Midterm - Survival Analysis Flashcards
What’s right censoring?
▶ only know Xi > Ci with observed time Ci .
▶ Data: (Ti, δi ), i = 1, . . . , n
where Ti = min(Xi , Ci ), δi = I(Xi ≤ Ci)
What’s Type 1 Censoring?
Type I Censoring:
the event is observed only if it occurs prior to some pre-specified time.
What’s Type II Censoring?
Type II Censoring:
the study continues until the failure of the 1st r individuals.
What’s Competing Risks Censoring?
Competing Risks Censoring:
We are interested in estimating marginal distribution of some event. But some individuals under study may experience competing events which causes them to be removed from the study.
What’s Left Censoring?
Left censoring
▶ Only know Xi < Ci with observed Ci
▶ Data: (Ti, δi ), i = 1, . . . , n, where
Ti = max (Xi, Ci ), δi = I(Xi ≥ Ci)
What’s Double Censoring?
Both Right- and Left-Censoring.
We use Ti = max[min(Xi, Cri ), Cli ], and
delta_i = 1 if event of interest, 0 if right-censored, -1 if left-censored.
What’s left truncation?
Left truncation (delayed entry time)
▶ Observe Y_Li ; Only observe (exact or censored) Xi if and only if Xi > Y_Li
▶ Left-truncated data: (YLi, Xi ), i = 1, . . . , n
▶ L-T + R-C data: (YLi, Ti, δi ), i = 1, . . . , n
What’s Right Truncation?
Right truncation
▶ Observe Y_Ri ; Only observe (exact or censored) Xi iff Xi < Y_Ri
What’s a survival function?
What’s the exponential distribution?
What’s the weibull distribution?
What’s the hazard function
Note, it’s possible to have hazard greater than 1, since it’s not a probability but a ratio.
What’s the cumulative hazard function?
What properties connect the survival function, hazard function, and cumulative hazard function?
What’s the Weibull’s hazard function?
What’s the definition of the discrete time survival function?
What’s Mean (residual) life function & median?
Again, what’s the hazard rate, survival function, PDF, and mean of exponential and weibull?
what’s the hazard rate, survival function, PDF, and mean of gompertz?
How do we construct a likelihood in the context of survival analysis?
What’s the Kaplan-Meier (KM) Estimator?
Note, d_i/ y_i is an estimate of the hazard function at particular time point i.
What’s Greenwood’s Formula?
What’s Nelson-Aalen estimator of H?
What’s a 95% wald ci for S(t) on the linear scale?
Where we use Greenwood’s Formula to estimate the variance.
How might we estimate the 95% ci for the median?
What’s the method 1 for estimating the hazard function?
What’s the method 2 for estimating the hazard function?
What’s the method 3 for estimating the hazard function?
