| nomogram {Design} | R Documentation |
Draws a partial nomogram that can be used to manually obtain predicted
values from a regression model that was fitted with Design in effect.
The nomogram does not have lines representing sums, but it has a reference
line for reading scoring points (default range 0-100). Once the reader
manually totals the points, the predicted values can be read at the bottom.
Non-monotonic transformations of continuous variables are handled (scales
wrap around), as
are transformations which have flat sections (tick marks are labeled
with ranges). If interactions are in the model, one variable
is picked as the "axis variable", and separate axes are constructed for
each level of the interacting factors (preference is given automatically
to using any discrete factors to construct separate axes) and
levels of factors which are indirectly related to interacting
factors (see DETAILS). Thus the nomogram is designed so that only
one axis is actually read for each variable, since the variable
combinations are disjoint. For
categorical interacting factors, the default is to construct axes for
all levels.
The user may specify
coordinates of each predictor to label on its axis, or use default values.
If a factor interacts with other factors, settings for one or more of
the interacting factors may be specified separately (this is mandatory
for continuous variables). Optional confidence intervals will be
drawn for individual scores as well as for the linear predictor.
If more than one confidence level is chosen, multiple levels may be
displayed using different colors or gray scales. Functions of the
linear predictors may be added to the nomogram.
print.nomogram prints axis information stored in an object returned
by nomogram. This is useful in producing tables of point assignments
by levels of predictors. It also prints how many linear predictor
units there are per point and the number of points per unit change in
the linear predictor.
legend.nomabbrev draws legends describing abbreviations used for
labeling tick marks for levels of categorical predictors.
nomogram(fit, ...)
## S3 method for class 'Design':
nomogram(fit, ..., adj.to,
lp=TRUE, lp.at, lplabel="Linear Predictor",
fun, fun.at, fun.lp.at,
funlabel="Predicted Value", fun.side,
interact=NULL, intercept=1, conf.int=FALSE,
col.conf=c(1, if(under.unix).3 else 12),
conf.space=c(.08,.2),
conf.lp=c("representative","all", "none"),
est.all=TRUE, abbrev=FALSE, minlength=4,
maxscale=100, nint=10, label.every=1, force.label=FALSE,
xfrac=0.35, cex.axis=0.85, cex.var=1, col.grid=FALSE,
vnames=c("labels","names"), varname.label=TRUE,
varname.label.sep="=",
ia.space=.7, tck=-.009, lmgp=.4, omit=NULL, naxes,
points.label='Points', total.points.label='Total Points',
total.sep.page=FALSE, total.fun, verbose=FALSE)
## S3 method for class 'nomogram':
print(x, dec=0, ...)
legend.nomabbrev(object, which, x, y, ncol=3, ...)
fit |
a regression model fit that was created with library(Design) in
effect, and (usually) with options(datadist="object.name") in effect.
|
object |
the result returned from nomogram
|
which |
a character string giving the name of a variable for which to draw a legend with abbreviations of factor levels |
x |
|
y |
coordinates to pass to the legend function. This is the upper left
corner of the legend box. You can omit y if x is a list with
named elements x and y. To use the mouse to locate the legend,
specify locator(1) for x. For print, x is
the result of nomogram.
|
... |
settings of variables to use in constructing axes. If datadist
was in effect, the default is to use pretty(total range, nint)
for continuous variables, and the class levels for discrete ones.
For legend.nomabbrev, ... specifies optional parameters to pass
to legend. Common ones are bty="n" to suppress drawing the
box. You may want to specify a non-proportionally spaced font
(e.g., courier) number if abbreviations are more than one letter long.
This will make the abbreviation definitions line up (e.g., specify
font=2, the default for courier). Ignored for print.
|
adj.to |
If you didn't define datadist for all predictors, you will have to
define adjustment settings for the undefined ones, e.g.
adj.to=list(age=50, sex="female").
|
interact |
When a continuous variable interacts with a discrete one, axes are
constructed so that the continuous variable moves within the axis, and
separate axes represent levels of interacting factors. For interactions
between two continuous variables, all but the axis variable must have
discrete levels defined in interact.
For discrete interacting factors, you may specify levels to use in
constructing the multiple axes. For continuous interacting factors,
you must do this. Examples: interact=list(age=seq(10,70,by=10),
treat=c("A","B","D")).
|
lp |
Set to FALSE to suppress creation of an axis for scoring
X beta.
|
lp.at |
If lp=TRUE, lp.at may specify a vector of settings of
X beta.
