# Significance testing with survival analysis (actuarial method)

#### Gabriel

##### New Member
Hi,

I'm teaching myself survival analysis with free resources on the web. I'm quite confident that I'm correct, but I just want to clarify that I have interpreted everything correctly!

I am comparing the survival of a control and test group. I want to determine whether there is a significant difference in survival at 12 months.

I am using SAS proc lifetest. I have a very large dataset (in the 100s of thousands) so I am using the actuarial method. My syntax is as follows.

proc lifetest data=sample_data method=life width=30 plots=(s,h) graphics outs=survival;
time days_in_study*event (0);
strata group;
run;

My main question is:
How do I determine whether there is a significant difference in survival between the control and test groups at 12 months?

I can think of two options.

Option 1 (I think this is best): Plot out the survival function of the two groups and compare. The SAS output provides lower and upper 95% confidence intervals for the survival distribution functions. if the confidence interval for the cumulative survival functions of the control group and test group do not overlap at 12 months, then they are significantly different. Is this correct?

Option 2: Do some sort of t test of independent proportions where I find the effective sample size at 12 months for each group and the cumualtive survival for each group and then see if there's a significant different. This seems like it would lead to an incorrect repsonse as it is unclear which sample size to use. I.e. what effective sample size do you use, is it the effective sample size at 12 months? Or the effective sample size at time zero?
Keep in mind that I contrinually have subjects coming in and out of the study. Hence the need for survival analysis.

Thank you so much in advance for your help! Also, please let me know if you require any additional information

Note: I am aware that I can look at the tests of equality of strata ouput (which provides log-rank, wilcoxen and -2log(LR) ). However, this just shows whether the two survival curves are significantly different at any point in time, not whether they are specifically different at 12 months. It also doesn't indicate directionality of differences (is test>group or group>test). For example, the two survival curves could criss cross wildly and this would come up as significantly different I believe. But for my purpose there would be no clear conclusions I could draw about one having lower survival than the other, just that they're different. Please let me know if I am correct here as well!

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#### Gabriel

##### New Member
Also, if no one here knows the answer to this (as it is somewhat of a specialised technique) could people recommend a forum/listserv etc where I may be able to get an answer?

Thanks!

#### Mean Joe

##### TS Contributor
How are you treating individuals that enter at different times, are you taking into account the date of entry?

#### Gabriel

##### New Member
Survival analysis takes it into account automatically.
You just have to specify how long the individual has been followed (i.e. days between entry and exit) and then whether they need to be censored or not (i.e. whether they exited due to the event under investigation or due to another reason such as dropping out). The main reason for using survival analysis is that it can deal with the continuous entry and exit of participants.

See http://www.ats.ucla.edu/stat/sas/seminars/sas_survival/default.htm
It explains it well.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
This seems like something you should be able to do. I have not done a Lifetest for a few years, but if no one proposes an easy way to do it, I would say perhaps the following (similar to what you proposed) may work for now. Change your data so if a person was censored after 12 months they are no longer censored. Then in your output look at the "Summary of the Number of Censored and Uncensored Values", which presents the data per Strata. Then perform a Chi-sq or Fisher Exact Test using these count data. So this would be a comparision of the proportions at 12 months. Though, I hope some else proposes a better way that uses something like a contrast statement.

#### Mean Joe

##### TS Contributor
Are you using the WIDTH= option (alternatively, the INTERVALS statement)?

proc lifetest width=1;
time days*event(0);
strata group;

The output will give Effective Sample Size, Survival, and Survival Standard Error. Unfortunately with the WIDTH= option, if your data goes well beyond 12 months then the output will be long.

Alternatively,
proc lifetest;
intervals 1 2 3 4 5 6 7 8 9 10 11 12;
time days*event(0);
strata group;

#### Gabriel

##### New Member

Yes, I am using the WIDTH= option. Please refer to my initial post where I include my code. I am using a Width of 30 days (so effectively monthly intervals).

So, what then do I do with the output when it provides Effective Sample Size, Survival, and Survival Standard Error? If I use the OUTS= statement, then it also provides the 95% upper and lower bounds of the confidence interval for the survival distribution function. These are labelled in the output as SDF_LCL and SDF_UCL. I was thinking that the best method would be to plot these out for each group and see whether the confidence intervals overlap at 12 months. If they do not overlap, then there is a significant difference between groups. If they do overlap then there is no significant difference.
Is that correct?

Are you using the WIDTH= option (alternatively, the INTERVALS statement)?

proc lifetest width=1;
time days*event(0);
strata group;

The output will give Effective Sample Size, Survival, and Survival Standard Error. Unfortunately with the WIDTH= option, if your data goes well beyond 12 months then the output will be long.

Alternatively,
proc lifetest;
intervals 1 2 3 4 5 6 7 8 9 10 11 12;
time days*event(0);
strata group;