9.4.10 Survival Curves, Kaplan-Meier Plots and Hazard Ratios

Interprets “Survival” Curves: Median Survival, Relative Survival and Kaplan-Meier Plots and Hazard Ratios

Survival analysis is a branch of statistics that deals with time-to-event data, such as time to death, time to disease progression, or time to recovery. A common way to display survival data is through survival curves, which show the proportion of subjects who have not experienced the event of interest over time.

In medical research, particularly in the field of oncology, survival curves are used to visualize the survival probabilities of patients over time. There are various types of survival curves, each providing a different perspective on survival analysis. The most common survival curves include median survival, relative survival, and Kaplan-Meier plots.

Median “survival” curves:

Median survival is a measure used to describe the time at which half of the patients in a study are still alive. This is often reported as the “median survival time” and is a useful way to summarize the overall survival experience of a group of patients. The median survival can be determined by examining the point at which the survival curve intersects the 50% probability line. It is important to note that median survival time does not provide information on the entire distribution of survival times and should be interpreted along with other measures of survival, such as the range of survival times or the proportion of patients surviving at specific time points.

Relative “survival” curves:

Relative survival is a measure of survival that compares the survival of a group of patients to the expected survival of a similar group of people in the general population. This takes into account the fact that some patients may die from causes unrelated to the disease of interest. It is often used in cancer research to account for differences in background mortality rates.

Relative survival is a measure that compares the observed survival of patients with the expected survival of a comparable group of individuals from the general population. This allows researchers to estimate the excess mortality risk associated with a specific disease or treatment. Relative survival is calculated by dividing the observed survival of patients by the expected survival of the general population. A relative survival rate of 1 indicates that patients have the same survival probability as the general population, whereas a rate greater than 1 indicates better survival and a rate less than 1 indicates worse survival. Relative survival can be useful in comparing the survival of different patient groups or assessing the impact of new treatments on survival.

Kaplan-Meier plots:

Hazard Ratios:

Interpreting hazard ratios (HRs) is an important aspect of understanding the results of clinical studies, particularly those involving time-to-event data, such as survival studies. Here’s a short guide on how to interpret hazard ratios:

Hazard ratios are often represented graphically on a Kaplan-Meier curve, also known as a survival curve. The Kaplan-Meier curve is a popular tool used in medical research to display the survival probabilities over time for different groups, such as treatment and control groups in a clinical trial.

A hazard ratio (HR) is a measure used in survival analysis to compare the risk of a specific event occurring at any given point in time between two groups. It is commonly used in medical research to assess the effect of treatments or risk factors on the time to an event, such as death, disease progression, or another outcome of interest. Here’s what the values mean:

Interpreting Hazard Ratios:

• HR = 1: Indicates no difference in risk between the two groups. The event rate is the same in both groups.

• HR < 1: Indicates a reduced risk in the treatment or exposed group compared to the control or unexposed group. For example, HR = 0.58 means that the treatment group has a 42% lower risk of the event occurring compared to the control group (1 – 0.58 = 0.42 or 42% reduction).

• HR > 1: Indicates an increased risk in the treatment or exposed group compared to the control or unexposed group. For example, HR = 3.07 means that the treatment group has a 207% higher risk of the event occurring compared to the control group (3.07 – 1 = 2.07 or 207% increase).

High and Low Hazard Ratios:

• High Hazard Ratios (> 1): Indicate that the event of interest is more likely to occur in the treatment or exposed group. High HRs suggest a potentially harmful effect of the treatment or risk factor. For instance, an HR of 3.07 for lofepramine indicates a substantially increased risk of myocardial infarction.
• Low Hazard Ratios (< 1): Indicate that the event of interest is less likely to occur in the treatment or exposed group. Low HRs suggest a protective effect of the treatment or risk factor. For example, an HR of 0.58 for selective serotonin reuptake inhibitors (SSRIs) indicates a reduced risk of myocardial infarction.

Confidence Intervals (CIs):

• The HR is usually presented with a 95% confidence interval (CI).
• If the CI includes 1 (e.g., 0.8 to 1.2), the difference in hazard between the two groups is not statistically significant.
• If the CI does not include 1 (e.g., 0.6 to 0.9), the difference is considered statistically significant.

Context and Clinical Significance:

• The magnitude of the HR and the clinical context must be considered. For example, an HR of 0.8 may be clinically significant in a study with a major endpoint like mortality.
• Also, consider the baseline risk of the event; HR does not provide information about the baseline risk, only the relative difference between groups.

Causality:

• HRs do not imply causation. They show an association between the treatment and the outcome in the context of the study.

Examples:

• If a study reports an HR of 0.75 for mortality with a new drug compared to a placebo, it suggests that the risk of death is 25% lower in the drug group than in the placebo group at any given time during the study.
• If an HR for disease recurrence is 1.3 with a new treatment, it suggests that there is a 30% higher risk of disease recurrence with the treatment compared to the control.

Limitations:

• HRs depend on the follow-up time and are affected by dropouts and crossovers in clinical trials.
• They assume the ratio of hazards is constant over time, which may not always be the case.

In summary, hazard ratios are a valuable tool in clinical research for comparing the risk of events between groups over time. However, they must be interpreted in the context of the whole study, including the confidence intervals, clinical significance, and study design.

It is important to note that survival analysis can be influenced by several factors, such as censoring, missing data, and confounding variables. Therefore, careful statistical methods and interpretation are necessary when analyzing and interpreting survival data.

References:

1. Kleinbaum, D. G., & Klein, M. (2012). Survival analysis: A self-learning text. Springer Science & Business Media.