Survival analysis Flashcards
What information is required for each individual in survival analysis?
a length of time after study enrolment during which no event occurred (until a fixed end-date)
a binary indicator of whether the end-point of that time period corresponds to an event or just the end of the observation period for that individual
Describe the distribution of survival times and what this means
usually positively skewed
better to use medians and IQRs than means and SDs
What is meant by a censored observation?
Individual observations where we do not know what happened after the end of the study are described as being right-censored
Describe the Kaplan-Meier Plot
graphs cumulative probability of survival against time as a step function
The plot is useful when used to compare two or more groups
How is the cumulative probability of survival calculated?
(1-dk/rk) x (previous cumulative frequency)
Describe the log-rank test
used to test differences in survival times between two or more groups
This is a non-parametric test
Ho; there’s no difference in the groups’ survival times
Describe the Cox proportional hazards model
a widely used method in cohort studies and clinical trials that allows times to be modelled in terms of continuous and categorical variables
What is the hazard function h(t)
The probability of an individual dying in time (t)
We model the effect of an exposure on the hazard rate compared to the background hazard rate
What is the proportional hazards assumption?
anything changing the value of the hazard function does so by the same magnitude, whatever the value of t
How is the hazard ratio / relative hazard calculated?
h(t)/Ho(t) where Ho(t) is the background hazard function, for which all other explanatory variables are equal to zero. h(t) is the hazard function in the exposed group
Describe the proportional hazards model
it is semi-parametric
makes no assumptions about the shape of the distribution of the survival times but need to keep the proportional hazards assumption
Describe multi-variate cox models
include multiple covariates in the same model at the same time
we investigate the independent effect of those covariates on the outcomes.
similar to a regression - used to reduce the impact of confounding variables
roughly how many events are needed to carry out multi-variate cox models?
at least 10 events in the data for each explanatory variable in the model
