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Fig. 1.

Multi-state model with 4 states: 0, ICU admission without a VAE; 1, VAE (exposed); 2, discharge; and 3, death. All patients entered into the initial state 0. Then the patient may acquire a VAE, moving to intermediate state 1, be discharged without a VAE, moving to state 2, or die without a VAE. Once acquired a VAE, the patient can move from state 1 to 2 or from 1 to 3. Hazard rates are denoted by k. with indices i and j indicating the states which they connect. VAE, Ventilator-Associated Event.
Multi-state model with 4 states: 0, ICU admission without a VAE; 1, VAE (exposed); 2, discharge; and 3, death. All patients entered into the initial state 0. Then the patient may acquire a VAE, moving to intermediate state 1, be discharged without a VAE, moving to state 2, or die without a VAE. Once acquired a VAE, the patient can move from state 1 to 2 or from 1 to 3. Hazard rates are denoted by k. with indices i and j indicating the states which they connect. VAE, Ventilator-Associated Event.

Fig. 2.

Plot of the expected LOS in ICU. The black line shows that a VAE has occurred, and the red line indicates a lack of VAE up to 30 days after ICU hospitalization. The weights (distribution of the time to VAE) are illustrated in the upper plot. VAE, ventilator-associated event; LOS, length of stay.
Plot of the expected LOS in ICU. The black line shows that a VAE has occurred, and the red line indicates a lack of VAE up to 30 days after ICU hospitalization. The weights (distribution of the time to VAE) are illustrated in the upper plot. VAE, ventilator-associated event; LOS, length of stay.

Death and discharge hazard ratio for patients with VAE

Types of VAE Death hazard ratio (95% CI) Discharge hazard ratio (95% CI)
VAC 1.401 (0.938–2.063) 0.704 (0.509–0.960)
IVAC 1.223 (0.721–1.984) 0.755 (0.494–1.116)
PVAP 1.471 (0.701–2.788) 0.493 (0.233–1.044)
VAEs 1.582 (1.101–2.278) 0.614 (0.470–0.797)

Mean additional length of stay associated with VAEs

Additional ICU days regarding discharge ± SE 95% BCa CI Additional ICU days regarding death ± SE 95% BCa CI Total additional ICU days ± SE 95% BCa CI
VAC 4.50 ± 1.93 1.14–8.87 2.43 ± 1.22 0.21–4.81 6.93 ± 2.38 2.45–11.83
IVAC 1.92 ± 1.81 −0.93–6.18 5.35 ± 2.45 0.85–10.48 7.27 ± 2.94 1.68–13.08
PVAP 3.99 ± 2.65 −0.25–10.30 7.09 ± 5.38 −1.21–18.57 11.08 ± 5.65 0.60–22.05
All VAEs 3.25 ± 1.37 0.71–6.08 3.30 ± 1.17 1.10–5.64 6.55 ± 1.78 2.76–9.73

Multi-state analysis of Ventilator-Associated Events

Constant hazards from MSM
VAE hazard λ01
Discharge hazard without VAE λ02
Death hazard without VAE λ03
Discharge hazard with VAE λ12
Death hazard with VAE λ13

Multi-state model constant hazards

Constant hazards (95% CI) VAE VAC IVAC PVAP
λ01 VAE hazard 0.026 (0.022–0.030) 0.011 (0.009–0.014) 0.005 (0.003–0.007) 0.001 (0.001–0.002)
λ02 Discharge hazard without VAE 0.033 (0.028–0.038) 0.029 (0.026–0.034) 0.028 (0.025–0.032) 0.028 (0.025–0.032)
λ03 Death hazard without VAE 0.010 (0.007–0.013) 0.011 (0.009–0.014) 0.012 (0.010–0.014) 0.012 (0.010–0.014)
λ12 Discharge hazard with VAE 0.020 (0.016–0.025) 0.021 (0.015–0.027) 0.021 (0.014–0.031) 0.014 (0.006–0.027)
λ13 Death hazard with VAE 0.016 (0.012–0.020) 0.016 (0.011–0.022) 0.014 (0.091–0.023) 0.018 (0.008–0.033)

The direct additional cost per VAE episode

Direct additional cost per VAE episode, €
Additional cost regarding death Additional cost regarding discharge Total additional cost
VAC 1,197.50 2,217.60 3,415.10
IVAC 2,636.48 946,17 3,582.65
PVAP 3,493.95 1,966.27 5,460.22
All VAEs 1,626.24 1,601.60 3,227.84

The characteristics of patients with and without ventilator-associated events

VAE P Value

Yes N = 143, % No N= 235, %
Gender 0.451
Male 88 (61.5) 134 (57)
Age, years (Median, Interquartile range) 59 (46–73) 61 (45–74) 0.649

Type of patient
  Medical 74 (51.7) 115 (48.9) 0.671
  Surgical 69 (48.3) 120 (51.1)

McCabe score
  Non-fatal disease 49 (34.3) 114 (48.5) 0.007
  Ultimately fatal disease 16 (11.2) 20 (8.5) 0.470
  Rapidly fatal disease 78 (54.5) 101 (43) 0.034

Admission diagnosis
  Trauma 42 (29.4) 43 (18.3) 0.016
  Neurological disease 30 (21) 42 (17.9) 0.500
  Pulmonary disease 33 (23.1) 35 (14.9) 0.053
  Post-operative observation 18 (12.6) 66 (28.1) 0.000
  Cardiovascular disease 11 (7.7) 26 (11.1) 0.372
  Malignancy 5 (3.5) 17 (7.2) 0.175
  Other (burn, poisoning) 4 (2.8) 6 (2.6) 1.000
Death 63 (44.1) 55 (23.4) 0.000
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