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### Left truncation

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

Truncation (LEFT),

### 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

###
Calculating hk

Calculating "hazard"

[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)

###
Calculating H-km(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

-PHA

-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

### Ecologic Fallacy

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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