A competing risk model to estimate the hospitalisation story of a cohort of diabetic patients. The additive regression model. PHD Thesis Project Rosalba Rosato Dept.of Statistics, University of Florence, Italy Prof. Annibale Biggeri Prof. Dario Gregori 27/09/2002 1
The aim of the study is to analyse the hospitalisation story of a cohort of diabetic patients. Each patient during the period could have one or more hospital admissions. The admissions are classified according to the main cause in: 1. Hospital admission related to diabetes 2. Hospital admission for other causes Mortality patients has been also evaluated. Our analysis include two different outcomes: - one absorbing state as death - and hospitalisation classified in: - Admission related to diabetes - Admission for other causes 27/09/2002 2
Database A cohort of 3892 of type 2 diabetic patients, attending the Diabetic Clinic of the Major Hospital of Turin, Italy during 1995 and alive at 1 st January 1996 was identified. For each patient we have some information (relative to the year 1995) selected as potential risk factors for hospitalisation: 1. Demographic data (age, sex area of residence) and 2. Clinical data (weight, duration of disease, glycated haemoglobin, type of anti-diabetic treatment and presence of other comorbidities). A mortality follow-up of the cohort was carried out up to 30 th June 2000. Hospital admissions were recorded for all patients from 1 st January 1996 to 30 th June 2000. 27/09/2002 3
Possible transition 1 People start with 0 hospitalisation Diab. Admis Other Admis. DEATH Diab. Admis. Other admis. Diab. Admis. Other admis Diab. Admis Other admis Diab. Admis Other admis Diab. Admis Other admis Diab. Admis Other admis 1/1/1996 27/09/2002 4
Possible transition 2 1 st event 2 nd event 3 rd event. Diab. A Diab. A Diab. A Other A Other A Other A People start with 0 hospitalisation 1/1/1996 DEATH DEATH DEATH 27/09/2002 5
During the follow-up (Jannuary1996-June June 2000) we have: *** 1770 patients with 0 hospital admission *** 2122 patients have had 1 or more admissions (total 5465 hospital admissions) *** 599 patients died type admission frequencies percentage 0 NO 1770 24,5 1 DIABETES 1988 27,5 2 OTHER 3477 48,0 27/09/2002 6
EXAMPLE subject 1 has had 3 hospital admission during the period and then is dead ID NH TYPE AD STAT SSMORT START D.IN.H D.OUT.H DDEC T_IN_HOSP STARTTY ENDTY 1 1 1 1 0 01/01/1996 14/11/1997 05/12/1997 21 0 683 1 2 2 1 0 02/01/1996 19/05/1999 21/05/1999 2 0 530 1 3 2 1 0 03/01/1996 07/10/1999 27/10/1999 20 0 139 1 3 2 1 01/12/1999 0 35 EXAMPLE PATIENT 1 638 days 530 days diabetes other 139 days other 35 days 21 2 20 1/1/1996 1/12/1999 Time of observation since last event The outlined line represents time when the patient was in hospital 27/09/2002 7
Frequency distribution variable: number of hospitalisation (NH) Cumulative NH Frequency Percentage frequency percentage ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 0 1770 24.46 1770 24.46 1 2122 29.33 3892 53.79 2 1232 17.03 5124 70.82 3 744 10.28 5868 81.11 4 451 6.23 6319 87.34 5 294 4.06 6613 91.40 6 193 2.67 6806 94.07 7 133 1.84 6939 95.91 8 87 1.20 7026 97.11 9 62 0.86 7088 97.97 10 44 0.61 7132 98.58 11 27 0.37 7159 98.95 12 22 0.30 7181 99.25 13 15 0.21 7196 99.46 14 10 0.14 7206 99.60 15 8 0.11 7214 99.71 16 5 0.07 7219 99.78 17 2 0.03 7221 99.81 18 2 0.03 7223 99.83 19 2 0.03 7225 99.86 20 2 0.03 7227 99.89 21 2 0.03 7229 99.92 22 1 0.01 7230 99.93 23 1 0.01 7231 99.94 24 1 0.01 7232 99.96 25 1 0.01 7233 99.97 26 1 0.01 7234 99.99 27 1 0.01 7235 100.00 27/09/2002 8
Characteristics of the patients by number of hospital admissions. N of hospital admissions: 0 1 2 Number of patients (%) 1770 (45.5) 890 (22.9) 1232 (31.6) Number of admissions: mean 0 1 3.71 (2-27) (range) Days of hospital stay: mean 0 10.2 (9102) 15.0 (68482) (total) Age: mean (SD) 62.7 (10.1) 65.3 (10.3) 67.0 (9.8) Male % 52.0 51.5 51.5 BMI kg/m 2 : mean (SD) 28.1 (4.8) 28.2 (4.8) 28.4 (4.7) Diabetes duration in years: mean 10.4 (8.1) 12.0 (8.5) 13.2 (8.9) (SD) HbA 1 c %: mean (SD) 7.76 (1.58) 7.99 (1.61) 8.15 (1.57) Hypertension % 71.0 78.9 79.5 Insulin treatment % 19.7 26.7 35.8 Retinopathy % 26.2 28.5 34.2 Nephropathy % 29.9 37.3 48.2 Coronary artery disease % 8.0 12.9 19.1 Peripheral artery disease % 6.6 11.0 14.1 Co-morbidity % 8.5 11.9 17.8 Cirrhosis % 2.1 2.1 4.6 Cancer % 3.4 5.6 7.9 Chronic obstructive pulmonary 1.1 2.7 3.7 diseases % 27/09/2002 Psychiatric diseases % 2.1 1.9 2.7 9
Risk factors for hospitalization without classification of admissions. sions. Conditional Cox model for repeated events HR* 95 % CI p Age (years) 1.02 1.01 1.02 <0.0001 Sex (males) 1.04 0.98 1.10 0.230 Duration of diabetes (years) 1.00 1.00 1.01 0.090 HbA 1 c % 1.02 1.00 1.04 0.047 BMI 25 (kg/m 2 ) 1.05 0.98 1.14 0.176 BMI 30 (kg/m 2 ) 1.10 1.03 1.17 0.005 Hypertension 0.94 0.87 1.01 0.108 Insulin treatment 1.21 1.13 1.29 <0.0001 Retinopathy 1.04 0.98 1.11 0.226 Nephropathy 1.25 1.18 1.33 <0.0001 Coronary artery disease 1.27 1.18 1.36 <0.0001 Peripheral artery disease 1.22 1.13 1.33 <0.0001 Co-morbidity 1.40 1.30 1.51 <0.0001 Cirrhosis 1.44 1.27 1.64 <0.0001 Cancer 1.41 1.26 1.58 <0.0001 Chronic obstructive pulmonary 1.28 1.13 1.44 <0.0001 diseases Psychiatric diseases 1.25 1.04 1.49 0.014 27/09/2002 10
Comments The additive regression model has been proposed to estimate survival probability in presence of competing risk for modelling each transition as a Markov chain on the basis of subject information and their previous story (Aalen et al. 2001). In order to estimate the probability to have one or more hospital admissions is very important to keep in mind what is happened previously. The hospitalisation story of a patient follow a Markov chain model? When stooped transition Goodness of fit and selection model Other and other. 27/09/2002 11