3 - Life Tables

Question 1

What is the difference between a 1 sample t test and a 2 sample t test?

Answer 1

• 1 sample = compare 1 group to a standard

- 2 sample = compare 2 groups to each other

Question 2

What is the difference between Ho and Ha?

Answer 2

• Ho = null hypothesis, that there isn’t a difference between the 2 samples groups
• Ha = alternative hypothesis, that there is a difference between the 2 sample groups

Question 3

What is survival time?

Answer 3

Time to an “event” (may or may not be fatal)

Question 4

What are censored cases? How are they denoted in life tables?

Answer 4

• Those that don’t experience the event (either b/c they didn’t experience it during the study or b/c they dropped out of the study before experiencing it)
• Normally denoted w/ “+”

Question 5

What is commonly used as the outcome in trials?

Answer 5

• t-year survival rate

- t-survival rate = # of individuals who survive longer than t years / total # of individuals in data set

Question 6

Describe the product limit method of estimating survival curves (for Kaplan-Meier curves)

Answer 6

1) Order survival times both censored and uncensored in order from smallest to largest (if censored and uncensored have same value, uncensored appears first); label column as t
2) In a second column rank from 1 to n (n = total number of survival times)
3) Make a 3rd column, same as 2nd, but only for uncensored observations; label column as r
4) Make a 4th column for [n - r] / [n - r + 1] for every r in the 3rd column
5) To obtain survival rate at time t (any number in column 1), multiply all values in column 4 up to and including t

Question 7

What is survival probability?

Answer 7

• # of px surviving divided by # of px at risk (w/in a time segment)
• Px dropped out or died before start of time segment are not counted as “at risk”; neither are censored px

Question 8

When does the product limit method for Kaplan-Meier curves not work? What is used instead?

Answer 8

• Larger data sets (over 100 px) b/c not practical

- Actuarial method is used

Question 9

What occurs in the actuarial method?

Answer 9

• Px are classified according to the last time interval their condition was recorded
• Columns are 1 (t to t+1), 2 (d/died), 3 (c/censored), and 4 (n/ living at start)
• Can obtain the # of px at risk at the start of the interval by cumulating the d and c columns from the bottom up (this makes up the 4th column)

Question 10

How do you determine the # at risk at start using the actuarial method?

Answer 10

• # of px at risk interval t to t+1 is n* = n - (c/2)
• Start from bottom and cumulate up
• Censored subjects are only at risk for part of the interval; we assume they are at risk for 1/2 of interval

Question 11

How do you determine the interval death rate using the actuarial method?

Answer 11

q (interval death rate) = d/n*

Question 12

How do you determine the interval survival rate using the actuarial method?

Answer 12

p (interval survival rate) = 1 - q

Question 13

How do you determine the survival at time t using the actuarial method?

Answer 13

Multiply all the probabilities (p) up to (**not including) the interval t to t+1