Ch 1 - Introduction to Survival Analysis

Question 1

Outcome variable of Survival Analysis

Answer 1

Time until an event occurs

Question 2

Reasons for censored data (3)

Answer 2

(1) a person does not experience the event before the study ends;
(2) a person is lost to follow-up during the study period;
(3) a person withdraws from the study because of death (if death is not the event of interest) or some other reason (e.g., adverse drug reaction or other competing risk)

Question 3

Right censored data

Answer 3

True survival time (T) is equal to or greater than observed survival time

Question 4

Left censored data

Answer 4

true survival time (T) is less than or equal to the observed survival time t₀

Question 5

Interval censored

Answer 5

True survival time (T) is within a known specified time interval

Question 6

Survivor function (definition)

Answer 6

The survivor function S(t) gives the probability that a person survives longer than some specified time t: that is, S(t) gives the probability that the random variable T exceeds the specified time t.

S(t) = P(T > t)

Question 7

Characteristics of the survivor functions (3) (Theoretical properties of the survivor curves)

Answer 7

• they are non-increasing; that is, they head downward as t increases;
• at time t = 0, S(t) = S(0) = 1; that is, at the start of the study, since no one has gotten the event yet, the probability of surviving past time 0 is one;
• at time t = Inf, S(t) = S(Inf) = 0; that is, theoretically, if the study period increased without limit, eventually nobody would survive, so the survivor curve must eventually fall to zero.

Question 8

The hazard function h(t) formula

Answer 8

h(t) equals the limit, as ‘delta’t approaches zero, of a probability statement about survival, divided by ‘delta’t, where ‘delta’t denotes a small interval of time.

Sometimes called: conditional failure rate. Probability per unit time.

Question 9

The hazard function: conceptual interpretation

Answer 9

The hazard function h(t) gives the i_nstantaneous potential per unit time for the event to occur, given that the individual has survived up to time t._

Gives the instantaneous potential for failing at time t per unit time, given survival up to time t. in contrast to the survivor function, which focuses on not failing, the hazard function focuses on failing, that is, on the event occurring.

Question 10

The hazard function: characteristics (2)

Answer 10

h(t) > 0

h(t) has no upper bound

Question 11

Why use the hazard function h(t) and not just the S(t) (1+3)

Answer 11

S(t) directly describes survival

h(t):

• is a measure of instantaneous potential whereas a survival curve is a cumulative measure over time
• it may be used to identify a specific model form, (such as an exponential, a Weibull, or a lognormal curve that fits one’s data);
• it is the vehicle by which mathematical modeling of survival data is carried out; that is, the survival model is usually written in terms of the hazard function.

Question 12

Relationship of S(t) and h(t)

Answer 12

S(t) equals e to the power minus lambda times t.

S(t) equals the exponential of the negative integral of the hazard function between integration limits of 0 and t.

h(t) equals minus the derivative of S(t) with respect to t divided by S(t)

Question 13

Goals of Survival Analysis (3)

Answer 13

Goal 1: To estimate and interpret survivor and/ or hazard functions from survival data.

Goal 2: To compare survivor and/or hazard functions.

Goal 3: To assess the relationship of explanatory variables to survival time.

Question 14

Censoring assumptions (3)

Answer 14

Independent(vs.non-independent) censoring

Random (vs. non-random) censoring

Non-informative (vs. informative) censoring

Question 15

Random censoring concept

Answer 15

Subjects who are censored at time t should be representative of all the study subjects who remained at risk at time t with respect to their survival experience.

In other words, the failure rate for subjects who are censored is assumed to be equal to the failure rate for subjects who remained in the risk set who are not censored

Question 16

Independent censoring concept

Answer 16

Means that within any subgroup of interest, the subjects who are censored at time t should be representative of all the subjects in that subgroup who remained at risk at time t with respect to their survival experience.

In other words, censoring is independent provided that it is random within any subgroup of interest.

Question 17

Non-informative censoring concept

Answer 17

Non-informative censoring occurs if the distribution of survival times (T) provides no information about the distribution of censorship times (C), and vice versa. Otherwise, is informative.