```
# For a study of back pain (none, mild, moderate, severe) here are the
# expected proportions (averaged over 2 treatments) that will be in
# each of the 4 categories:
p <- c(.1,.2,.4,.3)
popower(p, 1.2, 1000) # OR=1.2, total n=1000
posamsize(p, 1.2)
popower(p, 1.2, 3148)
# If p was the vector of probabilities for group 1, here's how to
# compute the average over the two groups:
# p2 <- pomodm(p=p, odds.ratio=1.2)
# pavg <- (p + p2) / 2
# Compare power to test for proportions for binary case,
# proportion of events in control group of 0.1
p <- 0.1; or <- 0.85; n <- 4000
popower(c(1 - p, p), or, n) # 0.338
bpower(p, odds.ratio=or, n=n) # 0.320
# Add more categories, starting with 0.1 in middle
p <- c(.8, .1, .1)
popower(p, or, n) # 0.543
p <- c(.7, .1, .1, .1)
popower(p, or, n) # 0.67
# Continuous scale with final level have prob. 0.1
p <- c(rep(1 / n, 0.9 * n), 0.1)
popower(p, or, n) # 0.843
# Compute the mean and median x after shifting the probability
# distribution by an odds ratio under the proportional odds model
x <- 1 : 5
p <- c(.05, .2, .2, .3, .25)
# For comparison make up a sample that looks like this
X <- rep(1 : 5, 20 * p)
c(mean=mean(X), median=median(X))
pomodm(x, p, odds.ratio=1) # still have to figure out the right median
pomodm(x, p, odds.ratio=0.5)
# Show variation of odds ratios over possible cutoffs of Y even when PO
# truly holds. Run 5 simulations for a total sample size of 300.
# The two groups have 150 subjects each.
s <- simPOcuts(300, nsim=5, odds.ratio=2, p=p)
round(s, 2)
# An ordinal outcome with levels a, b, c, d, e is measured at 3 times
# Show the proportion of values in each outcome category stratified by
# time. Then compute what the proportions would be had the proportions
# at times 2 and 3 been the proportions at time 1 modified by two odds ratios
set.seed(1)
d <- expand.grid(time=1:3, reps=1:30)
d$y <- sample(letters[1:5], nrow(d), replace=TRUE)
propsPO(y ~ time, data=d, odds.ratio=function(time) c(1, 2, 4)[time])
# To show with plotly, save previous result as object p and then:
# plotly::ggplotly(p, tooltip='label')
# Add a stratification variable and don't consider an odds ratio
d <- expand.grid(time=1:5, sex=c('female', 'male'), reps=1:30)
d$y <- sample(letters[1:5], nrow(d), replace=TRUE)
propsPO(y ~ time + sex, data=d) # may add nrow= or ncol=
# Show all successive transition proportion matrices
d <- expand.grid(id=1:30, time=1:10)
d$state <- sample(LETTERS[1:4], nrow(d), replace=TRUE)
propsTrans(state ~ time + id, data=d)
pt1 <- data.frame(pt=1, day=0:3,
status=c('well', 'well', 'sick', 'very sick'))
pt2 <- data.frame(pt=2, day=c(1,2,4,6),
status=c('sick', 'very sick', 'coma', 'death'))
pt3 <- data.frame(pt=3, day=1:5,
status=c('sick', 'very sick', 'sick', 'very sick', 'discharged'))
pt4 <- data.frame(pt=4, day=c(1:4, 10),
status=c('well', 'sick', 'very sick', 'well', 'discharged'))
d <- rbind(pt1, pt2, pt3, pt4)
d$status <- factor(d$status, c('discharged', 'well', 'sick',
'very sick', 'coma', 'death'))
label(d$day) <- 'Day'
multEventChart(status ~ day + pt, data=d,
absorb=c('death', 'discharged'),
colorTitle='Status', sortbylast=TRUE) +
theme_classic() +
theme(legend.position='bottom')
```

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