# Sign of coefficients in survreg (survival analysis)

I am working on survival analysis and I want to know what does the sign of coefficients mean? I read this and this. One says if sign is positive, survival time is longer and the other says the opposite. I'm using the following code. The time variable in my data shows the time of death.

summary(srFit)
survreg(formula = Surv(time) ~ f1 + f2 + f3 + f4 + f5 + f6 + f7 + f8 + f9 + f10, data = train, dist = 'lognormal')

Value Std. Error       z        p
(Intercept)              1.59e+03   632.0632  2.5092 1.21e-02
f1                      -2.07e+00     1.2283 -1.6881 9.14e-02
f2                       1.03e+00     1.8070  0.5677 5.70e-01
f3                      -7.61e-02     1.3764 -0.0553 9.56e-01
f4                      -3.24e+00     1.4836 -2.1843 2.89e-02
f5                       4.37e-01     0.0961  4.5474 5.43e-06
f6                      -1.36e+00     0.7555 -1.8011 7.17e-02
f7                      -6.26e-03     0.0081 -0.7719 4.40e-01
f8                       3.92e-03     0.0186  0.2111 8.33e-01
f9                      -4.82e-01     0.4291 -1.1235 2.61e-01
f10                     -7.79e-01     0.3139 -2.4809 1.31e-02
Log(scale)               2.73e+00     0.0314 86.9447 0.00e+00

Scale= 15.4

Student-t distribution: parmameters= 4
Loglik(model)= -4542.1   Loglik(intercept only)= -4570.1
Chisq= 56 on 10 degrees of freedom, p= 2.1e-08
Number of Newton-Raphson Iterations: 5
n= 1008


\begin{align}Y=log(T) &= \mu + \beta_1 X_1 +\ldots+\beta_p X_p +\sigma W \\ &= \boldsymbol{\beta}^TX+\sigma W \end{align}
where $T$ stands for time. If we switch to survival functions we may interpret each coefficient as follows: If $\exp\left\{-\boldsymbol{\beta}^T \mathbf{X} \right\} >1$ then the survival process accelerates and if $\exp\left\{-\boldsymbol{\beta}^T \mathbf{X} \right\} <1$ then the survival process decelerates. You can do that for every variable keeping everything else fixed.
• @Erin $\mu$ is just survival notation for the intercept which corresponds to the case of all $X$s being zero (baseline case), $W$ is the equivalent of the error in the regression setting and has a specific distribution, depending on the desired distribution of your response while $\sigma$ is just a scalar that may be thought of as part of the error variance. This representation is meant to emphasize the similarities between an accelerated time failure model and a standard GLM. – JohnK Oct 16 '15 at 22:59