48h_of_landmark  events_after_48h  pct_of_events_within_48h

          <=1.9 727          63                             51                12                      81.0

        2.1-3.0 486          50                             39                11                      78.0

        3.8-5.9 573          77                             61                16                      79.2

     8.6 capped 109          17                             17                 0                     100.0



Adjusted cause-specific hazard ratios split at 48 hours:

     window    n  events  events[lac_2.1-3.0]  HR[lac_2.1-3.0] HR[lac_2.1-3.0]_ci  p[lac_2.1-3.0]  events[lac_3.8-5.9]  HR[lac_3.8-5.9] HR[lac_3.8-5.9]_ci  p[lac_3.8-5.9]  events[lac_8.6 capped]  HR[lac_8.6 capped]    HR[lac_8.6 capped]_ci  p[lac_8.6 capped]

0 to 2 days 1895     168                   39            1.128          0.74-1.72          0.5744                   61            1.568          1.07-2.29          0.0202                      17               2.758                1.57-4.84             0.0004

2 to 6 days 1609      39                   11            1.236          0.54-2.85          0.6192                   16            1.503          0.70-3.21          0.2940                       0                 NaN not estimable (0 events)                NaN



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

D. IS THE CENSORING INFORMATIVE?

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

Hazard of losing renal follow-up, by lactate stratum (reference <=1.9):

     covariate  HR_censoring        ci      p

   lac_2.1-3.0        0.9309 0.82-1.05 0.2516

   lac_3.8-5.9        0.9312 0.83-1.05 0.2382

lac_8.6 capped        0.8243 0.66-1.03 0.0894



Complete-case versus IPCW-reweighted incident-AKI model:

  analysis    n  events  top_stratum_OR        ci      p

unweighted 1110     161           1.514 0.75-3.07 0.2498

      IPCW 1110     161           1.493 0.82-2.73 0.1935



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

E. HOW MUCH HIDDEN AKI WOULD OVERTURN THE GRADIENT?

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

                                                        scenario  risk_<=1.9  risk_2.1-3.0  risk_3.8-5.9  risk_8.6 capped  trend_z  trend_p

all hidden patients are non-events (the manuscript's assumption)        8.67         10.29         13.44            15.60    3.157 0.001593

                  all hidden patients developed AKI (worst case)       48.83         48.77         51.83            45.87    0.494 0.621219

        hidden risk equals the observed risk in the same stratum       12.15         14.25         18.60            20.32    3.547 0.000390



hidden-AKI-eligible censored patients by stratum: [292.0, 187.0, 220.0, 33.0]

observed events by stratum                      : [63.0, 50.0, 77.0, 17.0]



Tipping point: the trend loses significance once delta reaches 0.26, i.e. once 26% of every censored patient's unobserved tail is assumed to hide an AKI event.



Trend p at selected deltas:

 delta  risk_<=1.9  risk_2.1-3.0  risk_3.8-5.9  risk_8.6 capped  trend_z  trend_p

  0.00        8.67         10.29         13.44            15.60    3.157   0.0016

  0.05       10.67         12.21         15.36            17.11    2.832   0.0046

  0.10       12.68         14.14         17.28            18.62    2.567   0.0103

  0.15       14.69         16.06         19.20            20.14    2.343   0.0191

  0.20       16.70         17.98         21.12            21.65    2.150   0.0316

  0.30       20.72         21.83         24.96            24.68    1.828   0.0675

  0.50       28.75         29.53         32.64            30.73    1.341   0.1799

  1.00       48.83         48.77         51.83            45.87    0.494   0.6212



Outputs: <local path>\analysis\results\gate2

