Solved – Sign of coefficients in survreg (survival analysis)

rsurvival

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

Best Answer

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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