Reporting survival analysis

Reporting Survival (Time-to-Event) Analyses in Research Manuscripts

Survival analysis, also known as time-to-event analysis, is a powerful and crucial tool in statistics to study the time until a specific event occurs, such as death, disease recurrence, or any other defined endpoint.

Reporting Survival Analyses

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Introduction

Survival analysis, also known as time-to-event analysis, is a powerful and crucial tool in statistics to study the time until a specific event occurs, such as death, disease recurrence, or any other defined endpoint. Survival analyses are frequently used in clinical studies, epidemiological studies, and in several contexts when researchers are interested in how time changes the outcome of interest. Careful, accurate, and standardised reporting of survival analysis is important when it comes time to discuss the interpretation, reproducibility, and clinical relevance. We aim to introduce a structured approach to reporting survival analyses based on guidelines and a review of the literature.

1. State the Purpose of the Analysis

  • The first step in reporting survival analysis is defining the purpose of the analysis clearly. Specifically, you should explain what problem you were investigating or the hypothesis you were testing in the analysis. Doing so is helpful in making sure the reader knows what you are attempting to analyse and why!
  • For example, “to estimate the survival probability and assess treatment group differences in a cohort of patients with lung cancer” (Zhang et al., 2022). The purpose should also be consistent with the overall type of survival analysis used in the analysis (i.e., overall survival (OS), progression-free survival (PFS), etc.). Outlining the purpose provides context for the reason and choice of a specific statistical method (i.e., Kaplan-Meier Curves; Cox Regression) that will be used to answer that specific question.

    • 2. Define the Time Frame

  • In survival analysis, a temporal definition must be stated to measure the event of interest consistently. The analysis typically begins at a well-defined start point (e.g., the point of diagnosis or the start of treatment) and continues until a well-defined end point (e.g., death, recurrence, or last follow-up). By providing the timelines, ambiguity is eliminated, and researchers need not guess if they want to do a replicated study.
  • As an example, time zero could be the date of diagnosis for all patients in the cohort, and the event could be time until death or the occurrence of a specific event of interest (Coemans et al., 2022). Time begins and continues in this manner; all participants have a consistent means to have their survival time calculated.
  • Censoring is one of the main concerns in survival analysis. It occurs when a participant has not experienced the event of interest by the end of the study or is lost to follow-up. It is important to state with certainty how you treated censoring in your analysis, as censoring will have an impact on your results and their interpretation.
  • Censoring may occur for various reasons, including loss to follow-up and the end of the study period. For example, patients randomised to a trial may not have experienced the event by the time the study concludes, or random participants in a cohort study may decide to drop out of the trial. Clearly defining these censoring criteria, including the reason for censoring and how you handled it, where possible, is a means to ensure validity in your results (Mansournia et al., 2022).
  • Furthermore, it is important to explain how censoring is expected to impact the various statistical procedures you will use to obtain survival estimates (e.g., Kaplan-Meier) to understand the influence of censoring on those estimates.
  • There are various ways to estimate survival probabilities, and this ought to be reported. The Kaplan-Meier estimator is a non-parametric estimate that is frequently used in health economics development for estimating survival probabilities over time. The Kaplan-Meier estimator produces survival curves, which allow comparisons between groups. Life tables may also be useful, especially when dealing with grouped data and time intervals.
  • Alternatively, if applicable, a Cox proportional hazards model may be employed to estimate the relationship between survival over time and covariates (Li et al., 2022). In doing so, it is important to consider that the Cox model is based on different assumptions than the Kaplan-Meier or life tables (e.g., the proportional hazards assumption) and to test and validate those assumptions to ensure the Cox model can be used in the way it was intended to be used (Westin et al., 2023).
  • There are various ways to estimate survival probabilities, and this ought to be reported. The Kaplan-Meier estimator is a non-parametric estimate that is frequently used in health economics development for estimating survival probabilities over time. The Kaplan-Meier estimator produces survival curves, which allow comparisons between groups. Life tables may also be useful, especially when dealing with grouped data and time intervals.
  • Alternatively, if applicable, a Cox proportional hazards model may be employed to estimate the relationship between survival over time and covariates (Li et al., 2022). In doing so, it is important to consider that the Cox model is based on different assumptions than the Kaplan-Meier or life tables (e.g., the proportional hazards assumption) and to test and validate those assumptions to ensure the Cox model can be used in the way it was intended to be used (Westin et al., 2023).

    • 6. Report Median Survival Time

  • Median survival time is a common statistic used to summarise survival data because it is the time point in which 50% of the subjects have experienced the event of interest. This statistic is particularly useful in survival analysis because it provides a valid summary of survival time with censoring present.
  • For example, “The median survival time for patients receiving treatment A was 15 months with a 95% confidence interval (CI) of 12 to 18 months” (Zhang et al., 2022). It is important to report this statistic when comparing treatment groups and evaluating the relative efficacy of treatment.

