Hi all,
I ran a survival analysis in STATA using the streg command. The found the following in the manual.
"Regression results are often presented in a metric other than the natural regression coefficients, that is, as hazard ratios, relative risk ratios, odds ratios, etc. In those cases, standard errors are calculated using the delta method. However, the Z test and p-values given are calculated from the natural regression coefficients and standard errors. Although a test based on, say, a hazard ratio and its standard error would be asymptotically equivalent to that based on a regression coefficient, in real samples a hazard ratio will tend to have a more skewed distribution because it is an exponentiated regression coefficient. Also, it is more natural to think of these tests as testing whether a regression coefficient is nonzero, rather than testing whether a transformed regression coefficient is unequal to some nonzero value (one for a hazard ratio). Finally, the confidence intervals given are obtained by transforming the endpoints of the corresponding confidence interval for the untransformed regression coefficient. This ensures that, say, strictly positive quantities such as hazard ratios have confidence intervals that do not overlap zero."
What does this mean for the interpretation of the hazard ratios? I mean, streg reports hazard ratio. If I understand correctly, the p-values report if the regression coefficient is significantly different from zero and not if the hazard ratio is significantly different from 1??
Thanks in advance!
Regards,
Ishwaya
I ran a survival analysis in STATA using the streg command. The found the following in the manual.
"Regression results are often presented in a metric other than the natural regression coefficients, that is, as hazard ratios, relative risk ratios, odds ratios, etc. In those cases, standard errors are calculated using the delta method. However, the Z test and p-values given are calculated from the natural regression coefficients and standard errors. Although a test based on, say, a hazard ratio and its standard error would be asymptotically equivalent to that based on a regression coefficient, in real samples a hazard ratio will tend to have a more skewed distribution because it is an exponentiated regression coefficient. Also, it is more natural to think of these tests as testing whether a regression coefficient is nonzero, rather than testing whether a transformed regression coefficient is unequal to some nonzero value (one for a hazard ratio). Finally, the confidence intervals given are obtained by transforming the endpoints of the corresponding confidence interval for the untransformed regression coefficient. This ensures that, say, strictly positive quantities such as hazard ratios have confidence intervals that do not overlap zero."
What does this mean for the interpretation of the hazard ratios? I mean, streg reports hazard ratio. If I understand correctly, the p-values report if the regression coefficient is significantly different from zero and not if the hazard ratio is significantly different from 1??
Thanks in advance!
Regards,
Ishwaya
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