MATLAB: How to use the output arguments of the COXPHFIT function in MATLAB 7.13 (R2011b) to evaluate the Cox proportional hazards model at new points

Question

I am using the COXPHFIT function in MATLAB 7.13 (R2011b).

I have used the COXPHFIT function in MATLAB 7.13 (R2011b) to perform a regression on a set of predictors and responses. I see from the documentation that the function returns the estimated coefficients and "H" which is a two-column matrix containing y values in the first column and the estimated baseline cumulative hazard evaluated at those values in the second column. How can I use these outputs to evaluate the Cox proportional hazards model at new points?

Answer 1

The example below illustrates the use of COXPHFIT.

Please note that the use of the STAIRS function when evaluating the model at a variety of responses in 'y'. This is because the estimated baseline cumulative hazard function (i.e., h(t) in the documentation) is not smooth. The function COXPHFIT is doing a type of maximum likelihood estimation. The likelihood is maximized if the cumulative hazard jumps at observed failure times and is flat otherwise.

% Number of observations
n = 30;
% Number of predictors
p = 5;
%Observed Data
X_observed = rand(n,p);
y_observed = rand(n,1);
%Get mean of X
Xbar = mean(X_observed);
%Get model
[b, ~, H] = coxphfit(X_observed,y_observed);
%Use model
%Make new observation
x_new = rand(1,p);
%Evaluate the model for a variety of y for this new, fixed observation
stairs( H(:,1), H(:,2) * exp((x_new - Xbar)*b));
title('Model');
%Plot estimated baseline survivor function for a variety of y
figure;
stairs( H(:,1), exp(-H(:,2)));
title('Survivor');