Definition

Question 1

hazard rate

Answer 1

probability per unit of time (rate) of an event “immediately after time t, conditioned on suvival up to a time t

Question 2

censoring observation

Answer 2

Survival observation is often incomplete
S.T for subject is said to be censored when it´s not known exactly
censoring occurs independent of S.T and in non-informative (no additional information, occurs for unrelated reasons)

Question 3

Survival Time

Answer 3

observed times to a certain event (end-point)

Question 4

Examples S.T

Answer 4

time until development of a disease
time for medical treatment to response
length of remission after treatment
duration of first marriage or first job after graduation (sociology)
time until insurance claim due to an accident, death or risk (insurance companies)

Question 5

Comparing Nested Models

Answer 5

Asses significance of a particular covariate:

1. remove it fro the model and fit the reduced model to the same data
2. compare performance of the 2 models to evaluate significance
   - this is based using statistical test (greatest LH is preferred)

Question 6

Test Statistic - log L

Answer 6

we use MLogLH to compare the nested models
possibility to asses statistically if difference are significant
1. Logarithm allows using normal approximation (-2 used just for convenience)
2. statistic cannot be used on it´s own as a measure of model adecuacy, as it´s dependent upon the number of observations

Question 7

left censoring

Answer 7

end-point event occurs prior to a certain time but exact time of occurrence is unknown
E.g. study of illness diagnoses subject recruited is found to have the conditioned but with no record of an earlier diagnosis

Question 8

interval censoring

Answer 8

end-point has occurred between two time instants

Eg.onset of breast tumour between two annual breast screenings

Question 9

study design to cause censoring

Answer 9

study time is fixed- nr of events observed is random

study is continued until fixed number have occurred - here the study time is random

Question 10

Weighted Log-Rank Test

Answer 10

hazard rates might expect to occur (earlier/later) with(no/ strong) significant difference between groups later
weights ni are used to enhance the role of deviations between observed & expected number (of deaths) at earlier stages of the study (this case)

Question 11

Stratified Log-Rank test

Answer 11

idea of stratification is to ensure that information is homogenous within stratum
Thus to avoid potential impact of differences across the strata
Importance of stratification if variable affects time & category
E.g. stratify by age for testing two different types of vaccine

Question 12

LH Ratio Test

Answer 12

-2 * log of the Ratio between LH including covariates in the model and LH without covariates in the model

Question 13

Score Test

Answer 13

obtained by taking the derivative of the Log LH to beta and filling in B=0
Statistic = score divided by the square root of the variance
This follows a normal distribution

Question 14

Rj - Risk Set

Answer 14

The set of individuals at risk at time t(j)
[i.e. those alive and uncensored just before t(j)
Remember - those censored at ti are included as well (as it says it´s before ti (not at ti))

Question 15

tpx

Answer 15

Survival Function for the residual Time Tx

Probability of Survival for at least time t after the current age x

Question 16

p-value

Answer 16

it shows how likely (under H0) to observe a value at least as extreme as UL
The smaller the p-value the stronger the evidence against Ho

Question 17

Ph-Property

Answer 17

defined as a class H=h(.) of h(t) that for each h e H and any constant (epsilon) we have epsilon * h(t) e H(t)