How can I calculate the 95% confidence intervals of the hazard ratio from coxphfit?

Hi everybody.

I am using coxphfit to compute P-values and hazard ratios for data related to clinical trials and need to be able to compute a the 2-sided 95% confidence interval of the hazard ratio.

Any help will be appreciated

[Star Strider]

I’m somewhat surprised that it’s not among the ‘stats’ data in the output. Of interest, I can’t find anything on it in my many hardcopy references or online.

It’s probably best to contact MathWorks (use the ‘Contact Us’ link in the upper right corner of this page) and see what they recommend.

Please post back here with MathWorks’s reply. I’ve seen this regularly reported in the clinical literature, but never have had to calculate it myself.

[Alexander MacFarlane IV]

Hi Star Strider.

I can't use the contact us link because I'm using R2016b, and don't have over $600 to renew my service contract for the purpose of asking this question.

If we don't get an answer here I will try to get an answer out of our in-house statisticians and will reply here if I do.

They all use Stata, but some of them also know a bit of Matlab.

[Star Strider]

Hi Alexander,

I submitted a Service Request just now, asking about the confidence intervals. I’ll post back here with MathWorks’ reply. I included the URL of this post for their reference. It’s possible that they may contact you for further details.

It’s interesting that apparently Stata and R apparently produce these statistics (or so it seems when I did a search for the confidence interval information).

[Alexander MacFarlane IV]

Wow, thanks!

I see now why you have MVP next to your name.

[Star Strider]

My pleasure!

It's an interesting problem, since MATLAB usually provides these, or an easy way to calculate them.

Answer 1

[Mau Coen Moraga]

Hi Alexander,

My name is Mau and I can confirm that there is no documentation provided to calculate the confidence intervals for the Cox Proportional Hazards Model. Upon further deliberation with my colleagues, we will consider adding the confidence interval functionality to “coxphfit” in a future release of MATLAB.

In the meantime, in order to calculate a confidence interval from the fitted Cox Proportional Hazards Model, you can follow the commands below:

% Generate Weibull data depending on predictor |X|. 
rng('default') % for reproducibility
X = 4*rand(100,1);
A = 50*exp(-0.5*X); 
B = 2;
y = wblrnd(A,B);

% Fit a Cox proportional hazards model. 
[b,logL,H,stats] = coxphfit(X,y);
% Hazard Ratio exp(b)
exp(b)

ans = 
   2.5623

% Calculate 95% confidence interval of Hazard Ratio
CI = exp(b + [-1 1]*1.96*stats.se)

CI =
  2.0030    3.2778

Feel free to respond here for further questions.

Sincerely,

Mau Coen

[Alexander MacFarlane IV]

Thank you Mau Coen, and thanks again to Star Strider.

I tried that with some of my data and confirmed the results with our in-house statisticians and it works perfectly.

[Victor Fernandes]

so we're assuming a normal distribution here?? Does that make sense?