    • 7. Use Visual and Tabular Presentation

  • Survival analysis data is communicated and presented visually and also in tables for the best clarity. Displays of survival curves in the form of Kaplan-Meier plots are useful in displaying survival curves and tables providing important contextual information (detailed time points, number of participants at risk, and survival probabilities with confidence intervals).
  • Kaplan-Meier plots allow the reader to assess the survival differences between groups quickly, and the reader may notice at what time point or points the survival curves are diverging, which may suggest an important treatment effect or difference (Han & Jung, 2022). A table enhances the information with numerical data corresponding to the Kaplan-Meier curves by presenting numbers for the time point as well as the number of participants remaining at risk.

    • 8. Comparing Survival Between Groups

  • It is advisable to be explicit when referring to the statistical test you used to compare survival across groups. When making comparisons of survival curves, the log-rank test is generally used (Zurakowski & Staffa, 2023). The log-rank test asks the question of whether the survival experiences of the groups diverged significantly over the time frame under study. In addition, a p-value must be reported from this test with some emphasis on how we interpret those about whether we treat the differences observed as statistically significant or not.
  • For example, as Li et al. (2022) noted, “The p-value from the log-rank test showing a comparison of survival between Treatment A and Treatment B was 0.03, which guided us to the conclusion there was a statistically significant difference in survival rates.”
  • There is something very reassuring about having differences that have mathematically significant supporting evidence to help confirm or reject our hypothesis about whether groups had different experiences in their “lives”.

    • 9. Report Survival Regression Models

  • If you utilise survival regression models to explore the relationship between covariates and survival, you should describe the results in detail. The Cox proportional hazards model is the most widely used for estimating the effect of explanatory variables (age, gender, treatment group, etc.) on a survival time. Other parametric survival models (e.g., the Weibull model) can also be used.
  • For each covariate, you must report the hazard ratio (HR), the 95% confidence interval (CI), and the p-value. The HR, CI, and p-value provide an understanding of the relative risk of the event happening to individuals in each category of the explanatory variable of interest.
  • For example, “The hazard ratio of Treatment A compared to Treatment B was 0.65 (95% CI: 0.50-0.85, p = 0.002)” suggests that Treatment A was associated with a lower risk of the event than Treatment B (Westin et al., 2023).

    • 10. Specify Statistical Software Used

  • To explicitly provide transparency and reproducibility in the analysis, it is appropriate to name the statistical software used. Various kinds of statistical software are used to conduct a survival analysis, such as R, SPSS, SAS, and STATA. When you report the software, you are, in providing other researchers the opportunity to conduct a replication of your analysis using the same set of software tools.
  • You can state something like, “Survival analysis was performed using R package ‘survival’ version 3.2-7” (Denfeld et al., 2023) and be very specific about what you did. This allows the reader good detail to replicate the survival analysis in R and confirm the results.

    • Conclusion

    It is important to report survival (time-to-event) analyses accurately for transparency, validity, and reproducibility of research findings. When researchers adhere to reporting guidelines in this area, they will further ensure that their results are interpretable and meaningful to their clinical fields. Whether reporting Kaplan-Meier survival curves, median time to survival, or regression analysis with predicted survival, care must be taken to report and communicate the details of the survival analysis in a way that clearly conveys the outcomes of that analysis. Following reporting best practices enhances research and adds credibility to the collective knowledge and enhances the robustness of any conclusions derived from survival data.

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    References

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    2. Zhang, Y., Chen, L., Hu, G. Q., Zhang, N., Zhu, X. D., Yang, K. Y., … & Tang, L. L. (2022). Final overall survival analysis of gemcitabine and cisplatin induction chemotherapy in nasopharyngeal carcinoma: a multicenter, randomized phase III trial. Journal of Clinical Oncology, 40(22), 2420-2425.

    3. Wang, Z., & Sun, J. (2022, August). Survtrace: Transformers for survival analysis with competing events. In Proceedings of the 13th ACM International Conference on Bioinformatics, Computational Biology and Health Informatics (pp. 1-9).

    4. Westin, J. R., Oluwole, O. O., Kersten, M. J., Miklos, D. B., Perales, M. A., Ghobadi, A., … & Locke, F. L. (2023). Survival with axicabtagene ciloleucel in large B-cell lymphoma. New England Journal of Medicine, 389(2), 148-157.

    5. Li, Y., Hwang, W. T., Maude, S. L., Teachey, D. T., Frey, N. V., Myers, R. M., … & Shaw, P. A. (2022). Statistical considerations for analyses of time-to-event endpoints in oncology clinical trials: illustrations with CAR-T immunotherapy studies. Clinical Cancer Research, 28(18), 3940-3949.

    6. Denfeld, Q. E., Burger, D., & Lee, C. S. (2023). Survival analysis 101: an easy start guide to analysing time-to-event data. European Journal of Cardiovascular Nursing, 22(3), 332-337.

    7. Mansournia, M. A., Nazemipour, M., & Etminan, M. (2022). A practical guide to handling competing events in etiologic time-to-event studies. Global Epidemiology, 4, 100080.

    8. Zurakowski, D., & Staffa, S. J. (2023). Statistical power and sample size calculations for time-to-event analysis. The Journal of Thoracic and Cardiovascular Surgery, 166(6), 1542-1547.