I have a doubt with Weibull Accelerated failure time model Hazard ratio's confident intervals interpret from SAS output, thake this as an example:

Standard 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 0.4258 0.8463 -1.2329 2.0845 0.25 0.6148 hodgkins 1 -1.3746 0.6465 -2.6417 -0.1075 4.52 0.0335 Scale 1 1.2733 0.2044 0.9297 1.7440 Weibull Shape 1 0.7854 0.1260 0.5734 1.0757

for the variable hodgkins the hazard ratio is: HR= exp(-BETA_hodgkins/Scale_est) = exp(-(-1.3746)/1.2733) = 2.943

the confidence interval can be calculated in the same manner as:

exp(-1_conf/Scale_IC) = exp(-(-2.6417)/0.9297)

exp(-2_conf/Scale) = exp(-(-0.1075)/1.7440)


Example reference: http://www4.stat.ncsu.edu/~dzhang2/st745/chap5.pdf

  • $\begingroup$ "If the Weibull model is a reasonable model for your data and you use Proc Lifereg and Proc Phreg to fit the data, then the regression coefficient estimates not only have opposite signs (except possibly for the intercept) but also have different magnitude" which procedure are you using? $\endgroup$ – Deep North Jan 7 '18 at 23:05
  • $\begingroup$ Thank you for your interest, i had using proc lifereg (dist=Weibull) $\endgroup$ – Surv Jan 8 '18 at 6:40

for the aft you are interested in the ratio of medians or acceleration factor. If you did cox regression then you'd want the hazard ratio. See for example this paper: "In particular if the error distribution is symmetric, then the coefficient of the treatment indicator represents the (adjusted) difference in the median survival times on the log scale between the two treatment groups and its exponentiated value is the ratio of the medians on the time scale itself" https://www.ncbi.nlm.nih.gov/pubmed/17080754

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