Kaplan-Meier Model

aka: Product Limit Method

• Downward stepped graph from left to right
• Y-axis = Pct chance of survial
• X-axis = Time
• At t=0 you have a 100% chance of surviving. As you increase in time you have lower probability of surviving.
• KM is non-parametric. E.g. it is a step function that steps down

This is an example of how to calculate the Kaplan-Meier:

Given the following data set: Time (months) Died (1=Yes, 0=No) ------------- ------------------ 2 1 3 0 6 1 6 1 7 1 10 0 15 1 15 1 16 1 27 1 30 1 32 1

For each row: Time Risk # Died HAZ I-HAZ SURV = S(t) ---- ---- ------ --- ----- ----------- 0 12 0 0/12 12/12 1 = 100% 2 12 1 1/12 11/12 (11/12) = 0.917 6 10 2 2/10 8/10 0.917(8/10) = 0.734 7 8 1 1/8 7/8 0.734(8/10) = 0.642 15 6 2 2/6 4/6 0.642(4/6) = 0.428 16 4 1 1/4 3/4 0.428(3/4) = 0.321 27 3 1 1/3 2/3 0.321(2/3) = 0.214 30 2 1 1/2 1/2 0.214(1/2) = 0.107 32 1 1 1/1 0/1 0.107(0) = 0

A couple of things to note about this methodology: - The person at 3 months who was censored was simply not included - both excluded from the table, and also excluded from the hazard.

To draw a graph for this: - Y-axis = S(t) - X-axis = Time (months) - It manifests as a chart that starts at 100%, high on the left side, then zigs downward to the right toward 0% at the bottom right. - Easy to see that “median survival” is 15 months - 50% of people survive past this, and 50% do not.

LOG-RANK TEST

A way of testing whether there is a significant difference between two survival curves 113.020.020.40.10 Kaplan-Meier model - Log Rank Test