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Left truncation

incomplete data due to follow up starting after origin

--> study truncates individuals with events between 0 and W

--> 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

-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),

Truncation (LEFT),

Conditions for Confounding (1998 definition)

1.

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

2. associated with exposure

3. associated with outcome

Confounding

The presence of common cause

Selection bias

Conditioning on common causes

Calculating hk

Calculating "hazard"

[Is there an actual difference between these two things?]

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)

hazard = slope of S(t) / S(t)

Note: hazard is also the negative differential of the log S(t)

Calculating S(t) at k

1 - (# events/ # at risk)

Calculating H-km(t)

--> Cumulative hazard (=Kaplan-Meier estimate)

--> 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

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

Selection bias: Define in-selection

Bias (potentially) creating when adding late entries

Selection bias: Define out-selection

Bias (potentially) created when you have drop-outs

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

-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

-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)

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

w/ chi-square distribution with df equal to difference in parameters

How to compare non-nested models?

AIC

Poisson and NBR: Difference

Both calculate incidence density (i.e. rate)

-NBR inludes an error term, Poisson has no error term

-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)

-Mean = Variance

(if variance > mean then overdispersed, if variance < mean, then underdispersed)

Assumption of Negative Binomial

model error term --> estimate variance

How do I test for confounding in Incidence Density Ratio (IDR)

ln(CoIDR) --> large change = strong confounder, small change --> not a great confounder

How to handle time-varying variables?

1. Counting process (in-out)

2.

2.

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

-->

--> average effect says nothing about distribution among individuals

-->

What's the bias called when you make a time-varying variable time-fixed?

misclassification bias!