function [H]=lemeshow(data,show) %[H]=lemeshow(data,show) % %data -(Nx2) where N is the number of cases (4000 for each of sets A, B, and C), % the first column is the true outcome (IHD from the Outcomes file), % and the second column is the estimated risk (from the challenge % entry outputs for event2) % %show -(logical) If true (non-zero), this function will plot the percentiles % %H -(scalar) Hosmer-Lemeshow H statistic % %Written by Ikaro Silva, 2012 % %Version 1.3 (24 March 2012) % %Reference: Hosmer, David W., Lemeshow, Stanley (2000). Applied Logistic %Regression, New York : Wiley % % http://en.wikipedia.org/wiki/Hosmerâ€“Lemeshow_test % %Change Log %1.0 -> 1.1 Fixed issue where Obs variable was being overestimated % D=10; % Use D-iles (i.e., deciles as in Lemeshow's original paper) N=length(data(:,1)); M=floor(N/D); % M should always be 400 for the challenge data=sortrows(data,2); % rearrange the matrix by estimated risk CM=zeros(D,3)+NaN; centroid=zeros(D-1,1)+NaN; for i=1:D %Set number of deaths proportional to Y true value ind2=i*M; % highest bin in decile D ind1=ind2-M+1; % lowest bin Obs=sum([data(ind1:ind2,1)]); % number of observed deaths within decile D centroid(i)=mean(data(ind1:ind2,2)); % mean estimated risk within decile Exp=M*centroid(i); % expected number of deaths within decile Htemp=(Obs-Exp)^2/(M*centroid(i)*(1-centroid(i)) + 0.001); CM(i,:)=[Obs Exp Htemp]; end H=sum(CM(:,3)); % Hosmer-Lemeshow H statistic if(show) plot(centroid,CM(:,1),'bo','MarkerSize',10) grid on;xlim([0 1]);hold on plot(centroid,CM(:,2),'rx','MarkerSize',10) xlabel('Predicted Risk') ylabel('Number of Deaths') legend('Observed','Predicted') end