# Expressing prognosis with life tables

In this video, you will learn how to express prognosis with the help of life tables. It’s essential to understand these concepts when learning about Kaplan-Meier curves later on. Need some background on this concept? Watch our video on ways to express prognosis.

In this video from our Epidemiology Essentials course, you'll learn how to express prognosis with the help of life tables. It’s essential to understand these concepts when learning about Kaplan-Meier curves. Need some background on this concept? Watch our video on ways to express prognosis.

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## Video Transcript

**[00:00:00] **Let's now turn to the so-called life-table approach, which is a commonly used technique to assess survival and prognosis. Here's how it works. Let's say we conducted a study of a certain type of lymphoma. The study is conducted over a five-year time period starting in 2010 and ending in 2015. In 2010, 100 patients joined the study, that's when they received treatment. Let's assume nobody's lost to follow-up, so people can only live to study, by dying. So, of the 100

**[00:00:30] **initial patients, only 55 are still alive in 2011, 36 in 2012, 25 in 2013, 18 in 2014, and 14 in 2015. In 2011, another 95 patients joined the study and received treatment. Of these patients, 52 are still alive in 2012, 34 in 2013, 24 in 2014, and 17 in 2015.

**[00:01:00] **In 2012, another set, 75 patients joined and received treatment, 41 of whom are still alive in 2013, 27 in 2014, and 19 in 2015. 2014 was the last year of recruitment. 99 patients joined and received treatment. 54 of whom were still alive in 2015 when the study ended. So, you see, we have various durations of follow-up. Folks who joined in 2010 were followed up for a total of five

**[00:01:30] **years. Patients who joined in 2011 were followed up for four years. Patients from 2012, for three years. Patients from 2013, for two years. And patients from 2014, for only one year. So, if we wanted to calculate the five years of our rate the way we learned previously. We could only do so for the 2010 cord because everyone else had shorter follow up, right? But let me tell you something. There is a way how we can use all the data presented

**[00:02:00]** here, so that it's not lost and so that we can use it for the calculation of five-year survival rates anyway. And the good news is you'll learn it in the next couple of minutes. If we wanted to assess survival in the first, second, third, fourth, and fifth years after the initiation of therapy, we'd have to rearrange the data slightly, since year one for the cohort of 2010 is the year from 2010 to 2011. Year one for the cohort of 2011 is the year from 2011 to 2012 and so

**[00:02:30] **forth. So, in order to compare the first, second, third, fourth, and fifth years of all of these cohorts, we have to move the data to the left. Now, the years are appropriately aligned, so that we can perform the necessary calculations. Let's copy the numbers into a table real quick. So, this is the year of treatment or the year when they joined the study. This is the number of patients that joined in that year and these are the numbers of patients alive at the end of each year follow up.

**[00:03:00] **Now, in order to calculate the proportion of people who survived year one, we need to know the number of people who survived until the end of year one, in all cohorts, divided by all study participants, that's 249 divided by 453 equals a P1 of 0.55. So, 55% survived the first year. In order to know what proportion survived the second year, we need to know how many people survived until the end of year two and divide that by the number of people, who were

**[00:03:30] **at risk of dying during that year. And that's everyone who went through that year, right? How many people are those? Pause the video and come back when you think you know the answer. Okay, so everyone in that column was still alive at the end of year one, right? But the patients who joined the study in 2014, those down here, were only observed during their first year, right? So, these folks could not become part of the numerator in year two because there was no year two for them.

**[00:04:00] **So, we need to exclude them from the denominator. So, the probability of surviving year two is 127, the survivors of year two, divided by all people at risk in year two, and that's everyone who was alive at the end of year one, minus 54 people from the 2014 cohort. So, 0.65 or 65%. Now, please pause the video and calculate the probabilities of surviving years three, four, and five, that's P3, P4,

**[00:04:30] **and P5, yourself and come back when you're done. Okay, so the probability of surviving year three is 68, all the people who are alive at the end of year three, divided by 127, minus the 30 people who are not followed up in the third year. So, 0.7 or 70% probability of surviving year three. Year four is 34 divided by 68, minus

**[00:05:00] **the 19 for whom there was no year four. So, also 0.7 or 70%. In year five, is 14 divided by 34, minus 17, equalling 0.8 or 80%. Let's put these probabilities into a table. So, the probability of surviving year one was 0.55. The probability of surviving in year two, in patients who survived year one, was 0.65. The probability of surviving year three, in patients who survived year two, was 0.7.

**[00:05:30] **The probability of surviving year four, in those who survived year three, was 0.7, and the probability of surviving year five, in those who survived year four, was 0.8. Now, let's look at the data slightly differently. What's the probability of surviving to the end of each year for someone who joins the study. Let's start with year one. What's the probability of surviving to the end of year one for someone who joins the study? Well, that's the same as surviving year one,

**[00:06:00] **so 0.55. What's the probability of surviving until the end of year two for someone who joins the study? Well, that's the product of the probability of surviving year one and year two. So, 0.55 times 0.65 and that's 0.36. The probability of surviving to the end of year three is P1 times P2 times P3 or 0.25 and so forth. So, the five-year survival rate for someone

**[00:06:30] **who joined the study was 0.14 or 14%. Not so good, right? This data can also be presented in the form of a survival curve, like this one. If you prefer looking at graphs instead of tables like me. So, coming up, more cool stuff.