When do we use survival analysis?

When main interest is how long it takes an event to occur and when risk is not constant over time.

Not just that it happened but WHEN it happened.

AKA Time to event.

What characteristics may alter during that time.

Recall incidence rate.

Number of new cases of diseases/person time in exposed versus unexposed populations.

Why do we do per thousand person years?

To be able to compare the groups. Allows us to include all time contributed.

What do we assume about risk when we calculate incidence rate?

That risk is constant over the time period of interest. This is not the case. This is where survival analysis comes in.

What is a life table?

Statifies incidence of outcome by by time period.

Strata is chosen by researcher.

Estimates probability of surviving one or multiple time intervals.

What are the columns in a life table?

1) Time (t)

2) Number disease free at start of interval (n)

3) Number of events in interval (d)

4) Interval-specific disease risk (p)

5) Interval-specific disease-free survival (s)

6) Cumulative survival to end of interval (S)

How to calculate interval specific disease risk (p)?

Divide total number of events by disease free at start of interval: d/N

How to calculate interval-specific disease-free survival (s)?

1-p

OR

1 - interval-specific disease risk.

How to calculate culumative survival?

Take S (cumulative survival) and multiply by interval-specific disease-free survival:

S *s

This is because it is the probability of disease-free survival at the end of year 2 CONDITIONAL on disease-free survival at the end of year 1

What are some limitations of life tables?

Assumes risk is uniform across time interval.

The researcher makes the time intervals.

What is a hazard rate?

Instantaneous potential for event to occur given to survival to that time in point.

Assuming I have reached a place, what is the hazard that I will drop out here?

Is a rate not proportion.

Will increase over time.

What is the difference between hazard and survival?

Hazard will increase over time while survival will decrease ove time.

What is the difference between intervals in Kaplan-Meier table and life table?

Life table intervals determined by researcher while Kaplan-Meier determined by data.

What is the difference between intervals in Kaplan-Meier table and life table?

Life table intervals determined by researcher while Kaplan-Meier determined by data (does not assume constant risk within interval).

What are the columns in Kaplan Meier table?

1) Time (t) - only shows events that happend

2) Number at risk (N)

3) Number of events (d)

4) Number surviving (s)

5) Hazard (h)

6) Probability of survival (p)

7) Cumulative survival (S)

How do we calculate hazard?

Number of events/number at risk

OR

d/N

How do we calculate probability of survival (p)?

1 - h

1- Hazard

What is censoring?

PPTs no longer available for observation and did not experience outcome (attrition, death, etc.)

What is right censoring?

Survival time is greater than follow-up time. The amount of time they survive is not known because we cannot see them after study ends.

What is left censoring?

Survival time is less than a specified amount of time.

What does a Kaplan-Meier table with censoring look like?

1) Time interval (t)

2) Number at risk (N)

3) Number of events (d)

4) Number censored (I)

5) Number surviving (s)

6) Hazard (h)

7) Probability of survival (p)

8) Cumulative survival (S)

How do we count censored people?

People censored at the week it happened or up to the next week.

EX: Censored in week 9 but interval of:

Week 6

Week 7

Week 10

Censor in week 9 would go to Week 7 because UP TO week 10, not including week 10.

What does log-rank test show?

Assesses statistical significance of differences between KM survival curves.

Time to event different for one group compared to another?

What is null hypothesis for log rank test?

The survival curves are the same for both groups.

What is right-censoring?

Right censoring occurs when a subject leaves the study before an event occurs, or the study ends before the event has occurred.

What is left-censoring?

PPT has already had event prior to first follow-up.

What is interval censoring?

We know that the event occurred, but not the time.