National Research and Development Centre for Welfare and Health Knowledge for welfare and health...

31.5.2005 / AL

National Research and Development Centre for Welfare and Health

Knowledge for welfare and health A propensity score approach to comparing medical costs between hospital districts

A propensity score approach to comparing medical costs between hospital districts

Hailuoto workshop 31. 5. 2005

Antti Liski

National Research and Development Centre for Welfare and Health 31.5.2005 / AL


The study a part of Reijo Sund’s (STAKES) ”Utilisation of routinely

collected register data in health system performance assessment” –project part of a bigger project led by Pekka Rissanen and funded by the

Academy of Finland

my master’s thesis



The aim of this study to compare the costs of hip fracture patients between

care districts

there is indication that the prolonged in-hospital operative delay has an effect on mortality (Sund & Liski)

does the prolonged in-hospital operative delay have an effect also on the costs



Hip fractures common with older people

lead to lower quality of life

usually surgically operated

the operation is expensive



The data collected from the Finnish Health Care Register, Finnish

Hospital Discharge Register, Finnish Health and Social Welfare Care Register, the data warehouse of the Finnish Hospital Benchmarking project and the National Causes of Death Register

the final data set consisted of 16881 hip fracture patients in 20 hospital districts in 1998-2001 that hadn’t had a hip fracture during the preceding 10 years



The data… only surgically operated patients

three types of hip fractures

the costs are based on Diagnosis Related Costs (DRG) classification

every patient has the costs from year 2001

the follow-up period was one year



Problems in comparing the costs of hospital districts heterogeneity of patients in different hospital districts

censoring caused by deaths patients who have died quickly after the surgery are ”too cheap”







The propensity score Rosenbaum & Rubin, Biometrika 1983

e(x)=P(y=1|x), where y = 1 indicates that a patient with observed covariates x will be assigned to a given hospital district (y = 0, a control district)

subclassification on the propensity score will balance x, in the sense that within subclasses that are homogeneous in e(x), the distribution of x is the same for study and control districts

P(x,y|e)=P(x|e)P(y|e)



Calculating the propensity score using a logit-model consider the probability π(x) that a patient is assigned to

a given hospital district as a function of covariates x

P(y=1|x) =π(x); compare study district (y=1) vs. control (y=0)

we use the model:

logit[π(x)]=log[π(x)/(1- π(x))]=α+β’x



Calculating the propensity score using the logit model… the explanatory variables include: age, sex, days of

care, type of fracture, type of surgery, did the patient come from home, days in care during the preceding 60 days, did the patient die during the follow up, days alive during the follow up and most important comorbidities classified into 13 classes

the predicted values were calculated and used as the propensity score



The costs the patients were sorted by the propensity score within the

hospital districts

the costs were smoothed over the propensity score using local linear regression with normal weights w and h as the standard deviation of the normal distribution used

the estimator:

nhxxwxxhxs

wherehxshxshxs

yhxxwxxhxshxs

nxm

ir

ir

n

i

iii

/)};()({);(

,);();();(

);()})(;();({1)(

12

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The costs of hosp. dist. no. 1 (green) and hosp. dist no. 2 (black)



The costs of hosp. dist. no 1 (green) and hosp. dist. no 3 (black)



Calculating the propensity score using a multinomial logit model the estimation can be done using the whole data

all of the cost curves are comparable with each other and not only pairwise as in the case of the binomial logit –model

let πj(xi) denote the probability of response j, j=1,…,J at the ith setting of values of k explanatory variables xi=(1,xi1,…,xik)’.

log[πj(xi) / πJ(xi)]= βj’xi , j=1,…,J-1 , where the last category J is the baseline



Calculating the propensity score using a multinomial logit model again the predicted values were calculated and the logit

value corresponding to the probability hospital district 1 (say) is used as the propensity score

now the patients with the same (or almost the same) propensity score should have similar distribution of covariates x within every district



The costs of hpd. 1(green), 2(blue) and 3(black)



Prolonged in-hospital waiting time and costs patients should be operated as soon as possible after

the fracture, provided that their condition is sufficiently good

there is indication that a waiting time over three nights increases mortality

the patients are divided into prolonged (waiting time three nights or longer) and early (waiting time less than three nights) surgery within the hospital districts

the costs were again smoothed inside these subclasses



The cost of patients with ≥3 nights (green) waiting time and <3 nights (black) waiting time in hpd 1



The cost of patients with ≥3 nights (green) waiting time and <3 nights (black) waiting time in hpd 2

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