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Table 2 Result of the semi-markov model with penalized likelihood estimation incorporating frailty terms: HR (exp( β )) estimates and corresponding confidences intervals for the different transition intensities

From: Investigating hospital heterogeneity with a multi-state frailty model: application to nosocomial pneumonia disease in intensive care units

Three independent frailties for transitions 01, 02 and 03

01 (VAP)

02 (death)

03 (discharge)

 

exp(β)

95%CI

exp(β)

95%CI

exp(β)

95%CI

Sex (men=1)

1.51

(1.23-1.87)

-

-

0.85

(0.78-0.94)

Age ≥ 62

-

-

-

-

0.95

(0.86-1.05)

33 < SAPSII ≤ 45

-

-

1.62

(1.03-2.54)

0.66

(0.58-0.75)

45 < SAPSII ≤ 58

-

-

2.70

(1.75-4.14)

0.56

(0.49-0.64)

58 < SAPSII

-

-

4.83

(3.18-7.35)

0.40

(0.34-0.47)

Type of Admission :

      

Elective surgery

1

 

-

-

1

 

Emergency surgery

0.58

(0.41-0.83)

-

-

1.04

(0.90-1.20)

Medicine

0.89

(0.66-1.20)

-

-

0.96

(0.82-1.12)

Chronic diseases

-

-

1.37

(1.14-1.66)

0.84

(0.76-0.92)

Diabetes

1.48

(1.10-2.00)

1.30

(0.97-1.76)

-

-

Diagnostic or symptoms on ICU admission:

    

ARDS

1.71

(1.16-2.54)

-

-

-

-

Trauma

2.52

(1.12-5.67)

-

-

-

-

Coma

1.23

(0.95-1.60)

2.90

(1.99-4.22)

1.06

(0.91-1.25)

Shock

1.21

(0.96-1.53)

2.12

(1.47-3.06)

0.73

(0.63-0.84)

Acute respiratory failure

-

-

1.79

(1.22-2.62)

0.65

(0.56-0.75)

Use in the first 24 h of ICU admission :

    

Antimicrobials

0.61

(0.50-0.75)

0.66

(0.54-0.81)

0.86

(0.77-0.95)

Inotropes

-

-

-

-

0.74

(0.67-0.82)

Enteral nutrition

1.21

(0.97-1.50)

0.76

(0.60-0.95)

0.62

(0.55-0.71)

Parenteral nutrition

-

-

-

-

1.00

(0.87-1.14)

Variance of the frailty γ (SE)

0.19(0.11)

0.09(0.06)

0.15(0.07)

Two independent frailties for transitions 12 and 13

12 (death with VAP)

13 (discharge with VAP)

  
 

exp(β)

95%CI

exp(β)

95%CI

  

Age ≥ 62

-

-

0.84

(0.66-1.07)

  

33 < SAPSII ≤ 45

2.13

(1.05-4.31)

-

-

  

45 < SAPSII ≤ 58

2.60

(1.27-5.31)

-

-

  

58 < SAPSII

4.81

(2.38-9.72)

-

-

  

Parenteral nutrition

-

 

0.70

(0.51-0.97)

  

Variance of the frailty γ (SE)

0.04(0.06)

0.11(0.08)

  

A joint subject-specific frailtyterm for transitions 12 and 13

12 (death with VAP)

13 (discharge with VAP)

  
 

exp( β )

95%CI

exp( β )

95%CI

  

Age ≥ 62

-

-

0.78

(0.61-0.98)

  

33 < SAPSII ≤ 45

2.22

(0.99-4.97)

-

-

  

45 < SAPSII ≤ 58

2.65

(1.17-6.01)

-

-

  

58 < SAPSII

5.19

(2.31-11.65)

-

-

  

Parenteral nutrition

-

 

0.67

(0.49-0.90)

  

Common frailty variance η (SE)

0.77 (0.13)

    

Power coefficient ζ (from η ζ)

-0.16 (0.29)

    
  1. −: the corresponding covariate has not been selected for this transition by the descendant strategy based on model without frailties. SAPS II = Simplified Acute Physiology Score, version II at admission (33, 45, and 58 separate the four quartiles); ARDS = Acute Respiratory Distress Syndrome; Acute Respiratory failure: indicate the need for respiratory supportive therapy; Coma: admission for a neurological disease and a Glasgow coma score of less than 9; Shock: admission in the ICU with sign or symptoms of shock according to common definitions.