How to interpret -streg- result for a one-standard-deviaiton increase in a covariate

[Xinyu Yu]

Hello,
I am runing AFT models using the - streg- command, but have trouble interpreting the result. I am using Stata 18 for Windows.

I understand that a positive coefficient (or a time ratio greater than 1) indicates that time is decelerated by a unit increase in the covariate. For example, a coefficient of 0.416 means a one-unit increase in the covariate increases the survival time by 51.6% (calculated as exp(0.416) - 1).
However, I am unsure how to calculate the effect of a one-standard-deviation increase in the covariate on time. Does the time change to exp(coefficient*standard deviation of the covariate)? Is there a specific Stata command that can handle this?

Thank you so much.

[Clyde Schechter]

Does the time change to exp(coefficient*standard deviation of the covariate)?

Yes.

Is there a specific Stata command that can handle this?

-help nlcom-

All of that said, why do you want to do this? If the variable to which the coefficient in question applies has natural units that people are familiar with, then the difference in survival time associated with a 1 unit difference in the variable is a natural, and easily understood concept. By contrast, who knows what the standard deviation is? You do. But who else has looked as your outputs? Suppose the standard deviation is something like 3.786219. Why would anybody want to know what the difference in survival time associated with a difference of 3.786219 units is? Worse, since only you actually know the standard deviation in your sample is 3.786219, why would anybody want to know what the difference in survival time associated with some undisclosed, mysterious difference in the variable is. Oh, perhaps the undisclosed mysterious difference can be related to some percentiles if that variable has a normal (or, for that matter, some other known parametric) distribution. But what if the variable's distribution is more complicated than that--which is so often the case in real life.

My point is that if your variable has natural units of its own, all you accomplish by reporting things in terms of standard deviation changes is obfuscating the results and confusing your audience. This approach really should be restricted to variables that have no natural units of their own, or whose natural units would not be familiar to anyone but a specialist in the measure itself.

[Xinyu Yu]

Thank you! I agree that reporting with unit changes is more straightforward and understandable.

My covariate of interest is a Blau's index that ranges from 0 to 1. It is unlikely, in practice, for the covariate to change by one unit. Therefore, I thought using a one-standard deviation change would be more appropriate (or realistic) when discussing its economic significance, given the nature of the variable. Suggestions are welcome. Thanks.

[Clyde Schechter]

In a situation like this where a 1-unit change in the variable is impossible or unrealistic, why not show the outcome difference associated with a 0.1 unit change in the the Blau index? (Or if a 0.1 unit change is also unrealistic, a 0.01 unit change, etc.)

[Xinyu Yu]

Thanks a lot, Clyde. I truly appreciate this—it’s very helpful.