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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 
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What you have fitted is a parametric survival model where you have assumed that your response follows a log-normal distribution. Your model may be written as

$$\begin{align}Y=log(T) &= \mu + \beta_1 X_1 +\ldots+\beta_p X_p +\sigma W \\ &= \boldsymbol{\beta}^TX+\sigma W \end{align}$$

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.

Seeing that most of your estimates are negative, you would find youself in the first case, i.e. deaths or in general event times will occur faster for unit increases in the said variables. On the other end, for your positive coefficients, the survival process will slow down and events will come at a slower rate.

Hope this helps.

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  • $\begingroup$ Thanks for your clear explanation. I'm just wondering what does μ and σW represent. Also what do you exactly mean by switching to survival functions? Also by Survival process accelerates, you mean death happens earlier, right? $\endgroup$ – Erin Oct 16 '15 at 22:52
  • $\begingroup$ @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. $\endgroup$ – JohnK Oct 16 '15 at 22:59

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