
popower
computes the power for a two-tailed two sample comparison
of ordinal outcomes under the proportional odds ordinal logistic
model. The power is the same as that of the Wilcoxon test but with
ties handled properly. posamsize
computes the total sample size
needed to achieve a given power. Both functions compute the efficiency
of the design compared with a design in which the response variable
is continuous. print
methods exist for both functions. Any of the
input arguments may be vectors, in which case a vector of powers or
sample sizes is returned. These functions use the methods of
Whitehead (1993).
pomodm
is a function that assists in translating odds ratios to
differences in mean or median on the original scale.
simPOcuts
simulates simple unadjusted two-group comparisons under
a PO model to demonstrate the natural sampling variability that causes
estimated odds ratios to vary over cutoffs of Y.
propsPO
uses ggplot2
to plot a stacked bar chart of
proportions stratified by a grouping variable (and optionally a stratification variable), with an optional
additional graph showing what the proportions would be had proportional
odds held and an odds ratio was applied to the proportions in a
reference group. If the result is passed to ggplotly
, customized
tooltip hover text will appear.
propsTrans
uses ggplot2
to plot all successive
transition proportions. formula
has the state variable on the
left hand side, the first right-hand variable is time, and the second
right-hand variable is a subject ID variable.\
multEventChart
uses ggplot2
to plot event charts
showing state transitions, account for absorbing states/events. It is
based on code written by Lucy D'Agostino McGowan posted at https://livefreeordichotomize.com/posts/2020-05-21-survival-model-detective-1/.
popower(p, odds.ratio, n, n1, n2, alpha=0.05)
# S3 method for popower
print(x, ...)
posamsize(p, odds.ratio, fraction=.5, alpha=0.05, power=0.8)
# S3 method for posamsize
print(x, ...)
pomodm(x=NULL, p, odds.ratio=1)
simPOcuts(n, nsim=10, odds.ratio=1, p)
propsPO(formula, odds.ratio=NULL, ref=NULL, data=NULL, ncol=NULL, nrow=NULL )
propsTrans(formula, data=NULL, labels=NULL, arrow='\u2794',
maxsize=12, ncol=NULL, nrow=NULL)
multEventChart(formula, data=NULL, absorb=NULL, sortbylast=FALSE,
colorTitle=label(y), eventTitle='Event',
palette='OrRd',
eventSymbols=c(15, 5, 1:4, 6:10),
timeInc=min(diff(unique(x))/2))
a list containing power
, eff
(relative efficiency), and
approx.se
(approximate standard error of log odds ratio) for
popower
, or containing n
and eff
for posamsize
.
a vector of marginal cell probabilities which must add up to one.
For popower
and posamsize
, The i
th element specifies the probability that a patient will be
in response level i
, averaged over the two treatment groups. For
pomodm
and simPOcuts
, p
is the vector of cell
probabilities to be translated under a given odds ratio. For
simPOcuts
, if p
has names, those names are taken as the
ordered distinct Y-values. Otherwise Y-values are taken as the integers
1, 2, ... up to the length of p
.
the odds ratio to be able to detect. It doesn't
matter which group is in the numerator. For propsPO
,
odds.ratio
is a function of the grouping (right hand side)
variable value. The value of the function specifies the odds ratio to
apply to the refernce group to get all other group's expected proportions
were proportional odds to hold against the first group. Normally the
function should return 1.0 when its x
argument corresponds to the
ref
group. For pomodm
and simPOcuts
is the odds
ratio to apply to convert the given cell probabilities.
total sample size for popower
. You must specify either n
or
n1
and n2
. If you specify n
, n1
and
n2
are set to n/2
. For simPOcuts
is a single number
equal to the combined sample sizes of two groups.
for popower
, the number of subjects in treatment group 1
for popower
, the number of subjects in group 2
number of simulated studies to create by simPOcuts
type I error
an object created by popower
or posamsize
, or a
vector of data values given to pomodm
that corresponds to the
vector p
of probabilities. If x
is omitted for
pomodm
, the odds.ratio
will be applied and the new
vector of individual probabilities will be returned. Otherwise if
x
is given to pomodm
, a 2-vector with the mean and
median x
after applying the odds ratio is returned.
for posamsize
, the fraction of subjects that will be allocated to group 1
for posamsize
, the desired power (default is 0.8)
an R formula expressure for proposPO
where the
outcome categorical variable is on the left hand side and the grouping
variable is on the right. It is assumed that the left hand variable is
either already a factor or will have its levels in the right order for
an ordinal model when it is converted to factor. For
multEventChart
the left hand variable is a categorial status
variable, the first right hand side variable represents time, and the
second right side variable is a unique subject ID. One line is
produced per subject.
for propsPO
specifies the reference group (value of
the right hand side formula
variable) to use in computing
proportions on which too translate proportions in other groups, under
the proportional odds assumption.
a data frame or data.table
for propsTrans
is an optional character vector
corresponding to y=1,2,3,... that is used to construct plotly
hovertext as a label
attribute in the ggplot2
aesthetic. Used with y is integer on axes but you want long labels in
hovertext.
character to use as the arrow symbol for transitions in
propsTrans. The default is the dingbats heavy wide-headed
rightwards arror.
see facet_wrap
maximum symbol size
unused
character vector specifying the subset of levels of the left hand side variable that are absorbing states such as death or hospital discharge
set to TRUE
to sort the subjects by the
severity of the status at the last time point
label for legend for status
label for legend for absorb
a single character string specifying the
scale_fill_brewer
color palette
vector of symbol codes. Default for first two symbols is a solid square and an open diamond.
time increment for the x-axis. Default is 1/2 the shortest gap between any two distincttimes in the data.
Frank Harrell
Department of Biostatistics
Vanderbilt University School of Medicine
fh@fharrell.com
Whitehead J (1993): Sample size calculations for ordered categorical data. Stat in Med 12:2257--2271.
Julious SA, Campbell MJ (1996): Letter to the Editor. Stat in Med 15: 1065--1066. Shows accuracy of formula for binary response case.
simRegOrd
, bpower
, cpower
, impactPO
# 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'
require(ggplot2)
multEventChart(status ~ day + pt, data=d,
absorb=c('death', 'discharged'),
colorTitle='Status', sortbylast=TRUE) +
theme_classic() +
theme(legend.position='bottom')
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