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I have a database with patients and did survival analysis in SPSS. SPSS gave me the mean and median survivals with 95% confidence intervals. However, I also want the 1-,3-, and 5-year survival times with 95% confidence interval. I can of course estimate it from the curve but I was wondering if there is a more precise way? And from the curve I cannot get the 95% confidence intervals...

Also, the log-rank test is giving me no significant p-value. But this test is for the entire survival curve if I understood it correctly. I was wondering if I can also do a test for group differences in the 1-,3-, and 5-year survival times? And how?

Thanks for your help in advance!

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  • $\begingroup$ You just index the survival times you're interested in in the saved Kaplan Meier limit and standard error estimates. Not really any point testing the specific times unless they're prespecified hypotheses. There are advanced methods (cochrane mantel haenszel and restricted mean survival) for testing survival at specific points, but SPSS doesn't do that. ibm.com/support/pages/… $\endgroup$
    – AdamO
    Mar 17, 2021 at 21:59
  • $\begingroup$ Hi thanks for answering! What do you mean with "index the survival times"? Where can I find the 1-,3, and 5-year survival with SE and 95% confidence interval like you suggested? Sorry I am a student and just started with doing survival analysis. $\endgroup$
    – Roos
    Mar 18, 2021 at 9:33
  • $\begingroup$ The stored Kaplan Meier limit estimates should be a matrix with the first vector $t$ of survival times (failure times, actually). You find the latest time $t$ prior to the time point you're interested in, and report the survival and 95% CIs from that. It's numerically the exact same value that's shown in the plot of the KM curve and 95% CI. $\endgroup$
    – AdamO
    Mar 18, 2021 at 16:21

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A log-rank test is a test of whether the hazard as a function of time differs between 2 groups. If the log-rank test doesn't show a significant difference between 2 curves in this respect, then you should be very reluctant to evaluate differences at specific survival times. That's a general principle of statistical tests: if the overall test isn't significant it's best to stop there. (The part of the question specific to how to do this in SPSS is off-topic on this site.)

That said, if you have a multiple-regression or other model that takes several covariates into account (generally a good idea in survival modeling), a log-rank test between 2 groups might not be informative if they differ in other covariate values. So if you have a more elaborate survival model than what you examined with your log-rank test, you certainly can examine survival estimates at specific times in the more elaborate model if it is significant overall.

In response to comment:

Unless you are examining a randomized controlled trial, trying to discern the actual effect of a treatment on outcome faces several problems. One good place to start learning about these issues is the freely available Causal Inference book by Hernán and Robins, which begins with simple, accessible situations and works up to analysis of complex longitudinal data sets with time-varying covariates and treatments.

There are several ways to try to adjust for differences in covariates between treatment groups. Otherwise, those differences between treatment groups could severely bias your estimate of the effect of treatment per se.

One way to approach this is a multiple regression that includes covariates associated with outcome as predictors. For survival analysis, this is often done with a Cox proportional hazards regression. See Harrell's Regression Modeling Strategies book or course notes for guidance in regression modeling.

Another way is to include or weight cases according to their probabilities, as a function of the covariates, of being in the treatment groups ("propensity scores," used for case matching or weighting). Those probabilities are often estimated by logistic regression, covered in the Harrell references.

Individually, those approaches require correctly specified models. As Hernán and Robins discuss, using both approaches together can provide a "doubly robust" assessment such that if either the regression or the propensity model is correct you can assess treatment-specific effects.

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  • $\begingroup$ Thank you! I will then only use the log-rank test. I am comparing 2 groups with different treatments. Of course I want the difference to be due to the treatment and not due to other variables. By doing multiple-regression you can find this out if I understand this correctly? For example, if age or gender is significantly different between the 2 treatment groups? $\endgroup$
    – Roos
    Mar 18, 2021 at 9:37
  • $\begingroup$ "A log-rank test is a test of whether the hazard as a function of time differs between 2 groups" that's not quite right. The log-rank test is the Score test of the Cox model. It's a test of the hazard ratio, invariant of time. (An advanced finding is that if the hazard ratio varies across time, the log-rank test is a test of the event-time weighted average hazard ratio) $\endgroup$
    – AdamO
    Mar 18, 2021 at 16:33
  • $\begingroup$ @AdamO the Wikipedia entry says: "The null hypothesis is that the two groups have identical hazard functions, $H_0 : h_1(t) = h_2(t)$." I appreciate that under proportional hazards the log-rank test is then the score test for a Cox model, but in the broader context I don't see that the Wikipedia statement, which I used as the basis for that part of this answer, is incorrect. If it is incorrect as stated there, a reference (and correction to the Wikipedia entry) would be helpful. $\endgroup$
    – EdM
    Mar 18, 2021 at 16:57

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