Default is to use pretty(range of linear predictors, nint).
|
lplabel |
label for linear predictor axis. Default is "Linear Predictor".
|
fun |
an optional function to transform the linear predictors, and to plot
on another axis. If more than one transformation is plotted, put
them in a list, e.g. list(function(x)x/2, function(x)2*x).
Any function values equal to NA will be ignored.
|
fun.at |
function values to label on axis. Default fun evaluated
at lp.at. If more than one fun was specified, using a vector
for fun.at will cause all functions to be evaluated at the same
argument values. To use different values, specify a list of vectors for
fun.at, with elements corresponding to the different functions
(lists of vectors also applies to fun.lp.at and fun.side).
|
fun.lp.at |
If you want to
evaluate one of the functions at a different set of linear predictor
values than may have been used in constructing the linear predictor axis,
specify a vector or list of vectors
of linear predictor values at which to evaluate the function. This is
especially useful for discrete functions. The presence of this attribute
also does away with the need for nomogram to compute numerical approximations of
the inverse of the function. It also allows the user-supplied function
to return factor objects, which is useful when e.g. a single tick
mark position actually represents a range.
If the fun.lp.at parameter is present, the fun.at
vector for that function is ignored.
|
fun.side |
a vector or list of vectors of side parameters for the axis function
for labeling function values.
Values may be 1 to position a tick mark label below the axis (the default),
or 3 for above the axis. If for example an axis has 5 tick mark labels
and the second and third will run into each other, specify
fun.side=c(1,1,3,1,1) (assuming only one function is specified as fun).
|
funlabel |
label for fun axis. If more than one function was given but
funlabel is of length one, it will be duplicated as needed. If fun is
a list of functions for which you specified names (see the final example
below), these names will be used as labels.
|
conf.int |
confidence levels to display for each scoring. Default is FALSE to display
no confidence limits. Setting conf.int to TRUE is the same as
setting it to c(0.7, 0.9),
with the line segment between the 0.7 and 0.9 levels shaded using
gray scale.
|
col.conf |
colors corresponding to conf.int. Use fractions for gray scale
(for UNIX S-PLUS).
|
conf.space |
a 2-element vector with the vertical range within which to draw confidence bars, in units of 1=spacing between main bars. Four heights are used within this range (8 for the linear predictor if more than 16 unique values were evaluated), cycling them among separate confidence intervals to reduce overlapping. |
conf.lp |
default is "representative" to group all linear predictors evaluated
into deciles, and to show, for the linear predictor confidence intervals,
only the mean linear predictor within the deciles along with the median
standard error within the deciles. Set conf.lp="none" to suppress
confidence limits for the linear predictors, and to "all" to show
all confidence limits.
|
intercept |
for models such as the ordinal logistic model with multiple intercepts, specifies which one to use in evaluating the linear predictor. |
est.all |
To plot axes for only the subset of variables named in ..., set
est.all=FALSE. Note: This option only works when zero has a special
meaning for the variables that are omitted from the graph.
|
abbrev |
Set to TRUE to use the abbreviate function to abbreviate levels of
categorical factors, both for labeling tick marks and for axis titles.
If you only want to abbreviate certain predictor variables, set abbrev
to a vector of character strings containing their names.
|
minlength |
applies if abbrev=TRUE. Is the minimum abbreviation length passed to the
abbreviate function. If you set minlength=1, the letters of the
alphabet are used to label tick marks for categorical predictors, and
all letters are drawn no matter how close together they are. For
labeling axes (interaction settings), minlength=1 causes
minlength=4 to be used.
|
maxscale |
default maximum point score is 100 |
nint |
number of intervals to label for axes representing continuous variables.
See pretty.
|
label.every |
Specify label.every=i to label on every ith tick mark.
|
force.label |
set to TRUE to force every tick mark intended to be labeled to have
a label plotted (whether the labels run into each other or not)
|
xfrac |
fraction of horizontal plot to set aside for axis titles |
cex.axis |
character size for tick mark labels |
cex.var |
character size for axis titles (variable names) |
col.grid |
If col.grid=1, no gray scale is used, but an ordinary line is drawn.
If 0<col.grid<1,
a col (gray scale) of col.grid is used to draw vertical reference
lines for major axis divisions and col.grid/2 for minor divisions.
