National Institute for Quality- and Organizational
Development in Healthcare and Medicines
COMPARING THREE DIFFERENT METHODS OF HALF-CYCLE CORRECTION
Bertalan Németh, Vera Szekér
National Institute of Quality- and Organizational Development in Healthcare and Medicines, Department of Health Technology Assessment, Budapest, Hungary
Introduction
The Department of Health Technology Assessment of the National Institute for Quality- and
Organizational Development in Healthcare and Medicines (GYEMSZI TEI) is responsible for the
critical evaluation of the reimbursement submissions of medicines and medical devices in Hungary.
The calculations in these submissions are often based on Markov models and some of these models
use half-cycle correction.
Half-cycle correction is a method used in health economics in Markov models to improve the
accuracy of the results. The basic idea behind this method is that the flow of patients between
Markov states is continuous therefore if the number of patients is measured at the beginning or at the
end of each cycle the result can be overestimated or underestimated. By using half-cycle correction
the difference from real data can be reduced.1 See Figures 1 to 4.
Figure 7
The flow of patients in case A of our model.
Figure 9
The flow of patients in case C of our model.
Figure 1
The flow of patients in a state
of a Markov model.
Figure 2
Determining the number of patients
at the end of each cycle.
Figure 8
The flow of patients in case B of our model.
Figure 10
The flow of patients in case D of our model.
Results
Table 1 shows the detailed results of our model in case A. It can be seen that without using one of the
three half-cycle correction methods the error of the results is generally higher. Of the three half-cycle
correction methods Simpson's rule was the most accurate but the difference from real data was less
than 1% in almost every case when we used any half-cycle correction method. Please note that our
model is based on a hypothetical set of paramaters so the exact numbers written in table 1 are less
important than their order of magnitude which we highlited with four different colors.
Table 1 The difference from the actual data in case A of our model.
Figure 3
Determining the number of patients
at the beginning of each cycle.
Figure 4
Determining the number of patients
by sing half-cycle correction.
Last year we examined the theoretical concept of half-cycle correction.2 Our conclusion was that it is
advised to use half-cycle correction when the number of cycles is small and the length of cycles is
too long and there is no possible way to reduce it. Our conclusion was in line with the findings of
Barendregt3 and Naimark et al.4 It is worth to note that in some rare cases half-cycle correction can
increase the difference from real data in the model. See Figures 5 and 6.
In this poster we aim to assess the relative performance of the alternatives to the standard half cycle
correction and to account for the connection between health states in a Markov model by using a
model we developed. All of our findings are based on our hypothetical Markov states.
Figure 5
Determining the number of patients
at the end of each cycle.
Figure 6
Determining the number of patients by using
half-cycle correction. Note the higher difference
from real data compared to Figure 5.
Decription of the model
Our model is a 5-state Markov model where the number of patients in health states follow different
courses. Each health state represented a typical shape for the flow of patients. The first two health
states were the ones where the number of patients was monotonously decreasing or increasing. In
the third health state the number of patients was increasing at the beginning but began decreasing
after a certain point. We added a health state with a continuously oscillating number of patients and
one where the number of patients remained the same after the first cycle.
We chose to compare three different half-cycle correction methods. We used the basic half-cycle
correction method, Simpson's method, and the mid-cycle method. It is important to note that the
description of the simple half-cycle correction method can slightly differ in the sources. In most
cases the two following descriptions are used 5:
In Figure 11 we compared the results from the five
different health states in four different cases. It can
be seen that in cases A, C and D determining the
number of patients at the beginning or at the end of
each cycle resulted in a higher difference from real
data than using the three half-cycle correction
methods which didn't differ from each other
significantly. The only exception is case B when
the standard half-cycle correction method resulted
in a higher difference from real data than
determining the number of patients at the end of
each cycle but the other two half-cycle correction
methods still resulted in more accurate results.
This case was similar to the hypothetical case we
presented in Figures 5 and 6 where the number of
patients in each health state shifted significantly
during the first cycle and changed less during later
cycles.
It can also be mentioned that the difference from
real data was higher in every case and with every
method if the number of cycles was lower.
Membership is counted at the beginning of each cycle
Membership is counted at the end of each cycle
Standard half-cycle correction
Simpson’s method
Mid-cycle method
Figure 11
The difference from the actual data
after 40, 30, 20 and 10 cycles
in the four cases of our model.
In table 2 we showed the method which was the most accurate in every case in every health state. It
can be seen that in 78 of the 80 possible cases Simpson's method and the mid-cycle method was the
most accurate and the standard half-cycle correction method resulted in the smallest difference
from real data in the remaining two cases. It can also be mentioned that Simpson's rule resulted in
the smallest difference from real data in the health states where the flow of patients was decreasing,
hill shaped or wave shaped.
Table 2 The half-cycle correction
method with the smallest
difference from the actual data.
- Add half of the number of patients at the end of the first cycle to the total patient population but
subtract half of the number of patients at the last cycle. This method means that we establish two
cycles with half of the original cycle length and between them there will be cycles with normal
cycle length.
Green: standard half cycle
correction method.
- Take the average of the patient numbers at the beginning and at the end of each cycle. This is also
called the life table method.
Purple: Mid-cycle method.
Blue: Simpson's rule.
It can be shown that the two methods equal on the total number of patients but with using the life
table method the dynamics of patient flow is more similar to the real data.3
The mid-cycle method is when we take into account the number of patients at the middle of each
cycle. Simpson's rule is a method used for numerical integration. In our model we used the definition
when we add the number of patients at the beginning and at the end of a cycle and add four times the
number of patients at the middle of each cycle then divide the sum by six.
For comparison we included the two cases when the number of patients is measured at the end or at
the beginning of each cycle.
We examined the results after 10, 20, 30 and 40 cycles and we ran the model with four different sets
of parameters. In these four cases the flow of patients in each health state differs significantly. See
Figures 7 to 10. We determined the exact number of patients in each health state by using numerical
integration and compared the results of each method to these numbers.
Conclusion
Based on the results of our model the most accurate method for half-cycle correction is Simpson's
method as in most cases it differed the least from the actual data. It's important to note that in most
cases the difference from real data was similar when we applied the other two methods, the
standard half-cycle correction method or the mid-cycle method. With one exception the accuracy of
the model was signficantly increased by using any half-cyle correction method in every case we
examined compared to cases when no half-cycle correction method was applied. The difference
from real data was also higher in every case and with every method when the number of cycles was
lower.
Literature
1.
Naimark DM, Bott M, Krahn M. The half-cycle correction explained: two alternative pedagogical approaches. Medical Decision Making. 2008 Sep-Oct; 28(5):706-12.
2.
Nemeth B, Vincziczki Á. The Role of Half-Cycle Correction in the Models Used for Health Technology Assessment. Poster presentation at the ISPOR 16th Annual European Congress.
3.
Barendregt JJ. The half-cycle correction: banish rather than explain It. Medical Decision Making. 2009 jul-Aug; 29(4):500-2.
4.
Naimark DM, Kabboul NN, Krahn MD. The half-cycle correction revisited: redemption of a kludge. Med Decis Making. 2014 Apr; 34(3):283-5.
5.
Clarke PM, Wolstenholme JL, Wordsworth S. Applied methods of cost-effectiveness analysis in healthcare. Oxford University Press; 2010. p. 224-5.