Chapter 5, Section 5.4

Treatment of Lead Exposed Children Trial (TLC)

Analysis of Response Profiles of Blood Lead Levels 

> library(foreign)

> ds <- read.dta("tlc.dta")

> tlclong <- reshape(ds, idvar="id", varying=c("y0","y1","y4","y6"), 

+    v.names="y", timevar="time", time=1:4, direction="long")

> attach(tlclong)

> week <- time

> week[time==1] <- 0

> week[time==2] <- 1

> week[time==3] <- 4

> week[time==4] <- 6

> interaction.plot(week, trt, y, type="b", pch=c(19,21), ylim=c(10, 30), 

+    xlab="Time (in weeks)", ylab="Blood Lead Levels", 

+    main="Plot of Mean Response Profiles in the Placebo & Succimer Groups", 

+    col=c(2,4))

> week.f <- factor(week, c(0,1,4,6))

> library(nlme)

> model <- gls(y ~ trt*week.f, corr=corSymm(, form= ~ time | id), 

+    weights = varIdent(form = ~ 1 | week.f))

> summary(model)

Generalized least squares fit by REML

  Model: y ~ trt * week.f

  Data: NULL 

       AIC      BIC    logLik

  2452.076 2523.559 -1208.038

Correlation Structure: General

 Formula: ~time | id 

 Parameter estimate(s):

 Correlation: 

  1     2     3    

2 0.571            

3 0.570 0.775      

4 0.577 0.582 0.581

Variance function:

 Structure: Different standard deviations per stratum

 Formula: ~1 | week.f

 Parameter estimates:

       0        1        4        6 

1.000000 1.325881 1.370473 1.524828 

Coefficients:

                      Value Std.Error   t-value p-value

(Intercept)          26.272 0.7102870  36.98787  0.0000

trtSuccimer           0.268 1.0044975   0.26680  0.7898

week.f1              -1.612 0.7919161  -2.03557  0.0425

week.f4              -2.202 0.8149207  -2.70210  0.0072

week.f6              -2.626 0.8885228  -2.95547  0.0033

trtSuccimer:week.f1 -11.406 1.1199385 -10.18449  0.0000

trtSuccimer:week.f4  -8.824 1.1524720  -7.65659  0.0000

trtSuccimer:week.f6  -3.152 1.2565609  -2.50843  0.0125

 Correlation: 

                    (Intr) trtScc wek.f1 wek.f4 wek.f6 trS:.1 trS:.4

trtSuccimer         -0.707                                          

week.f1             -0.218  0.154

week.f4             -0.191  0.135  0.680                            

week.f6             -0.096  0.068  0.386  0.385                     

trtSuccimer:week.f1  0.154 -0.218 -0.707 -0.481 -0.273              

trtSuccimer:week.f4  0.135 -0.191 -0.481 -0.707 -0.272  0.680       

trtSuccimer:week.f6  0.068 -0.096 -0.273 -0.272 -0.707  0.386  0.385

Standardized residuals:

       Min         Q1        Med         Q3        Max 

-2.1756424 -0.6849970 -0.1515552  0.5294182  5.6327491 

Residual standard error: 5.022487 

Degrees of freedom: 400 total; 392 residual

> anova(model)

Denom. DF: 392 

numDF   F-value p-value

(Intercept)     1 2583.7978  <.0001

trt             1    4.2267  0.0405

week.f          3   61.4938  <.0001

trt:week.f      3   35.9293  <.0001