The default is col.grid=FALSE, i.e., reference lines are omitted.
Specifying col.grid=TRUE is the same as specifying a gray scale level
of col.grid=.2 (5 for Windows S-PLUS).
|
vnames |
By default, variable labels are used to label axes. Set vnames="names"
to instead use variable names.
|
varname.label |
In constructing axis titles for interactions, the default is to add
"(interacting.varname=level) on the right. Specify varname.label=FALSE
to instead use "(level)".
|
varname.label.sep |
If varname.label=TRUE, you can change the separator to something other than
= by specifying this parameter.
|
ia.space |
When multiple axes are draw for levels of interacting factors, the default is to group combinations related to a main effect. This is done by spacing the axes for the second to last of these within a group only 0.7 (by default) of the way down as compared with normal space of 1 unit. |
tck |
see tck under par
|
lmgp |
spacing between numeric axis labels and axis (see par for mgp)
|
omit |
vector of character strings containing names of variables for which to suppress drawing axes. Default is to show all variables. |
naxes |
maximum number of axes to allow on one plot. If the nomogram requires more than one "page", the "Points" axis will be repeated at the top of each page when necessary. |
points.label |
a character string giving the axis label for the points scale |
total.points.label |
a character string giving the axis label for the total points scale |
total.sep.page |
set to TRUE to force the total points and later axes to be placed on a
separate page
|
total.fun |
a user-provided function that will be executed before the total points
axis is drawn. Default is not to execute a function. This is useful e.g.
when total.sep.page=TRUE and you wish to use locator to find the
coordinates for positioning an abbreviation legend before it's too late
and a new page is started (i.e., total.fun=function()print(locator(1))).
|
verbose |
set to TRUE to get printed output detailing how tick marks are chosen
and labeled for function axes. This is useful in seeing how certain
linear predictor values cannot be solved for using inverse linear
interpolation on the (requested linear predictor values, function values at
these lp values). When this happens you will see NAs in the verbose
output, and the corresponding tick marks will not appear in the nomogram.
|
dec |
number of digits to the right of the decimal point, for rounding
point scores in print.nomogram. Default is to round to the nearest
whole number of points.
|
ncol |
the number of columns to form in drawing the legend. |
A variable is considered to be discrete if it is categorical or ordered
or if datadist stored values for it (meaning it had <11 unique
values).
A variable is said to be indirectly related to another variable if
the two are related by some interaction. For example, if a model
has variables a, b, c, d, and the interactions are a:c and c:d,
variable d is indirectly related to variable a. The complete list
of variables related to a is c, d. If an axis is made for variable a,
several axes will actually be drawn, one for each combination of c
and d specified in interact.
Note that with a caliper, it is easy to continually add point scores
for individual predictors, and then to place the caliper on the upper
Points axis (with extrapolation if needed). Then transfer these
points to the
Total Points axis. In this way, points can be added without
without writing them down.
Confidence limits for an individual predictor score are really confidence
limits for the entire linear predictor, with other predictors set to
adjustment values. If lp=TRUE, all confidence bars for all linear
predictor values evaluated are drawn. The extent to which multiple
confidence bars of differing widths appear at the same linear predictor
value means that precision depended on how the linear predictor was
arrived at (e.g., a certain value may be realized from a setting of
a certain predictor that was associated with a large standard error
on the regression coefficients for that predictor).
On occasion, you may want to reverse the regression coefficients of a model
to make the "points" scales reverse direction. For parametric survival
models, which are stated in terms of increasing regression effects meaning
longer survival (the opposite of a Cox model), just do something like
fit$coefficients <- -fit$coefficients before invoking nomogram,
and if you add function axes, negate the function
arguments. For the Cox model, you also need to negate fit$center.
If you omit lp.at, also negate fit$linear.predictors.
a list of class "nomogram" that contains information used in plotting
the axes. If you specified abbrev=TRUE, a list called abbrev is also
returned that gives the abbreviations used for tick mark labels, if any.
This list is useful for
making legends and is used by legend.nomabbrev (see the last example).
The returned list also has components called total.points, lp,
and the function axis names. These components have components
x (at argument vector given to axis), y (pos for axis),
and x.real, the x-coordinates appearing on tick mark labels.
An often useful result is stored in the list of data for each axis variable,
namely the exact number of points that correspond to each tick mark on
that variable's axis.
