Ezzet and Whitehead (1991) analyze data from a two-treatment, two-period crossover trial to compare 2 inhalation devices for delivering the drug salbutamol in 286 asthma patients. Patients were asked to rate the clarity of leaflet instructions accompanying each device, using a 4-point ordinal scale.
Format
A data frame of 572 observations containing information on the following 5 variables.
- subject
The subject number
- rating
The rating of the inhaler instructions on a scale ranging from 1 to 4
- treat
A contrast to indicate which of the two inhaler devices was used
- period
A contrast to indicate the time of administration
- carry
A contrast to indicate possible carry over effects
Source
Ezzet, F., & Whitehead, J. (1991). A random effects model for ordinal responses from a crossover trial. Statistics in Medicine, 10(6), 901-907.
Examples
# \dontrun{
## ordinal regression with family "sratio"
fit1 <- brm(rating ~ treat + period + carry,
data = inhaler, family = sratio(),
prior = set_prior("normal(0,5)"))
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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#> Chain 1: Gradient evaluation took 0.000172 seconds
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#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
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#> Chain 4: Gradient evaluation took 0.000191 seconds
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summary(fit1)
#> Family: sratio
#> Links: mu = logit
#> Formula: rating ~ treat + period + carry
#> Data: inhaler (Number of observations: 572)
#> 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] 0.55 0.09 0.38 0.73 1.00 4940 2872
#> Intercept[2] 2.26 0.22 1.84 2.73 1.00 6163 3002
#> Intercept[3] 1.10 0.43 0.29 1.95 1.00 5338 2942
#> treat -0.75 0.23 -1.21 -0.30 1.00 3269 2628
#> period 0.21 0.17 -0.12 0.55 1.00 5756 2623
#> carry -0.22 0.17 -0.54 0.12 1.00 3347 2847
#>
#> Further Distributional Parameters:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> disc 1.00 0.00 1.00 1.00 NA NA NA
#>
#> 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)
## ordinal regression with family "cumulative"
## and random intercept over subjects
fit2 <- brm(rating ~ treat + period + carry + (1|subject),
data = inhaler, family = cumulative(),
prior = set_prior("normal(0,5)"))
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.000219 seconds
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#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 2).
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#> Chain 2: Gradient evaluation took 0.000195 seconds
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#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 3).
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#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 0.000188 seconds
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summary(fit2)
#> Family: cumulative
#> Links: mu = logit
#> Formula: rating ~ treat + period + carry + (1 | subject)
#> Data: inhaler (Number of observations: 572)
#> Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#> total post-warmup draws = 4000
#>
#> Multilevel Hyperparameters:
#> ~subject (Number of levels: 286)
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sd(Intercept) 1.20 0.24 0.73 1.67 1.00 729 964
#>
#> Regression Coefficients:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept[1] 0.70 0.14 0.44 0.97 1.00 2906 3109
#> Intercept[2] 3.85 0.32 3.25 4.49 1.00 1376 1812
#> Intercept[3] 5.14 0.45 4.31 6.07 1.00 2091 2043
#> treat -1.05 0.32 -1.70 -0.46 1.00 3103 2943
#> period 0.23 0.20 -0.17 0.62 1.00 8225 2733
#> carry -0.25 0.25 -0.73 0.23 1.00 3091 2961
#>
#> Further Distributional Parameters:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> disc 1.00 0.00 1.00 1.00 NA NA NA
#>
#> 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)
# }