I have been using streg to fit predictive survival models (for time from diagnosis to death) to some data on some fiendishly unpredictable patients, of which (according to their Kaplan-Meier curve) about 15 percent are dead after the first month, another 15 percent are dead after the first year, and the rest die at a much more relaxed pace afterwards over the following 17 years. To me, this seems to suggest choosing a Weibull model., which seems to predict 1-year survival a bit better than a Gompertz model in these patients. And my gut response is to choose the hazard rate parameterization, for comparability with other people's Cox regressions, although I am open to persuasion in favour of the accelerated failure time parameterization (which of course is an alternative parameterization of the same model with the same predicted k-year survival probabilities).
The main problem with a Weibull model seems to be how to interpret the intercept parameter to my colleagues. Assuming that we use an eform option, the intercept parameter of a logistic model is the baseline odds if all covariates are zero, the intercept parameter of a linear regression model for log-transformed data is the geometric mean when all covariates are zero, and the intercept parameter of a Gompertz model is the hazard rate at zero time if all covariates are zero. But, in a Weibull model with decreasing hazard rate (0<p<1 in the notation of [ST] streg where p is the power parameter), the hazard rate tends to infinity as time tends to zero.
One idea I can think of is to define the exponentiated intercept of a Weibull model as h(1)/p, where h(1) is the hazard rate at time 1 (in the units used which in my case are years). Another possibility is -log(S(1)), where S(1) is the 1-unit survival time (which would be a 1-year survival time in my case) and log() is the natural log. However, both of these quantities are expressed in counter-intuitive units. (I suppose I could end-point transform a confidence interval for the exponentiated intercept to get a confidence interval for the 1-year survival.)
Can anybody think of a better interpretation?
Best wishes
Roger
The main problem with a Weibull model seems to be how to interpret the intercept parameter to my colleagues. Assuming that we use an eform option, the intercept parameter of a logistic model is the baseline odds if all covariates are zero, the intercept parameter of a linear regression model for log-transformed data is the geometric mean when all covariates are zero, and the intercept parameter of a Gompertz model is the hazard rate at zero time if all covariates are zero. But, in a Weibull model with decreasing hazard rate (0<p<1 in the notation of [ST] streg where p is the power parameter), the hazard rate tends to infinity as time tends to zero.
One idea I can think of is to define the exponentiated intercept of a Weibull model as h(1)/p, where h(1) is the hazard rate at time 1 (in the units used which in my case are years). Another possibility is -log(S(1)), where S(1) is the 1-unit survival time (which would be a 1-year survival time in my case) and log() is the natural log. However, both of these quantities are expressed in counter-intuitive units. (I suppose I could end-point transform a confidence interval for the exponentiated intercept to get a confidence interval for the 1-year survival.)
Can anybody think of a better interpretation?
Best wishes
Roger
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