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My goal is to show independency of factors related to survival of a small size sample (26 patients) for a period of time, this sample was divided in 2 groups (16 vs 10 patients), the events were little (7 in total). I had multiple cases with expected values less than 5. Is it appropriate to use the Log-rank test in this study? If it isn't, what can I use instead?

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The biggest problem is that you don't have enough events to do much that's reliable. To avoid overfitting in survival analysis, you typically need about 15 events per predictor that you are evaluating. Even with this simple 2-group comparison (1 yes/no predictor, group membership), you're too low by about a factor of 2. The additional specific problem with the "expected values less than 5" is the potentially unreliable approximation needed to evaluate the significance of the chi-square statistic for the log-rank test with small numbers of counts.

With this small a sample you can avoid that approximation with a permutation test. You evaluate the statistic for all possible assignments of group membership to the cases (5311735 possibilities here for assigning 26 cases to groups of size 10 and 16) as a null distribution, and determine from that distribution the percentile of the value found for the statistic with the actual group assignments.

See the discussion of SurvivalTests in the manual for the R coin package for implementation and the different types of assumptions you need to choose among for permutation tests in survival analysis. Even then there's a big risk that vagaries of the sampling that gave you these 26 patients will make the results unreliable when applied to new patients. (I speak from personal experience.)

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    $\begingroup$ What are your thoughts on applying a parametric survival model? Even a simple exponential? $\endgroup$
    – AdamO
    Dec 22, 2022 at 16:41
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    $\begingroup$ @AdamO then one really should assess whether the parametric assumptions are met, with too few cases here to make a reliable assessment. Maybe permutations tests with Cox-model likelihood ratio statistics (versus the score/log-rank test statistics)? But I'm very reluctant to recommend any of those, based on personal experience with too few events. $\endgroup$
    – EdM
    Dec 22, 2022 at 16:51
  • $\begingroup$ EdM and AdamO, Thank you very very much, your answers enlightened me! Best regards $\endgroup$
    – Soffee
    Dec 22, 2022 at 18:24
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    $\begingroup$ @EdM I'm half curious about the robustness to violations of assumptions versus the power to infer a significant difference in survival... $\endgroup$
    – AdamO
    Dec 22, 2022 at 18:26

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