# nomogram

##### Draw a Nomogram Representing a Regression Fit

Draws a partial nomogram that can be used to manually obtain predicted
values from a regression model that was fitted with `rms`

.
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

`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.

- Keywords
- models, hplot, regression

##### Usage

```
nomogram(fit, ..., adj.to, lp=TRUE, lp.at=NULL,
fun=NULL, fun.at=NULL, fun.lp.at=NULL, funlabel="Predicted Value",
interact=NULL, intercept=1, conf.int=FALSE,
conf.lp=c("representative", "all", "none"),
est.all=TRUE, abbrev=FALSE, minlength=4, maxscale=100, nint=10,
vnames=c("labels","names"),
varname.label=TRUE, varname.label.sep="=",
omit=NULL, verbose=FALSE)
```## S3 method for class 'nomogram':
print(x, dec=0, \dots)

## S3 method for class 'nomogram':
plot(x, lplabel="Linear Predictor", fun.side,
col.conf=c(1,if(under.unix).3 else 12),
conf.space=c(.08,.2), label.every=1, force.label=FALSE,
xfrac=.35, cex.axis=.85, cex.var=1, col.grid=NULL,
varname.label=TRUE, varname.label.sep="=", ia.space=.7,
tck=NA, tcl=-0.25, lmgp=.4, naxes,
points.label='Points', total.points.label='Total Points',
total.sep.page=FALSE, total.fun, cap.labels=FALSE, ...)

legend.nomabbrev(object, which, x, y, ncol=3, ...)

##### Arguments

- fit
- a regression model fit that was created with
`rms`

, and (usually) with`options(datadist = "object.name")`

in effect. - ...
- 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.nomabb`

- 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")`

. - 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)`

. - 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 - 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 argumen - 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 evalu
- 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), thes - 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
- intercept
- for models such as the ordinal logistic model with multiple intercepts, specifies which one to use in evaluating the linear predictor.
- 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 bet - 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 - 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 predi - 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 - maxscale
- default maximum point score is 100
- nint
- number of intervals to label for axes representing continuous variables.
See
`pretty`

. - vnames
- By default, variable labels are used to label axes. Set
`vnames = "names"`

to instead use variable names. - omit
- vector of character strings containing names of variables for which to suppress drawing axes. Default is to show all variables.
- 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 (req - x
- an object created by
`nomogram`

, or the x coordinate for a legend - 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. - lplabel
- label for linear predictor axis. Default is
`"Linear Predictor"`

. - 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 a - col.conf
- colors corresponding to
`conf.int`

. - 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), cycli
- label.every
- Specify
`label.every = i`

to label on every`i`

th 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 left unspecified, no vertical reference lines are drawn. Specify a vector of length one (to use the same color for both minor and major reference lines) or two (corresponding to the color for the major and minor divisions, respectively) co
- 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 wa
- tck
- see
`tck`

under`par`

- tcl
- length of tick marks in nomogram
- lmgp
- spacing between numeric axis labels and axis (see
`par`

for`mgp`

) - naxes
- maximum number of axes to allow on one plot. If the nomogram requires more
than one
page , thePoints 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 coor - cap.labels
- logical: should the factor labels have their first letter capitalized?
- 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
- y
- y-coordinate 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 - ncol
- the number of columns to form in drawing the legend.

##### Details

A variable is considered to be discrete if it is categorical or ordered
or if `datadist`

stored `values`

for it (meaning it
had ```
<11< code=""> 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
```

```
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
```

`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`

.

##### Value

- 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.

##### References

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,

##### See Also

`rms`

, `plot.Predict`

, `plot.summary.rms`

, `axis`

, `pretty`

, `approx`

,
`latex.rms`

, `rmsMisc`

##### Examples

```
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)
nom <- 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")
#Instead of fun.at, could have specified fun.lp.at=logit of
#sequence above - faster and slightly more accurate
plot(nom, xfrac=.45)
print(nom)
nom <- nomogram(f, age=seq(10,90,by=10))
plot(nom, xfrac=.45)
g <- lrm(y ~ sex + rcs(age,3)*rcs(cholesterol,3))
nom <- nomogram(g, interact=list(age=c(20,40,60)),
conf.int=c(.7,.9,.95))
plot(nom, col.conf=c(1,.5,.2), naxes=7)
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
plot(nomogram(f, fun=function(x) med(lp=x), funlabel="Median Survival Time"))
nom <- nomogram(f, fun=list(function(x) surv(3, x),
function(x) surv(6, x)),
funlabel=c("3-Month Survival Probability",
"6-month Survival Probability"))
plot(nom, xfrac=.7)
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 <- attr(nom, 'info')$abbrev$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')
#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
g <- 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))
plot(g, lmgp=.2, cex.axis=.6)
options(datadist=NULL)
```

*Documentation reproduced from package rms, version 2.0-2, License: GPL (>= 2)*