Breslow and Clayton (1993) analyze data initially provided by Thall and Vail (1990) concerning seizure counts in a randomized trial of anti-convulsant therapy in epilepsy. Covariates are treatment, 8-week baseline seizure counts, and age of the patients in years.
Format
A data frame of 236 observations containing information on the following 9 variables.
- Age
The age of the patients in years
- Base
The seizure count at 8-weeks baseline
- Trt
Either
0or1indicating if the patient received anti-convulsant therapy- patient
The patient number
- visit
The session number from
1(first visit) to4(last visit)- count
The seizure count between two visits
- obs
The observation number, that is a unique identifier for each observation
- zAge
Standardized
Age- zBase
Standardized
Base
Source
Thall, P. F., & Vail, S. C. (1990).
Some covariance models for longitudinal count data with overdispersion.
Biometrics, 46(2), 657-671.
Breslow, N. E., & Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88(421), 9-25.
Examples
# \dontrun{
## poisson regression without random effects.
fit1 <- brm(count ~ zAge + zBase * Trt,
data = epilepsy, family = poisson())
#> Compiling Stan program...
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summary(fit1)
#> Family: poisson
#> Links: mu = log
#> Formula: count ~ zAge + zBase * Trt
#> Data: epilepsy (Number of observations: 236)
#> Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#> total post-warmup draws = 4000
#>
#> Regression Coefficients:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept 1.93 0.04 1.86 2.01 1.00 2012 2862
#> zAge 0.15 0.03 0.10 0.20 1.00 3186 2715
#> zBase 0.57 0.02 0.52 0.62 1.00 1928 2226
#> Trt1 -0.19 0.05 -0.30 -0.09 1.00 2483 2647
#> zBase:Trt1 0.05 0.03 -0.01 0.11 1.00 1825 1932
#>
#> Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
#> and Tail_ESS are effective sample size measures, and Rhat is the potential
#> scale reduction factor on split chains (at convergence, Rhat = 1).
plot(fit1)
## poisson regression with varying intercepts of patients
## as well as normal priors for overall effects parameters.
fit2 <- brm(count ~ zAge + zBase * Trt + (1|patient),
data = epilepsy, family = poisson(),
prior = set_prior("normal(0,5)"))
#> Compiling Stan program...
#> Start sampling
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summary(fit2)
#> Family: poisson
#> Links: mu = log
#> Formula: count ~ zAge + zBase * Trt + (1 | patient)
#> Data: epilepsy (Number of observations: 236)
#> Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#> total post-warmup draws = 4000
#>
#> Multilevel Hyperparameters:
#> ~patient (Number of levels: 59)
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sd(Intercept) 0.58 0.07 0.46 0.73 1.00 939 1675
#>
#> Regression Coefficients:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept 1.77 0.12 1.54 2.01 1.00 738 1447
#> zAge 0.09 0.09 -0.08 0.26 1.00 769 1264
#> zBase 0.70 0.12 0.47 0.94 1.01 873 1400
#> Trt1 -0.27 0.17 -0.60 0.05 1.00 841 1348
#> zBase:Trt1 0.05 0.16 -0.27 0.37 1.00 956 1664
#>
#> Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
#> and Tail_ESS are effective sample size measures, and Rhat is the potential
#> scale reduction factor on split chains (at convergence, Rhat = 1).
plot(fit2)
# }