# Time to Event Techniques

Sometimes you want to understand the odds of an event that everyone in the group will not experience. The best example in pregnancy and birth is the length of labor. When you try to get an average length of labor you need to decide how to handle the labors that end in a cesarean birth.

You see, some women will have zero labor because they will have a planned cesarean. Other women will labor for a time and then have a cesarean. Most of the women will labor and give birth vaginally. If you include the cesarean births you may have falsely low estimates of the length of labor. But if you exclude the cesarean births you lose data that helps you understand the trajectory of labor. What should you do?

One solution is to use a technique known as survival analysis or time-to-event analysis. This is a technique that breaks the data into time periods and then measures what proportion of the participants in the study are still in process during each time period. Once a woman has a cesarean, she is “censored” which means she is removed from analysis for the remaining time periods. This allows you to count the time she labors, but not count her as a natural end of labor.

Here are some examples of studies looking at average labor length:

Evaluation of the labor curve in nulliparous Japanese women. In this case the researchers excluded cesarean deliveries from the analysis. This may not matter if the cesareans were elective, but what if these were cesareans performed for long labor? All those women with longer than average labors may have made the labor curve even less steep, but we cannot know because we lost that data.

Epidural analgesia lengthens the Friedman active phase of labor. In this case, the researchers included the women who had a cesarean in the analysis, using the last cervical assessment at time of cesarean as the last data point for that woman. These researchers used a two-step regression, but could have easily performed a time to event regression instead.

### The Birth Worker Survey

The Birth Worker Survey included a question about length of labor and a question about cesarean birth. This allows us to compare the three methods of estimating length of labor using one data set. We will report both mean and median because labor length data tends to be skewed which means the median is a better measure of central tendency.

Including all births we find a mean length of labor is 6.9 hours, median is 4.5 hours.

Excluding the cesarean births we find a mean length of labor is 5.1 hours, median is 4 hours.

If we use a time to event analysis, we find a mean length of labor is 7.4 hours, median is 5 hours.

This shows the importance of understanding what data is included, and how it is analyzed, when comparing time outcomes. It also shows the value of cesarean data, even if it is generally excluded from analysis when considering length of labor. Next time will will begin to talk about how to synthesize the data from studies.