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incomplete data due to follow up starting after origin
--> study truncates individuals with events between 0 and W
Immortal person-time (0-W)
Interval in which:
-participant is not at risk for the event
-participant is not at risk for any censoring event --> because censored observations are assumed to have the event after censoring and are effectively events
Difference between censoring and truncation
Censoring (RIGHT), you know the people, but you don't know what their values are
Conditions for Selection Bias
1. Need drop-out (under <5% = no worries, over 20% forget about any kind of correction!)
2. associated with exposure
3. associated with outcome
[Is there an actual difference between these two things?]
hk = # events / (#at risk * delta-k)
hazard = slope of S(t) / S(t)
Note: hazard is also the negative differential of the log S(t)
--> Cumulative hazard (=Kaplan-Meier estimate)
H-km(t) = -log(S(t))
Note: Cumulative Hazard is not bounded by 100%
Note: log of the cumulative hazards need to be parallel --> PHA
Note: you also use cumulative hazards to decide about model fit
Cox Model - Deviance Residuals used for?
To test whether you've gotten the functional form right
-1 per subject
-are like standard residuals (mean = 0, SD = 1, anything outside ±3 is trouble)
--> you can't calculate the deviance, but you can calculate the deviance residual
Cox Model - Delta-beta residuals
To test outliers, see whether you have any coding problems
-one per regressor, per subject
-see how much each coefficient would change if you deleted that subject
Differences between Cox and Poisson
Poisson: has explicit saturated model (can calculate deviance)
Cox: no explicit saturated model (can only calculate deviance residuals)
How to compare nested models?
LRT = -2(Log La - Log Lb)
w/ chi-square distribution with df equal to difference in parameters
Poisson and NBR: Difference
Both calculate incidence density (i.e. rate)
-NBR inludes an error term, Poisson has no error term
Assumptions of Poisson
-Mean = Variance
(if variance > mean then overdispersed, if variance < mean, then underdispersed)
How do I test for confounding in Incidence Density Ratio (IDR)
ln(CoIDR) --> large change = strong confounder, small change --> not a great confounder
Inferences about individuals are based on average data for the group to which they belong
--> average effect says nothing about distribution among individuals
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