Pharmacoeconomics 2009; 27 (1): Supplementary Material
ORIGINAL RESEARCH ARTICLE
1170-7690/09/0001-0001/$49.95/0
© 2009 Adis Data Information BV. All rights reserved.
Estimating the Cost of Diabetes Mellitus-Related
Events from Inpatient Admissions in Sweden
Using Administrative Hospitalization Data
Ulf-G Gerdtham,1,2,3 Philip Clarke,4 Alison Hayes4 and Soffia Gudbjornsdottir5
1
Health Economics Research Unit, University of Aberdeen, Aberdeen, Scotland
2
Department of Economics, University of Aberdeen, Aberdeen, Scotland
3
Health Economics Program, Department of Clinical Sciences, Lund University, Lund, Sweden
4
School of Public Health, University of Sydney, Sydney, New South Wales, Australia
5
Diabetes Centre, Sahlgrenska University Hospital, Göteborg, Sweden
Supplementary Material
This supplementary material contains the information referred to in the full version of this article,
which can be found at http://pharmacoeconomics.adisonline.com
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Appendix: Overview of the statistical methods used to derive annual costs.
In the estimation of hospital costs a two-part model was employed. The equation in the first part
estimates the probability of being hospitalized in any given year and in the second part the total
annual hospital costs are estimated for those that incur costs. An important feature of these
administrative data is that the occurrence of events was ascertained using hospital records and so
the probability of attending hospital is equal to one in the year the event first occurs, hence only
the second equation is used to estimate these event costs.
A panel logistic regression estimator was used in the first part to calculate the probability of
incurring hospital costs based on a patient’s history of complications recorded within the study. To
determine the impact of various clinical events on the probability of attending hospital in the year
following an event we included an indicator variable for those patients with a history of each type
of complication since 1998.
In the second part, either fixed-effects panel data regression, or a Generalized Estimating Equation
(GEE) was used to estimate the hospital costs for patients that were admitted. The former was used
to aid interpretation as it assumes complications have an additive impact on costs. The latter is a
way of dealing with the skewed nature of cost data. For the sake of brevity we only report the
results of the linear fixed-effects model. Both models are contained in the cost calculator available
from the NDR website.
A fixed-effects model to estimate the hospital costs for patients that were admitted is:
(Cit Cit > 0) = β 0 + β1 * X it + µ i + ν it
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(1)
where Cit are the total annual hospital costs for i patient in year t of the study; X it is a vector of
indicator variables representing the year in which first and second events occurred and a history of
events for the types of complications for individuals. To capture fixed effects an indicator variable
( µi ) is included for each individual and is intended to capture influence of factors such as age and
sex of the patients on hospital costs in the second part of the model. Finally ν it is an error term.
To illustrate how these equations can be applied to estimate costs in 1998. Consider a female who
is 60 years old and who have had a fatal MI in the current year (α5=1). The annual probability of
attending hospital can be calculated using the coefficients reported in the second column of Table
A1. The formula for calculating the probability of attending a hospital is:
Pr ob (C it > 0) = exp(α 0 + α1 * 60 + α 2 * 602 + α 5 * 1) / (1 + exp(α 0 + α 2 * 60 + α 3 * 602 + α5 * 1)
(2)
Substituting the relevant coefficients into (2):
Pr ob (C it > 0 | X it ) =
exp(-8.14 + 60*0.068 + 60^2*-0.00018+4.935615)
(1 + exp(-8.14 + 60*0.068 + 60^2*-0.00018+4.935615))
Pr ob (C it > 0 | X itF 60 ) = 0.549848
The equation (1) can be used to estimate event and hospitalization costs in 1998 for each type of
complication if the predicted µ̂ i are recovered and used to calculate mean fixed-effects by age
group, sex and complication status. For example, for a woman aged 60 years the average fixed
effects in the year a fatal MI occurs are €€ 895. The cost of fatal MI can then be calculated by
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adding these to the fixed-effect model reported in table A1. Using this approach the fatal event
costs for MI are:
(C it C it > 0) = 895 + 2768 + 629 = €4,292
Thus one can also estimate the expected hospitalization costs of fatal MI for a 60 year female as
follows: Pr ob (C it > 0 | X it60 ) × (C it C it > 0) = 0.55 * 4,292 = €2,361
In the case of more frequent occurring events (MI, stroke, IHD and heart failure) additional
coefficients can be used to model the event costs associated with the second occurrence of these
complications. For less frequent complications (e.g. amputation) the costs associated with
subsequent occurrences of the same event (e.g. multiple amputations) are included in with state
costs.
The hospital cost equations were used to predict overall annual health care event are also reported.
The analysis was undertaken in STATA 9.0.
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A1: Regression equations to derive annual probability of incurring hospital costs (€
€ ), and
costs of hospital care conditional on incurring a cost
Part 1: Annual probability of
hospitalisation
Logistic regression
Variable
Coeff
Std error
Constant
-8.13912
0.168424
Male
0.275417
0.013579
Age
0.067526
0.005357
Age squared
-0.00018
4.21E-05
Estimates for the year in which the first event occurred
Non fatal MI
Fatal MI
4.935615
0.075681
Non fatal stroke
Fatal stroke
6.150345
0.124512
Ischaemic heart disease
Heart failure
Amputation
Renal failure
Ulcer
Coma
Ketoacidosis
Estimates for the year in which the second event occurred
Non fatal MI
Fatal MI
Non fatal stroke
Fatal stroke
10.06854
1.022452
Ischaemic heart disease
Heart failure
Subsequent years (state costs) t
Non fatal MI
0.589727
0.021736
Non fatal stroke
0.960232
0.027214
Ischaemic heart disease
1.218406
0.019159
Heart failure
1.559639
0.028343
Amputation
0.602765
0.098975
Renal failure
1.528515
0.114749
Ulcer
1.026627
0.11653
Coma
1.137337
0.146855
Ketoacidosis
1.388366
0.270965
D1999
0.183391
0.021103
D2000
0.259331
0.020731
D2001
0.41694
0.020232
D2002
0.576988
0.019858
D2003
0.723628
0.019631
Numbers of observation
Measures of fit
* Significant at the 5% level.
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Part 2: Annual cost of hospital care,
conditional on costs being incurred
Fixed Effects Model
Coeff
Std error
2768.214
103.2651
4719.569
628.9279
186.4845
259.7963
4588.542
2384.187
8796.938
6049.574
3659.996
2790.186
153.1618
147.9918
355.7143
377.8867
415.1084
631.8776
0
5018.929
5055.586
5748.5
4542.504
3011.129
2378.517
226.9553
799.5249
338.5519
1073.384
158.4874
273.3819
2011.375
-2804.985
2223.294
1342.647
-2019.097
2767.746
1667.645
1958.554
0
404.7984
669.276
1098.558
1192.828
1578.81
219.3425
142.4455
190.0136
176.8952
469.5829
518.9623
535.8583
768.5315
R2=0.0979
106.2991
113.0889
118.4986
126.4415
136.7371