An alternative, and more sensitive, approach to detecting differences in outcome in sepsis

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When comparing a characteristic (e.g. outcome) between two groups, tests of continuous (as opposed to categorical) data that assume parametric (as opposed to non-parametric) distributions are the most powerful. Currently, we measure outcome differences in sepsis trials in two ways. Typically, we compare mortality rates at a given time-point using categorical, parametric tests (e.g. ?² or Fisher's Exact test of differences in mortality at day 28) or we compare survival times using categorical, non-parametric tests (e.g. the Log-rank test to compare Kaplan-Meier curves). But survival after sepsis decreases exponentially [1]. Thus, survival could be described by exponential curves, which can be compared using continuous, parametric tests, such as the Cox's F-test. We therefore used this approach in a cohort of septic patients to determine sample size requirements in comparison to traditional approaches.

Methods

Patients: 1102 patients with severe sepsis enrolled in a US multi-center trial.

Sub-groups: We divided patients into those with and without septic shock to select two groups with a difference in survival (10-15%) typical for many power calculations in sepsis trials.

Statistical procedures: For each sub-group, we plotted the survival to day 28 and fit distributions with exponential curves using the maximum likelihood procedure. Curves were then compared using the Cox's F-test. We also compared differences in outcome using the Fisher's Exact test (for day-28 mortality) and the log-rank test. Statistical significance was assumed at P<0.05.

Sampling procedure: After comparing tests on the entire sample, we then drew progressively smaller random samples of the cohort and repeated the test comparisons to determine the point at which statistical significance was lost for each test.

Results

Patients with shock had a higher mortality than those without shock (see Table). This difference was statistically significant by Fisher's Exact and Log-rank tests until sample size fell below 500. Survival in all sub-groups was modeled by exponential curves with excellent fit (R² >0.98). Comparing these curves by Cox's F-test, statistical significance was maintained with a much smaller sample size (see Fig.).

Conclusion

Taking advantage of the parametric distribution that characterizes survival after sepsis, we can apply a test that finds statistical differences in survival with smaller sample sizes than traditional approaches. These data suggest that the application of exponentially-modeled survival curve comparisons may be the preferred approach in studies with small sample sizes, such as Phase II trials. Furthermore, this approach may prove to be generally preferable to categorical survival data comparisons, such as day-28 mortality.

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