BlandAltman
Analysis using SAS
(Using PROC REG & PROC PLOT)
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These SAS statistics tutorials briefly explain the use and
interpretation of standard statistical analysis techniques for Medical,
Pharmaceutical, Clinical Trials, Marketing or Scientific Research. The examples
include howto instructions for SAS Software
BlandAltman analysis (Updated 9142009)
The BlandAltman analysis is not a statistical test measured with a
pvalue. Instead, it is a process used to assess agreement between two
methods of measurement. (Bland and Altman 1986, 2003) An important requirement
of the BlandAltman method for measuring agreement is that the two methods for
measuring the same characteristic use the same scale of measurement. This
implies that when plotted, the points should line up along the line y
= x (line of identity).
It is possible for two measures to have strong linear agreement using a
Pearson’s correlation (r) when they are not measuring the same quantity
because a correlation analysis does not require that the two measurements be on
the same scale or to even be measurements of the same characteristic.
The analysis is based on examination of two plots:
·
Plot of identity: A scatterplot of the two measurements
along with the line y = x. If the measurements are in basic agreement
then the points in the scatterplot will line up closely to the line y = x.
·
BlandAltman plot: A scatterplot of variable means plotted
on the horizontal axis and the differences plotted on the vertical axis which
shows the amount of disagreement between the two measures (via the differences)
and lets you see how this disagreement relates to the magnitude of the
measurements. This plot includes approximate 95% limits (based on an assumption
of normal differences). If differences observed in this plot are not deemed
scientifically (or clinical) important (according to the researcher’s own
expertise), this is a confirmation of agreement. (The decision as to what
constitutes a clinically important difference should be made in advance of the
analysis.)
Example
This example uses data from Bland and Altman (1986): two
measurements of peak expiratory flow rate (PEFR) are compared. One of these
measurements uses a “Large” meter and the other a “Mini” meter. The research
question of interest is whether these two techniques are measuring the same
phenomenon. The first way to examine the two measure is with A plot of
identity. For this data, the plot is shown here:
Note that the line drawn here is the line y = x, not the
regression line. If the scatter of points in this plot lies near the
line, it indicates that the two ways of measuring PEFR are similar. From this
plot you can see that the scatterplot falls close to the line which suggests
that the two machines are measuring the same characteristic. The SAS code to
produce this graph follows.
Step 1: Calculate the differences and averages. (Actually the differences
are used in the plot of identity above) using this code:
DATA
BA;
input
large mini;
diff=largemini;
avg=(large+mini)/2;
datalines;
… data follow…
Step 2: Specify values for the x and y axes for the plot, and this is
done with macro variables in the following code:
%let
minx=100;%let
maxx=700;%let
tickx=50;
The “tick” variable specifies how often ticks will appear on the axis. For the X
axis the minimum and maximum should reflect values that fully encompass the
values of the original data (mini and large in this case.)
Step 3: Create necessary information to produce the mean line at 0 using
the information in the “anno” data set shown below:
data
anno;
function='move';
xsys='1';
ysys='1';
x=0;
y=0;
output;
function='draw';
xsys='1';
ysys='1';
color='red';
x=100;
y=100;
size=2;
output;
run;
Step 4: The plot of identity is produced using this code (using calculated upper and lower bound previously created.)
symbol1
i=none
v=dot
c=black
height=1;
* X AXIS  HORIZONTAL;
axis1
length=6.5
in
width=1
value=(font="Arial"
h=1)
order=&minx
to &maxx by &tickx;
* YAXIS  VERTICAL;
axis2
length=4.5
in
width=1
value=(font="Arial"
h=1)
order=&minx
to &maxx by &tickx;
footnote
;
proc
gplot
data=PERF;
plot
large*mini /
haxis=axis1
vaxis=axis2
vref= (&blower &bupper &bmeandiff) cvref=red;
run;
The second plot is a little more difficult to come up with. It is a
scatterplot of the average of the two measurements against the difference (large
minus mini) between measurements for each subject. This plot is a visual check
that the magnitudes of the differences are essentially constant throughout the
range of measurement. If the differences are approximately normally distributed,
then you would expect about 5% of the points to lie outside the limit lines.
