Repeated measurement of weights of calves with two treatments.

Repeated measurements of the weights of calves from a trial on the control of intestinal parasites.

Usage

data("kenward.cattle")

Format

A data frame with 660 observations on the following 4 variables.

animal

animal factor

trt

treatment factor, A or B

day

day, numberic, 0-133

weight

bodyweight, kg

Details

Grazing cattle can ingest larvae, which deprives the host animal of nutrients and weakens the immune system, affecting the growth of the animal.

Two treatments A and B were applied randomly to 60 animals (30 each in two groups) to control the disease.

Each animal was weighed 11 times at two-week intervals (one week between the final two measurements).

Is there a difference in treatments, and when does that difference first become manifest?

Source

Kenward, Michael G. (1987). A Method for Comparing Profiles of Repeated Measurements. Applied Statistics, 36, 296-308. Table 1. https://doi.org/10.2307/2347788

References

W. Zhang, C. Leng and C. Y. Tang (2015). A joint modelling approach for longitudinal studies J. R. Statist. Soc. B, 77 (2015), 219–238. https://doi.org/10.1111/rssb.12065

Examples

if (FALSE) { # \dontrun{
  
  library(agridat)
  data(kenward.cattle)
  dat <- kenward.cattle

  # Profile plots
  libs(lattice)
  foo1 <- xyplot(weight~day|trt, data=dat, type='l', group=animal,
                 xlab="Day", ylab="Animal weight", main="kenward.cattle")
  print(foo1)
  
  # ----------

  # lme4. Fixed treatment intercepts, treatment polynomial trend.
  # Random deviation for each animal
  libs(lme4)
  m1a <-lmer(weight ~ trt*poly(day, 4) + (1|animal), data=dat,
             REML = FALSE)
  # Change separate polynomials into common polynomial
  m1b <-lmer(weight ~ trt + poly(day, 4) + (1|animal), data=dat,
             REML = FALSE)
  # Drop treatment differences
  m1c <-lmer(weight ~ poly(day, 4) + (1|animal), data=dat,
             REML = FALSE)
  anova(m1a, m1b, m1c) # Significant differences between trt polynomials

  # Overlay polynomial predictions on plot
  libs(latticeExtra)
  dat$pred <- predict(m1a, re.form=NA)
  foo1 + xyplot(pred ~ day|trt, data=dat,
                lwd=2, col="black", type='l')
  
  # A Kenward-Roger Approximation and Parametric Bootstrap
  # libs(pbkrtest)
  # KRmodcomp(m1b, m1c) # Non-signif
  # Model comparison of nested models using parametric bootstrap methods
  # PBmodcomp(m1b, m1c, nsim=500)
  ## Parametric bootstrap test; time: 13.20 sec; samples: 500 extremes: 326;
  ## large : weight ~ trt + poly(day, 4) + (1 | animal)
  ## small : weight ~ poly(day, 4) + (1 | animal)
  ##          stat df p.value
  ## LRT    0.2047  1  0.6509
  ## PBtest 0.2047     0.6527

  # -----------

  # ASREML approach to model. Not final by any means.
  # Maybe a spline curve for each treatment, plus random deviations for each time
  if(require("asreml", quietly=TRUE)){
    libs(asreml)
    m1 <- asreml(weight ~  1 + lin(day) +    # overall line
                   trt + trt:lin(day),       # different line for each treatment
                 data=dat,
                 random = ~ spl(day) +       # overall spline
                   trt:spl(day) +            # different spline for each treatment
                   dev(day) + trt:dev(day) ) # non-spline deviation at each time*trt
    
    p1 <- predict(m1, data=dat, classify="trt:day")
    p1 <- p1$pvals
    
    foo2 <- xyplot(predicted.value ~ day|trt, p1, type='l', lwd=2, lty=1, col="black")
  
    libs(latticeExtra)
    print(foo1 + foo2)

    # Not much evidence for treatment differences
  
    # wald(m1)
    ##               Df Sum of Sq Wald statistic Pr(Chisq)    
    ## (Intercept)    1  37128459         139060    <2e-16 ***
    ## trt            1       455              2    0.1917    
    ## lin(day)       1    570798           2138    <2e-16 ***
    ## trt:lin(day)   1       283              1    0.3031    
    ## residual (MS)          267                             
  
    # lucid::vc(m1)
    ##               effect component std.error z.ratio constr
    ##             spl(day)  25.29    24.09        1       pos
    ##             dev(day)   1.902    4.923       0.39    pos
    ## trt:spl(day)!trt.var   0.00003  0.000002   18      bnd 
    ## trt:dev(day)!trt.var   0.00003  0.000002   18      bnd 
    ##           R!variance 267       14.84       18       pos
  }
  
} # }