Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

parameters>#observations )^binot valid GEE approach: common set of rs for each subject: Subjecti:{r 12 ,r 13 ,r 14 ,r 23 ,r 2 ...

VIII. Different Types of Correlation Structure Examples of correlation structures: Independent Exchangeable AR1 autoregressive S ...

Only onerestimated Order of observations within a cluster is arbitrary. Can exchange positions of observa- tions. K¼14 schools n ...

AR1 Special case of autoregressive Assumption:Yatt 1 andt 2 : rt 1 ;t 2 ¼rjt^1 t^2 j Cluster with four responses at timet¼1, 2, ...

Stationarym-dependent Assumption: Correlationskoccasions apart same fork¼1, 2,...,m Correlations>moccasions apart¼ 0 Stationa ...

rijk¼ri (^0) jkifi 6 ¼i^0 rA12 = rB12 = r 12 different clusters Order {Yi 1 ,Yi 2 ,...,Yik}notarbi- trary (e.g., cannot switchYA ...

IX. Empirical and Model- Based Variance Estimators GEE estimates have desirable asymptotic |fflfflfflfflfflfflffl{zfflfflfflfflf ...

To correctly specify a GEE model:  Specify correctg(m)  Specify correctCi ^bh consistent even ifCimisspeci- fied but ^bhmore e ...

Empirical (robust) variance esti- mators:  An adjustment of model-based estimators  Uses observedrjkbetween responses  Consis ...

Empirical estimator generally recommended. Reason: robust to misspecification of correlation structure Preferable to specify wor ...

To test several^bh simultaneously use  Score test  Generalized Wald test UnderH 0 , test statistics approxi- matew^2 with df¼n ...

XI. Score Equations and “Score-like” Equations L¼likelihood function ML solves estimating equations calledscore equations. S 1 ¼ ...

Sh+1 = ∂mi[var(Yi)]–1[Yi – mi] = 0 bh i= 1 K Σ partial derivative variance residual Solution: iterative (by computer) GLM score ...

Scale factor¼f Allows forextra variationin Y: varðYÞ¼fVðmÞ IfYbinomial:f¼1 and V(m)¼m(1m) f>1 indicates overdispersion f< ...

XII. Generalizing the “Score-like” Equations to Form GEE Models GEE models:  For cluster-correlated data model parameters: b an ...

Di¼diagonal matrix, with vari- ance functionV(mij) on diagonal Wi¼working covariance matrix (nini) Wi¼fD (^12) iCiD (^12) i GEE ...

Key differenceGEE vs. GLM score equations: GEE allow for multiple responses per subject GEE model parameters – three types: Reg ...

SLR: var(Y)¼m(1m) GEE logistic regression varðYÞ¼fmð 1 mÞ fdoes not affect^b faffectss^biff 6 ¼ 1 f>1: overdispersion f< ...

GEE vs. Standard Logistic Regression SLR equivalent to GEE model with: Independent correlation structure fforced to equal 1 Mod ...

Detailed Outline I. Overview(pages 492 – 493) A. Focus: modeling outcomes with dichotomous correlated responses. B. Observations ...