Reading survival rates through Kaplan Meier curves

[Susan Gilavani]

Hello,

it is my first time using Kaplan Meier curves and survival analysis, I am very confused about the results I am getting.
My study looks at the differences in remarriage rates for divorced men, divorced women, widows and widowers. I am using a nationally representative survey for China (called the CFPS/China family panel survey-wave 10) for this study.
I have generate Kaplan Meier survival curves to look at the rate and time at with people with differing characteristics from this group enter remarriage.
Here is how my data is coded:

This is the graph that is generated:

But when I check the remarriage rate by using the tab function, i get this result:

If i understand correctly, these numbers should not be different in the survival curves. Could someone help me figure out what might be wrong?

[Paul Dickman]

Yes, from the the Kaplan-Meier we estimate that around 65% of divorced men will remarry within 50 months whereas a simple tabulation of the data show that only 51% of the divorced men remarry.

The difference between these two numbers is most likely due to the fact that not all divorced men could be followed for 50 months. The survival times for some divorced men were most probably censored; that is, they had a duration less than 50 months but did not remarry. Possible reasons are that they died or could only be followed for a duration less than 50 months due to the design of the survey.

The Kaplan-Meier analysis essentially predicts what would happen to these men if they could be followed for 50 months. This is why it is giving a higher estimate for proportion who remarry; it is assuming that some of the men who were censored would have remarried if they could have been followed 50 months.

There are assumptions that you need to consider. The Kaplan-Meier approach assumes that the future remarriage rate of the censored men is predicted by what happens to the men who could be followed. If censoring is due to death then this means we are assuming that the remarriage rate among the dead men - if they did not die - can be predicted by the remarriage rate of the men who did not die. Since the men who die are more likely to be old, we would be assuming that the remarriage rate of the unobserved old men can be predicted by the observed remarriage rate of the young. If the censoring is due to death, then there will most likely be implications for your analysis since the death rate will differ by age and sex.

If you have censoring then comparing the proportions estimated from the tables is not correct since you will be comparing groups with different time-at risk. Use, for example, strate to compare rates.

The estimate from the Kaplan-Meier curve is the proportion who remarry in the hypothetical scenario that one has a complete follow-up (e.g., one cannot die). There are other quantities that can be estimated; see the concept of competing risks but that's another level of complexity.

[Susan Gilavani]

Thank you! that is extremely helpful--I certainly overlooked this concept