Survival models analyze the time until one or more events occur, such as death in biological organisms or failure in mechanical systems. These models are widely used across fields like medicine, biology, engineering, and public health to study time-to-event phenomena. To ensure accurate results, survival analysis relies on key assumptions and careful study design.

1. Survival Times Are Positively Skewed
   Survival times often exhibit positive skewness, unlike the normal distribution assumed in many other analyses. This means events tend to occur more frequently early on, with fewer occurrences as time progresses.
2. Censoring of Data
   Censoring occurs when the full survival time for an individual is not observed, but it is distinct from missing data. Common causes of censoring include participants withdrawing from a study, the study period ending before the event occurs, or participants experiencing unrelated events (e.g., death from an unrelated cause). For example, in a study on heart disease, a participant who dies in an accident would have their data censored at the time of death.
3. Independent Censoring
   This assumption posits that the reasons for censoring are unrelated to the likelihood of the event of interest. For instance, if participants with severe symptoms are more likely to drop out of a study, survival estimates may become biased. Ensuring that censoring is independent of the health status of participants is critical for reliable analysis.
4. Proportional Hazards (Specific to Cox Models)
   The Cox proportional hazards model assumes that the hazard ratio between any two individuals remains constant over time. For example, if one group's risk of an event is twice that of another at the start of a study, this risk ratio must hold throughout the study period.
5. Stationarity
   Stationarity assumes that the probability of the event changing over time does so similarly across all groups unless explicitly modeled. For example, when comparing survival times between patients treated with a new drug versus a standard treatment, external factors influencing survival should impact both groups equally unless accounted for.
6. Clear and Clinically Important Events
   The event of interest should be clinically significant and clearly defined to enable accurate measurement and analysis. Ambiguous or misclassified events (e.g., unclear relapse criteria) can compromise the validity of survival time data.
7. Adequate Follow-Up Period
   The follow-up duration should be long enough to observe a sufficient number of events for robust statistical power. Short follow-up times may miss critical events and lead to incomplete or biased conclusions. It is also essential to minimize differences in event risk among participants recruited at different times to avoid skewed results.

Design Considerations in Survival Analysis

Survival studies must be carefully designed to account for these assumptions. A clear definition of the event, sufficient follow-up time, and strategies to minimize censoring bias are vital. When these factors are well-managed, survival models can provide valuable insights into time-to-event phenomena across a range of disciplines.