Statistics Collaborative - Design and analysis for biomedical research


Survival analysis

Many clinical trials compare two or more treatment groups in terms of time to a defined event. Survival (time to death) is only one such outcome. Time to any well-defined event (e.g., re-occlusion of a grafted blood vessel, first metastasis, discharge from the hospital) is generally analyzed by means of survival analysis.

Statistics Collaborative, Inc. (SCI) has experience using a wide variety of survival-analysis methods in many different settings. We summarize survival outcomes using, for example, Cox proportional hazards and Kaplan-Meier estimates. We generally compare treatment groups with the log-rank test, but we may use other methods if we have a priori reason to believe the survival curves do not have proportional hazards.

SCI tailors survival analyses to the study design, the data sources, and the recipient of the analyses. For example, when preparing survival analyses for a Data Monitoring Committee (DMC), we may emphasize reporting how we found events in an interim database and use very basic survival analysis methods for summarizing the outcome. For a clinical study report or publication of the final results, we may propose a complicated method for censoring or suggest stratifying survival estimates. In every case, we work closely with the sponsor to make sure of using the appropriate survival analysis methods for the time-to-event outcomes in the study. In particular, when we make a recommendation for analysis, we include advice on how events should be detected during the study (e.g., in real-time or in regular, widely-spaced assessments).

SCI has developed several formats for presenting the results of survival analyses. In our reports, we typically include specially designed figures that display Kaplan-Meier curves. We annotate these figures with other relevant information, including the number at risk at certain timepoints, log-rank statistic and p-value, and median survival times. To supplement the figures, we may also include tables containing additional information. With these formats, we ensure the easy comprehensibility of our survival analyses to statisticians and non-statisticians alike, regardless of the complexity of the methods.

Examples of SCI's work in survival analysis:

  • Poisson regression: While analyzing the incidence of new episodes of malaria in a Phase 2b field trial in sub-Saharan Africa, SCI utilized Poisson regression methodology to assess whether subjects in either vaccine arm experienced a higher rate of clinical malaria over the course of the trial. This method allowed us to adjust for time, as some subjects were followed for less time due to early withdrawal or loss to follow-up.
  • Interval censoring: For an oncology trial, SCI performed sensitivity analyses of the trial's time to progression endpoint using interval-censored methods. Assessments of progression occurred roughly every three weeks during treatment and bimonthly following treatment. Through the parametric and semiparametric estimates that reflected the periodic nature of the assessments of progression, readers of the trial's statistical report were able to gauge the effect of the primary analysis's assumption of continuous assessments on the estimated hazard ratio.
  • Adjusted time at risk: During a Phase 2b field trial in sub-Saharan Africa for a candidate malaria vaccine, subjects were considered not-at-risk of infection if they left the endemic area for more than two weeks at a time or if they took medication to treat existing cases of malaria. SCI performed a standard log-rank test as the primary survival outcome, as well as analyses that adjusted for time that subjects were not at risk of malarial infection. This adjustment method enabled us to archive a more accurate assessment of the amount of time lapsing before someone contracted clinical malaria and whether this adjustment impacted the results of the trial.