**Exercise C5, Poison
model**

McKnight and van den Eeden (1993) and Hedeker (1999) analysed some multi-period, two treatment crossover data (headache2.dat) to establish whether the artificial sweetener (aspartame) caused headaches. The trial involved randomly assigning 27 patients to different sequences of placebo and aspartame. We ignore the crossover aspect of the trial in this exercise. The same data were used by Rabe-Hesketh and Skrondal (2005, exercise 6.2).

**Data description**

Number of observations (rows): 122

Number of variables (columns): 5

Variables:

id= subject identifier (1,2,…,27)

y=count of number of headaches over several days

cons=1 for all rows (not used in this analysis)

aspartame=1 if treatment was aspartame, 0 otherwise

days=number of days for which the headaches
were counted, which takes the values (1,2,…,7)

The first few lines of the data (headache2.dat) look like:

The data set has already been sorted by id.

Start Sabre and specify transcript file:

out headache.log

data id y constant aspartame
days

read headache2.dat

**Suggested exercise:**

(1) Create the offset lt=log(days)

(2) Fit a Poisson model to y (number of headaches) with a log link without any id random effects

(3) Fit a Poisson model to y allowing for the id random effect. Is the id random effect significant? How many quadrature points should we use to estimate this model?

(4) Add the treatment indicator aspartame to the previous model, is there a significant treatment effect?

The responses are actually in temporal order, but we do not use that feature of the data here. Hedeker found no evidence of a sequence effect.

**References**

Hedeker, D., (1999), MIXNO: A computer program for mixed effects logistic regression, Journal of Statistical Software, 4, 1-92

McKnight, B., and van den Eeden, S. K., (1993) A conditional analysis for two treatment multiple-period crossover design with binomial or Poisson outcomes and subjects who drop out, Statistics in Medicine, 12, 825-834

Rabe-Hesketh, S., and Skrondal, A., (2005), Multilevel and Longitudinal Modelling using Stata, Stata Press, Stata Corp, College Station, Texas