This plot is displayed here:
Notice that the 95% limit lines are at about plus or minus 75 for the
differences between readings, and the graph shows a few differences outside or
close to the limit lines, i.e. differences in the neighborhood of
±75 (the actual limits are 75.4 and
79.6). Bland and Altman (1986) argue that such large differences are
clinically important (a decision not based on any pvalue) and
therefore conclude that the two devices do not show sufficient agreement to be
used interchangeably. It is important to note that this lack of agreement is
not apparent in the plot of identity. The following steps are used to calculate
the values needed for this plot.
Step 1: Using the BA data set created above, calculate the mean and
standard deviation of the “diff” value and output that information to a file
(named diff in this case.) Merge the mean and std into the original data set
(name the combined data set PERF) and use that information to calculate the
upper 95% bound (ubound) and lower bound (lbound) using the following SAS code:
data
prelim;set
ba;
proc
means
noprint
data=prelim;var
diff;
output
out=diff
mean=meandiff
std=stddiff;
run;
data
PERF;set
prelim;
if
_N_=1
then
set
diff;
ubound=meandiff+stddiff*2;
lbound=meandiffstddiff*2;
* store upper and lower inputs in macro variables;
call symput('bupper',ubound);
call symput('blower',lbound);
call symput('bmeandiff',meandiff);
run;
The PERF data set contains the following information shown in the PERF data set
below. Notice the meandiff
and std columns
were from the PROC MEANS and the
ubound and
lbound were
calculated using the code above.
Step 2:
Specify the limits for the axes using macro variables:
*
AXIS LIMITS FOR GRAPHS;
%let
miny=100;%let
maxy=100;%let
ticky=20;
This information is something you must observe from the data – note that the
minimum and maximum for the Y axis should be the same magnitude (but one
negative) to create a balanced plot.
Step 3: The Bland –Altman graph is created using the following code. The
“symbol” statement specifies the type of dots, color and size of dots. The
“axis1” paragraph specifies information about the Xaxis and the “axis2”
paragraph specifies information about the Yaxis.In particular, the numbers used
for each are given by the “order” statements. The vref statement uses the information from the symput bupper, blower and bmeandiff macro variables to plot the three horizontal lines.
symbol1
i=none
v=dot
c=black
height=1;
* XAXIS  HORIZONTAL  AVERAGE;
axis1
length=6.5
in
width=1
label=(f="Arial"
h=2
'Average')
value=(font="Arial"
h=1)
order=&minx
to &maxx by &tickx;
* YAXIS  Vertical  Difference;
axis2
length=4.5
in
width=1
label=(f="Arial"
h=2
'Difference')
value=(font="Arial"
h=1)
order=&miny
to &maxy by &ticky;
footnote
h=2
f="Arial"
'BlandAltman Plot';
title
h=2
f="Arial"
'Example';
proc gplot data=PERF;
plot large*mini / haxis=axis1 vaxis=axis2
vref= (&blower &bupper &bmeandiff) cvref=red;
quit;
Reporting the results of a BlandAltman analysis
The following example illustrates how you might report the results of a
BlandAltman analysis in publication format.
Narrative for methods section:
“A BlandAltman assessment for agreement was used to compare the two peak flow
methods. A range of agreement was defined as mean bias ±2 SD.”
Or
“A BlandAltman analysis was used to assess the level of agreement between the
two methods to compare the new technique to the established one.”
Narrative for results section:
“The BlandAltman analysis indicates that the 95% limits of agreement between
the two methods ranged from 75.4 to 79.6. The two methods do not consistently
provide similar measures because there is a level of disagreement that includes
clinically important discrepancies of up to 80 l/min.”
References

Barnett, V. and Lewis, T. (1994). Outliers in Statistical Data, 3^{rd}
edition. New York: John Wiley and Sons.

Bland JM and Altman DG. (1986).Statistical methods for assessing agreement
between two methods of clinical measurement, Lancet, February, pp
30710.

Bland JM and Altman DG. (2003). Applying the right statistics: analyses of
measurement studies, Untrasound Obstet Gynecol 2003;22: 8593.

Elliott, AC, Woodward, WA (2007), Statistical Analysis Quick Reference
Guidebook, Sag, pp 107ff.

Kleinbaum DG, Kupper LL, Muller KE,
Nizam A.
(1997). Applied Regression Analysis and Other Multivariate Methods (3^{rd}
Edition), North Scituate, MA: Duxbury Press.

Mantel, N. (1970). Why stepdown procedures in variable selection,”
Technometrics 12, 621625.

SAS Institute Inc. (2003). SAS/STAT Software: Reference, Version 9.1,
Cary, NC: SAS Institute Inc.
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