Analyzing Analyzing Longitudinal DataLongitudinal Data

PART IPART I

Computerized Delivery of Computerized Delivery of Cognitive Behavior Therapy – Cognitive Behavior Therapy –

Beat the BluesBeat the Blues

Clinical Depression

• Major public health problem• Treatments:

– Antidepressants – may not respond, lack of medical compliance• Side effects include sexual dis-performance,

lack of emotions, stupor.

– CBT – Cognitive Behavioral Therapy• Psychotherapy, the modern “talking

treatments”• High demand for it, lack of availability.

Alternative Modes of Delivery

• Therapist replaced by a computer (Terminal client program: Beat the Blues)

• Main question: does the treatment still work.

The Setup

• Blues Program– Blues program– Pharmacology and/or general practice

with the exception of face-to-face counseling or psychological intervention

• TAU (Treatment as Usual)– Whatever treatment their GP

prescribed. I.e. medication, discussion of problems with GP, provision of practical/social help, referral to counselor/practitioner, or other examiners.

Possible Variables

• Beck Depression Inventory II (BDI)• Measured at several times:

– Before treatment– 2 Months after the beginning– At 1, 3, 6 month follow up (after the

two months)

Analyzing Longitudinal Data

• Longitudinal setup since variables are measured several times on each individual in the study.

• These measurements will most likely not be independent, hence correlated.

• Unique analysis needed to account for this.

Linear Mixed Effects Models for Repeated

Measures Data• Uses the idea that an individual

pattern of responses is likely to depend on many characteristics of that individual that may or may not be known.

• Two common forms.

Random Intercept Model

• yij= β0 + β1tj + ui + εij

• Total residual is partitioned into a subject-specific random component.

• ui is constant, normally distributed with zero mean, variance = δ2.

• Ui and εij are independent of each other and time. And ui considered the random intercept.

• The ui acts to model heterogenity in the intercepts

Random Slope and Intercept Model

• yij= β0 + β1tj + ui + vitj + εij

• We still have the ui term to explain the heterogeneity in the intercepts, but also the viti term to explain the heterogeneity in the slope parameters.

Analysis Using R

Fitting the Data so it frames “the long form”

(each separate repeated measure and associated covariate values appear as a

separate row)

data("BtheB", package = "HSAUR")> BtheB$subject <-factor(rownames(BtheB))> nobs<-nrow(BtheB)> BtheB_long<- reshape (BtheB, idvar = "subject",+ varying = c("bdi.2m", "bdi.4m", "bdi.6m", "bdi.8m"), direction = "long")> BtheB_long$time <-rep(c(2,4,6,8), rep(nobs, 4))

> subset (BtheB_long, subject %in% c("1", "2", "3")) drug length treatment bdi.pre subject time bdi1.2m No >6m TAU 29 1 2 22.2m Yes >6m BtheB 32 2 2 163.2m Yes <6m TAU 25 3 2 201.4m No >6m TAU 29 1 4 22.4m Yes >6m BtheB 32 2 4 243.4m Yes <6m TAU 25 3 4 NA1.6m No >6m TAU 29 1 6 NA

Run log-likelihood test

• Test two different models– Random intercept – one random effect

(intercepts)– Random slope and intercept model – two

random effects (intercepts and slopes)

– Conclusion: simpler random intercept model is adequate

Results from random intercept model

• pg. 168• We find that time and the Beck

Depression Inventory II values (bdi.pre) measured at baseline are significant (the coefficients are not equal to zero.

• No evidence that the other three covariates differ from zero.

• No clear evidence of treatment effect