Frank Harrell
Department of Biostatistics
Vanderbilt University
f.harrell@vanderbilt.edu
Banks J: Nomograms. Encylopedia of Statistical Sciences, Vol 6. Editors: S Kotz and NL Johnson. New York: Wiley; 1985.
Lubsen J, Pool J, van der Does, E: A practical device for the application of a diagnostic or prognostic function. Meth. Inform. Med. 17:127–129; 1978.
Wikipedia: Nomogram, http://en.wikipedia.org/wiki/Nomogram.
Design, plot.Design, plot.summary.Design, axis, pretty, approx,
latex.Design, Design.Misc
n <- 1000 # define sample size
set.seed(17) # so can reproduce the results
age <- rnorm(n, 50, 10)
blood.pressure <- rnorm(n, 120, 15)
cholesterol <- rnorm(n, 200, 25)
sex <- factor(sample(c('female','male'), n,TRUE))
# Specify population model for log odds that Y=1
L <- .4*(sex=='male') + .045*(age-50) +
(log(cholesterol - 10)-5.2)*(-2*(sex=='female') + 2*(sex=='male'))
# Simulate binary y to have Prob(y=1) = 1/[1+exp(-L)]
y <- ifelse(runif(n) < plogis(L), 1, 0)
ddist <- datadist(age, blood.pressure, cholesterol, sex)
options(datadist='ddist')
f <- lrm(y ~ lsp(age,50)+sex*rcs(cholesterol,4)+blood.pressure)
nomogram(f, fun=function(x)1/(1+exp(-x)), # or fun=plogis
fun.at=c(.001,.01,.05,seq(.1,.9,by=.1),.95,.99,.999),
funlabel="Risk of Death", xfrac=.45)
#Instead of fun.at, could have specified fun.lp.at=logit of
#sequence above - faster and slightly more accurate
nomogram(f, age=seq(10,90,by=10), xfrac=.45)
g <- lrm(y ~ sex + rcs(age,3)*rcs(cholesterol,3))
nomogram(g, interact=list(age=c(20,40,60)),
conf.int=c(.7,.9,.95), col.conf=c(1,.5,.2))
cens <- 15*runif(n)
h <- .02*exp(.04*(age-50)+.8*(sex=='Female'))
d.time <- -log(runif(n))/h
death <- ifelse(d.time <= cens,1,0)
d.time <- pmin(d.time, cens)
f <- psm(Surv(d.time,death) ~ sex*age, dist=if(.R.)'lognormal' else 'gaussian')
med <- Quantile(f)
surv <- Survival(f) # This would also work if f was from cph
nomogram(f, fun=function(x) med(lp=x), funlabel="Median Survival Time")
nomogram(f, fun=list(function(x) surv(3, x), function(x) surv(6, x)),
funlabel=c("3-Month Survival Probability",
"6-month Survival Probability"), xfrac=.5)
## Not run:
nom <- nomogram(fit.with.categorical.predictors, abbrev=TRUE, minlength=1)
nom$x1$points # print points assigned to each level of x1 for its axis
#Add legend for abbreviations for category levels
abb <- nom$abbrev$treatment
legend(locator(1), abb$full, pch=paste(abb$abbrev,collapse=''),
ncol=2, bty='n') # this only works for 1-letter abbreviations
#Or use the legend.nomabbrev function:
legend.nomabbrev(nom, 'treatment', locator(1), ncol=2, bty='n')
## End(Not run)
#Make a nomogram with axes predicting probabilities Y>=j for all j=1-3
#in an ordinal logistic model, where Y=0,1,2,3
Y <- ifelse(y==0, 0, sample(1:3, length(y), TRUE))
g <- lrm(Y ~ age+rcs(cholesterol,4)*sex)
fun2 <- function(x) plogis(x-g$coef[1]+g$coef[2])
fun3 <- function(x) plogis(x-g$coef[1]+g$coef[3])
f <- Newlabels(g, c(age='Age in Years'))
#see Design.Misc, which also has Newlevels to change
#labels for levels of categorical variables
nomogram(f, fun=list('Prob Y>=1'=plogis, 'Prob Y>=2'=fun2,
'Prob Y=3'=fun3),
fun.at=c(.01,.05,seq(.1,.9,by=.1),.95,.99),
lmgp=.2, cex.axis=.6)
options(datadist=NULL)