BlandAltman.m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Bland-Altman plot 
%
% Bland Altam is a method of data plotting used in analysing the agreement 
% between two different assays. 
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Written by:
% Andrea Padoan
% University Hospital of Padua, Italy
% 12-13-2008

% -------------------------------------------------------------------

% Please respect GNU General Public License agreement:
% Someone can distribute this program plus their own modifications. 
% Thus, all enhancements and additions to this software must also be
% distributed as free software

% -------------------------------------------------------------------

% You must define data array before use the code. It must contain 3 columns
% array:

%   data (:, 1) = first column = sample number (or patient number) 
%   data (:, 1) can id number or what you want or zero (it isnt' used by the
%                                                           program)
%   data (:, 2) = second column = instrument 1 output = S1
%   data (:, 3) = third column = instrument 2 output = S2

% Array funxy contains the Cartesian coordinates of Bland Altman function,
% given of sample S with value data (:, 1)=S1 and data (:, 2)=S2 determined by
% the two assays. The Bland Altman function is
%                  S(x,y)= ( (S1+S2)/2, (S1-S2) )

funxy(:,1) = (data(:,2) + data(:,3))/2;  %poin mean between two methods
funxy(:,2) = data (:,2) - data (:,3);    %point difference between two methods

disp ('Bland Altman Plot. Written by Andrea Padoan, 2008');

%Delete NaN if present. Bland Altman can't use missing values

funxy(any(isnan(funxy),2),:) = [ ];

%Calculate mean of differences
diffmean = mean (funxy (:, 2))

%Calculate standard deviation of difference
sdev = std(funxy(:,2), 1)
%You want to calculate 95 % confidence interval for the mean = +-2sd
twosdev = sdev * 1.96;



%Calculate max value of the mean
maxx = max (funxy (:, 1));

%Calculate max value of the difference
maxy = max (funxy (:, 2));

if (maxy < twosdev)

    maxy = twosdev;
    
end

%Add 1 sd to optimize graph 
maxy = maxy + sdev;

%Min value of difference
miny = min (funxy (:, 2));

if (miny > -twosdev)

    miny = -twosdev;
    
end

%Subtract 1 sd to optimize graph
miny = miny - sdev;

% scatterplot of funxy
figure (1);
scatter (funxy(:,1), funxy(:,2));
%xlim ([0 maxx]);
%ylim ([miny maxy]);
axis ([0 maxx miny maxy]);
axis on;
hold on;

%Title and axis titles
title ('Bland-Altman plot');

xlabel ('Average by two assays');
ylabel ('Difference (Assay A - Assay B)');


%Draw 2*sdev line
line ([0 maxx], [(twosdev+diffmean) (twosdev+diffmean)],'LineStyle','--');
text (maxx, twosdev, '  1.96 sd ', 'Color', 'b' , 'FontSize', 12, 'FontWeight', 'bold');

line ([0 maxx], [(diffmean-twosdev) (diffmean-twosdev)], 'LineStyle','--');
text (maxx, -twosdev, ' -1.96 sd', 'Color', 'b' , 'FontSize', 12, 'FontWeight', 'bold');

%Draw line as mean of differences
line ([0 maxx], [diffmean diffmean],'LineStyle','-', 'LineWidth', 2);

%Add text 'mean'
text (maxx, diffmean, ' mean', 'Color', 'b' , 'FontSize', 14, 'FontWeight', 'bold');

clear funxy miny maxy maxx twosdev;