Time to Event Data: What to Present? Hazard Ratio, Median Time, Survival Rate?

One of the common endpoints in clinical trials is time to event as calculated as the duration from the time of randomization to the time of occurrence of the specific event (either the good or bad event). In oncology studies, the time to event variable can be overall survival (OS) as calculated from the time of randomization to the time of death or progression-free survival (PFS) as calculated from the time of randomization to the time of disease progression or death (whichever occurs first). In non-oncology studies, the time to event variable is everywhere:

• Time to first exacerbation in COPD, bronchiectasis 
• Time to first clinical worsening event in pulmonary hypertension
• Time to clinical recovery in COVID-19 therapeutical trials
• Time to healing of all non-aborted genital herpes lesions in recurrent genital herpes infection treatment studies 

While time to event may not be related to the death (survival), the time to event analysis is still commonly called 'survival analysis'. 

The statistical analyses for time to event variable include mainly the Kaplan-Meier estimate along with the log-rank test for different survival curves and Cox proportional hazard regression model (or Cox regression in short). 

The statistics can include survival rate (or rate of subjects without an event), median survival time (median time to event), hazard ratio, and their 95% confidence intervals. 

Survival rate (or rate of subjects without an event) is the percentage of subjects in a study or treatment group who are still alive for a certain period of time after they were randomized and started treatment for a disease, such as cancer. It may be called a milestone survival rate. A five-year survival rate will be the percentage of people in a study or treatment group who are alive five years after their randomization or the start of treatment. For clinical trials with short durations, usually, a short survival rate (for example, 6-month survival rate, 1-year survival rate, 3-year survival rate) will be more commonly used.  

Median survival is a statistic that refers to how long subjects survive with a disease in general or after the randomization or initiation of the treatment. It is the time — expressed in weeks, months, or years — when half the subjects are expected to be alive. It means that the chance of surviving beyond that time is 50 percent. similarly, median time to event is a statistic that refers to how long subjects have no specific event after the randomization or initiation of the treatment. It is the time — expressed in weeks, months or years — when half the subjects are expected to be event free. It means that the chance of having an event beyond that time is 50 percent.

Hazard ratio is the ratio of hazards and equals to the hazard rate in the treatment group ÷ the hazard rate in the control group. Hazard rate represents the instantaneous event rate, which means the probability that an individual would experience an event at a particular given point in time after the intervention. 

To present the analysis results for time to event variable, all different statistics can be displayed in the same table. The summary table can be designed as the following: 

Table 14.2.x 

Summary and Analysis of Time to XXX Event

ITT Analysis Set

	Test Drug (N=xx)	Control (N=xx)	p-value
Number of Subjects with Event (n, %)	xx (xx.x)	xx (xx.x)	0.xxx [1]
Number of Subjects Censored (n, %)	xx (xx.x)	xx (xx.x)
Time to XXX Event (time unit)
Kaplan-Meier Estimate			0.xxx [2]
25th Quartile (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
Median (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
75th Quartile (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
Rate (%) of Subjects without an    Event for at Least
1 time unit (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
2 time unit (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
3 time unit (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
4 time unit (95% CI)	xx.x (xx.x, xx.x)	xx.x (xx.x, xx.x)
Etc.
Hazard Ratio (95% CI) (Test Drug     vs Control) [3]	x.xx (x.xx, x.xx)		0.xxx [3]

[1] p-value is calculated with Fisher’s exact test.
[2] p-value is calculated with Logrank test stratified by strata1 and strata2.
[3] Hazard ratio, 95% CI, and p-value are calculated with Cox proportional hazard model with treatment, strata1, strata2 as explanatory variables.

Notice that all three statistics are included: median time to event (or median survival time), rate of subjects without an event (or survival rate), and hazard ratio. Three p-values are calculated: a p-value from Fisher's exact test (or Chi-square test) to compare the event rates between two groups - time was not factored in the calculation; a p-value from log-rank test to compare two survival curves; and p-value from Cox regression model.   

Survival rate is mostly used in oncology studies and rate of subjects with no event is not very commonly used in non-oncology studies. We still see some publications in oncology area where only survival rate is reported and neither the median time nor the hazard ratio is reported - seems to be a little bit obsolete practice. For example, almost all studies from the Children's Oncology Group would only report the survival rate, not the median survival time, not the hazard ratio. 

Median survival time is a good measure if there are enough events that occurred during the study period. If not too many events are observed in the treatment group during the study, the median survival time can not be calculated. 

Hazard ratio is a good measure for the treatment effect when comparing two treatment groups or two sub-groups. see a previous post "Interpreting Hazard Ratio: Can we say "percent reduction in risk"?"