A competing risk model to estimate the hospitalisation story of a cohort of diabetic patients. The additive regression model.

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Benedict Jefferson
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1 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

2 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

3 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 Hospital admissions were recorded for all patients from 1 st January 1996 to 30 th June /09/2002 3

4 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/ /09/2002 4

5 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

6 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 ,5 1 DIABETES ,5 2 OTHER ,0 27/09/2002 6

7 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 /01/ /11/ /12/ /01/ /05/ /05/ /01/ /10/ /10/ /12/ EXAMPLE PATIENT days 530 days diabetes other 139 days other 35 days /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

8 Frequency distribution variable: number of hospitalisation (NH) Cumulative NH Frequency Percentage frequency percentage ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ /09/2002 8

9 Characteristics of the patients by number of hospital admissions. N of hospital admissions: Number of patients (%) 1770 (45.5) 890 (22.9) 1232 (31.6) Number of admissions: mean (2-27) (range) Days of hospital stay: mean (9102) 15.0 (68482) (total) Age: mean (SD) 62.7 (10.1) 65.3 (10.3) 67.0 (9.8) Male % 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 % Insulin treatment % Retinopathy % Nephropathy % Coronary artery disease % Peripheral artery disease % Co-morbidity % Cirrhosis % Cancer % Chronic obstructive pulmonary diseases % 27/09/2002 Psychiatric diseases %

10 Risk factors for hospitalization without classification of admissions. sions. Conditional Cox model for repeated events HR* 95 % CI p Age (years) < Sex (males) Duration of diabetes (years) HbA 1 c % BMI 25 (kg/m 2 ) BMI 30 (kg/m 2 ) Hypertension Insulin treatment < Retinopathy Nephropathy < Coronary artery disease < Peripheral artery disease < Co-morbidity < Cirrhosis < Cancer < Chronic obstructive pulmonary < diseases Psychiatric diseases /09/

11 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/

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Lucia Cea Soriano 1, Saga Johansson 2, Bergur Stefansson 2 and Luis A García Rodríguez 1* Cea Soriano et al. Cardiovascular Diabetology (2015) 14:38 DOI 10.1186/s12933-015-0204-5 CARDIO VASCULAR DIABETOLOGY ORIGINAL INVESTIGATION Open Access Cardiovascular events and all-cause mortality in