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Agreement package | R Documentation
Or, hell, go watch it on Youtube. Music Ordering Area Compact Disc. Long Playing inch. This is what weve got coming up in terms of shows. The latter are often used when studying the agreement between clinicians, definitions, formulas or different data sources.
Statistical tools for measuring agreement
In medicine, new or revised versions of measurement techniques are developed at a regular basis. However, before replacing an old device, for example a blood pressure device, by a new one we need to know whether the results of the old and the new device are similar.
If the disagreement between two devices is sufficiently small and the new device has advantages over the old one for example because it is cheaper or less invasive , we could consider replacing the old method by the new one, or use the two devices interchangeably. There are multiple ways to determine the agreement between two methods.
Ideally, we would like to have a measure that indicates whether the relationship between the results of two devices is linear, i. Second, we need a measure to show whether there are systematic differences between the results of the two devices, i. In this paper, we will first discuss various ways to determine agreement between methods to measure continuous variables, such as blood pressure or eGFR.
For illustration purposes, we created a hypothetical dataset including data from two devices to determine blood pressure with which we tested 15 individuals table 1 , and we assume that no gold standard is available. In the second part, we will discuss methods to determine agreement between categorical variables, such as the presence of comorbidities.
Statistical Tools for Measuring Agreement
The latter is often used when studying agreement between clinicians, definitions, formulas or different data sources. For this study, we will use the data from a published paper [ 1 ]. A first method to describe agreement between two continuous variables is comparing the mean values derived by the two devices. After comparing the mean, one could test for statistical significance of the difference between the two devices by performing a paired t test. As shown in table 1 , the means of the two blood pressure measurements were similar, and there was no statistically significant difference.
However, these results do not provide information on the possible differences for an individual patient.
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Furthermore, they do not show information on the linearity of the relationship or on the presence of a random difference. Therefore, this method is unsuitable to determine agreement between the two devices, and is not sufficient on its own. Another method to describe agreement is calculating a Pearson correlation coefficient, called r [ 2 ]. In our example, we obtained a correlation coefficient of 0. Although this might seem high, in some patients there was a difference of up to 20 mm Hg, which could have clinical implications for this patient, for example with respect to prescription of antihypertensive medication.
A second problem is that the correlation coefficient assumes a linear relation, and will calculate a correlation coefficient irrespective of the shape of the relationship, for example a U-shaped relation as shown in figure 2 a, a single outlier, or a true linear relation.
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Thirdly, as indicated above, it is important that the relationship is the same, i. Therefore, if the blood pressure increases by 10 mm Hg according to device A, it should also do so according to device B, and not by 8 mm Hg, see for example figure 2 b. The correlation coefficient does not consider this and will be the same if points would be on any straight line, thereby ignoring a systematic bias. A final problem is related to the range of the measurements.
The size of the correlation coefficient is partly determined by the range of the samples that are tested. If the range of values is larger, the overall r is on average larger than when one would for example divide the study into two subpopulations, for example in normal and pre-hypertensive patients and hypertensive patients fig. So, determining agreement in subpopulations will provide lower correlation coefficients than determining this in a study with a larger range of values. Correlation between two hypothetical systolic blood pressure measurements; data presented in table 1.
Line is the regression line used for calculation of the correlation coefficient. Therefore, for measuring agreement between two continuous variables, also the correlation coefficient by itself is unsuitable.
The remaining variability is considered a systematic difference. This test has the advantage over the Pearson correlation coefficient that it contains both information on the correlation and the systematic difference between readings.
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A more adequate method to graphically display the data was proposed by Bland and Altman in [ 4 ]. Figure 3 shows an example including our blood pressure data. Furthermore, an interesting feature of the Bland-Altman plot is its ability to show a relation between the value itself and the measurement error. In our example there is no clear relation. In addition to agreement coefficients, accuracy and precision coefficients are introduced and utilized to characterize these sources.
This book will appeal to a broad range of statisticians, researchers, practitioners and students, in areas of biomedical devices, psychology, medical research, and others, in which agreement assessment are needed. Many practical illustrative examples will be presented throughout the book in a wide variety of situations for continuous and categorical data.
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