International Journal of Statistics and Systems ISSN 0973-2675 Volume 10, Number 2 (2015), pp. 203-208 © Research India Publications http://www.ripublication.com
Risk Adjusted Control Chart for Monitoring HemoglobinA1C Level R.Sasikumar and S.Bangusha Devi Emails:
[email protected] and
[email protected] Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli-627 012.
Abstract Control charts methodology has been widely used for monitoring and improving the manufacturing product. Recently healthcare organizations focused the use of control charts techniques. Input of healthcare processes is not same. Because the input is usually patients and the characteristics of the patients are vary to each other. For that purpose risk adjusted control charts have been developed. In this paper first we applied unadjusted x control chart for HemoglobinA1C (HbA1C) level of Type 2 diabetic patients and then we used the risk adjusted x control chart for the same data and compared differences between unadjusted and risk adjusted x control chart. Keywords: Statistical process control, x control chart, Risk adjusted control chart, HgbA1C level.
Introduction Statistical process control (SPC) is based on continuous monitoring and has a long history of improving quality in industrial engineering. SPC is used to determine if a process is behaving with natural variability or if assignable causes are present. In last few years, healthcare researchers have used the SPC techniques in healthcare. But, healthcare differs from manufacturing in that its primary input, patients, are not expected to be uniform. Because, the patients may have the same disease, but they differ considerably by the severity of the disease prognosis of their illness. This modification requires healthcare researchers to modify control chart tools so that the chart is appropriate for the healthcare monitoring. Risk adjustments are needed so that clinicians can separate changes in outcomes due to the patient’s prognosis at the start of their visit from changes that are due to an intervention in processes of care. For example, suppose, some patient may be so ill that they cannot be saved by the best of care, while other patients will be saved despite the fact that they have received poor
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care. These interactions between patient outcomes, quality of care, and the severity of a patient’s illness suggest that when a patient not getting cure, the patients health condition might be attributed of either the severity of illness or to the quality of care the patients received. It is important that healthcare organizations be able to separate the influence of quality of care from those of severity of illness when assessing patient outcomes. Without this ability, instances of poor and good quality of care cannot be determined. This article shows how patient’s risks can be used to adjust control charts, particularly the x control charts and presents the importance of risk adjustments with the support of HbA1C level of diabetic patients. In order to understand the importance of the risk-adjusted control chart, the HbA1C level from the type 2 diabetic patients were collected for 10 times from 8 patients. Every 3 months ones the HbA1C level is checked for the diabetic patients.
Unadjusted x Control chart Shewhart developed control charts for distinguish between the common cause variation and assignable cause variation. Traditional control chart procedure make no adjustments for different risk profiles because machine inputs are usually relatively homogeneous and such adjustments are not required in industrial settings. The inputs variables required to construct the unadjusted x control chart procedure are given following. The number of cases in each time period (n i), HbA1C level for individual patient cases(xij) and the total HbA1C level in a time period (li). The formula for calculating the average HbA1C level ( X ), the standard deviation of HbA1C level(S), individual time period average HbA1C level ( xi ), Standard deviation of each time period (si), Upper Control Limit (UCLi) and Lower Control Limit (LCLi) are given below. ni
m
( xij
li X
i 1 m
S
n
ni
ni
.
i 1
i 1
UCLi
X
t
/2
X )2
j 1
1
xi
li ni
si
S ni
L Ci LX
t
/2
( si )
( si )
Risk adjusted x control chart Unlike traditional x control chart, risk adjusted x control chart depends on each patients risk profiles. In health science field, patient risk can vary considerably from patient to patient. The inputs variables required to construct the adjusted x control chart procedure are given following. The number of cases in each time period (n i), the actual HbA1C level for individual cases (xij), the average HbA1C level for specific time periods( xi ), and the expected HbA1C level for individual cases ( xˆ ij ). The average HbA1C level for the specific time periods was calculated like the unadjusted control chart and the expected HbA1C level for individual cases were computed using previously described patient-mix adjusted model (1). According to Alemi et al. (1) patient’s age and number of medicines taken by the patients were taken as the independent variables of the patient-mix adjusted model. The formula for calculating
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the expected HbA1C level for specific time periods ( xˆ i ), the average difference between actual and expected HbA1C level in specific time periods (d i), the standard deviation of di (sdi), adjusted UCLi and adjusted LCLi are given below. ni
xˆ i
ni
xˆ ij
j 1
ni
( xij di
j 1
ni
ni
xˆ ij )
( xij s di
j 1
ni
xi ) 2
UCLi
xˆi
t
/2
( s di )
LCLi
xˆi
t
/2
( s di )
Results and Discussions Unadjusted x control chart We used the formulae given for unadjusted control chart for calculating the unadjusted control chart statistic. They are given in Table 1. These results are shown graphically in Figure 1. The center line in Figure 1 is the average HbA1C level. The upper and lower line indicates the UCL and LCL for unadjusted control chart. The small squares are the average HbA1C level for each time periods. From the Figure 1, it is noted that the actual HbA1C level for first period is out of control. This indicates that the process is out of control. Table 1: Unadjusted HbA1C level Period Number of Cases Average HbA1C level UCLi 1 8 10.3 10.5 2 8 10.3 8.1 3 8 10.3 7.9 4 8 10.3 8.7 5 8 10.3 7.9 6 8 10.3 8.1 7 8 10.3 9.8 8 8 10.3 7.9 9 8 10.3 7.5 10 8 10.3 9.9
LCLi 6.9 6.9 6.9 6.9 6.9 6.9 6.9 6.9 6.9 6.9
CL 8.6 8.6 8.6 8.6 8.6 8.6 8.6 8.6 8.6 8.6
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Figure 1: Unadjusted x control chart
Risk-adjusted x control chart We used the formulae given for adjusted control chart for calculating the adjusted control chart statistic. These results graphically shown in Figure 2. The center line in Figure 2 is the patient mix-adjusted average HbA1C level. The upper and lower line indicate the UCL and LCL for adjusted control chart and the small squares represents the average HbA1C level for each time periods. After patient-mix adjustment there is no point falls out of control limit. Actual HbA1C level for first period is now within the control limits. Table 2: Adjusted HbA1C level Period 1 2 3 4 5 6 7 8 9 10
Number of Cases Average HbA1C level 8 8 8 8 8 8 8 8 8 8
10.5 8.1 7.9 8.7 7.9 8.1 9.8 7.9 7.5 9.9
Expected UCLi LCLi HbA1C level 11.7 12.4 11 10.4 16.8 4 10.1 13.8 6.4 10.8 12.6 9 10.1 15.7 4.5 10.2 18.7 1.7 11.4 12.7 10.1 10 12.2 7.8 9.7 14.3 5.1 11.6 12.8 10.4
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Figure 2: Adjusted x control chart
Conclusion This article concerns the use of risk-adjustment to analyze the process outcomes that take the form of measurements. Risk-adjusted control chart confirmed that the presence of out of control in first period of unadjusted control chart only because of the severity of illness and not the performance of the clinicians. So that riskadjustment method provides a logical way to adjusting patient characteristics that significantly affect the patient risk. This method is therefore perfectly suitable for settings where there is a variable mix of patients over time. Acknowledgements The authors acknowledge to University Grants Commission for providing financial support through Major Research Project (F.No.40-253/2011 (SR)) to carry out this work. References 1.
2. 3.
4.
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