Package 'anoint' reference manual

Title:	Analysis of Interactions
Description:	The tools in this package are intended to help researchers assess multiple treatment-covariate interactions with data from a parallel-group randomized controlled clinical trial. The methods implemented in the package were proposed in Kovalchik, Varadhan and Weiss (2013) <doi: 10.1002/sim.5881>.
Authors:	Ravi Varadhan [aut, cre], Stephanie Kovalchik [aut], Leon Wang [ctb]
Maintainer:	Ravi Varadhan <[email protected]>
License:	GPL (>= 2)
Version:	1.5
Built:	2026-05-10 06:35:46 UTC
Source:	https://github.com/cran/anoint

Analysis of interactions for generalized linear models (GLM) or Cox proportional hazards regression models.

Description

Testing procedures and models for investigating the heterogeneity of treatment effect in a clinical trial with multiple baseline covariates.

Details

Package:	anoint
Type:	Package
Version:	1.4
Date:	2015-7-10
License:	GPL

Author(s)

Ravi Varadhan <[email protected]> and Stephanie Kovalchik (maintainer) <[email protected]>

References

Follmann DA, Proschan MA. A multivariate test of interaction for use in clinical trials. Biometrics 1999; 55(4):1151-1155

Create analysis of interactions object

Description

Prepares formula and data to be used in methods with the analysis of interactions class.

Usage

anoint(formula,data,family="binomial",select=NULL,nfolds=10,
  type.measure="deviance",keep.vars=NULL,na.action=na.omit,...)
anoint(formula,data,family="binomial",select=NULL,nfolds=10,
  type.measure="deviance",keep.vars=NULL,na.action=na.omit,...)

Arguments

formula

analysis of interaction formula for glm or coxph, see details

data

data.frame containing the variables of formula

family

character specifying family of glm or character "coxph" if coxph model is fit

select

character for type of selection to perform, either "stepAIC" or "glmnet".

nfolds

number of folds used in cross-validation to find lasso penalty parameter when select is set to TRUE. Used only when select is glmnet. See cv.glmnet

type.measure

loss to use for cross-validation. Used only when select is glmnet. See cv.glmnet

keep.vars

vector of names of variables to retain if selection procedure is used. Used only when select is glmnet.

na.action

function, na.action to perform for handling observations with missing variables among variables in formula. Default is na.omit

...

additional arguments passed to cv.glmnet when select is glmnet or stepAIC when select is stepAIC.

Details

To test proportional multiple interactions between treatment variable indicator z (binary, 0 or 1) and variables a, b, with response y of a GLM model, formula must be y~(a+b)*z. If a Cox model with event time time and event indicator event, formula is Surv(time,event)~(a+b)*z.

Factors should not be included as a or b because this could change how the reference group is represented in the model. Separate 0/1 dummy variables must be supplied by the user.

When select is glmnet a Lasso method (cv.glmnet) is used to select prognostic factors using 10-fold cross-validation with the control data only. If select is set to stepAIC a stepwise selection procedure is used with specifications based on arguments passed to ....

Value

Returns instance of anoint class.

Author(s)

Stephanie Kovalchik <[email protected]>

References

Follmann DA, Proschan MA. A multivariate test of interaction for use in clinical trials. Biometrics 1999; 55(4):1151-1155

Examples


# NO INTERACTION CONDITION, LOGISTIC MODEL

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(c(1.5,2)),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival", n = 500
                             )

head(null.interaction)

object <- anoint(Surv(y, event)~(V1+V2)*trt,data=null.interaction,family="coxph")

object

summary(object)

# NO INTERACTION CONDITION, WITH PROGNOSTIC SELECTION

null.interaction <- data.anoint(
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = c(1.5,2,0,0),
                             gamma = rep(1,4),
                             mean = rep(0,4),
                             vcov = diag(4),
                             type="binomial", n = 500
                             )

head(null.interaction)

object <- anoint(y~(V1+V2+V3+V4)*trt,data=null.interaction,select="glmnet")

summary(object)

# FORCE V1, V2 INTO THE MODEL; INTERCEPT IS ALWAYS THE FIRST TERM OF MODEL
object <- anoint(y~(V1+V2+V3+V4)*trt,data=null.interaction,
			select="glmnet",keep.vars=c("V1","V2"))

summary(object)

# SELECTION WITH STEPWISE SELECTION AND AIC CRITERION
object <- anoint(y~(V1+V2+V3+V4)*trt,data=null.interaction,
			select="stepAIC")

summary(object)

# NO INTERACTION CONDITION, LOGISTIC MODEL

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(c(1.5,2)),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival", n = 500
                             )

head(null.interaction)

object <- anoint(Surv(y, event)~(V1+V2)*trt,data=null.interaction,family="coxph")

object

summary(object)

# NO INTERACTION CONDITION, WITH PROGNOSTIC SELECTION

null.interaction <- data.anoint(
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = c(1.5,2,0,0),
                             gamma = rep(1,4),
                             mean = rep(0,4),
                             vcov = diag(4),
                             type="binomial", n = 500
                             )

head(null.interaction)

object <- anoint(y~(V1+V2+V3+V4)*trt,data=null.interaction,select="glmnet")

summary(object)

# FORCE V1, V2 INTO THE MODEL; INTERCEPT IS ALWAYS THE FIRST TERM OF MODEL
object <- anoint(y~(V1+V2+V3+V4)*trt,data=null.interaction,
			select="glmnet",keep.vars=c("V1","V2"))

summary(object)

# SELECTION WITH STEPWISE SELECTION AND AIC CRITERION
object <- anoint(y~(V1+V2+V3+V4)*trt,data=null.interaction,
			select="stepAIC")

summary(object)

Fits and global tests of analysis of interaction models

Description

Fits one-by-one (OBO), unrestricted (UIM), and proportional interaction (PIM) regression models to investigate multiple treatment response factors in a parallel-group clinical trial.

Arguments

object

object of anoint class

level

significance level for global interaction tests

interval

interval of possible values for responsiveness parameter of PIM

Details

The global tests for the presence of treatment response factors (treatment-covariate interaction) are one-stage or two-stage likelihood ratio tests.

The fitted multiple interaction models include: one-by-one univariate interaction models (OBO), a full unrestricted model with all pairwise treatment-covariate interactions (UIM), and a proportional interactions model (PIM) fit with an exact or asymptotic approximate estimate for the likelihood ratio test and responsiveness parameter, theta.

Objects from the Class

Objects can be created by calls of the form anoint.fit(object, level = .05, interval=c(.5,3))

Slots

K: number of prognostic factors
responsiveness: list with exact and approximate estimates of PIM responsiveness parameter
tests: list of global interaction test results
pvalues: list of pvalues on which test rejections are based
fits: list of fitted models for each anoint method

Components of tests are the results of the global tests of interaction:

obo.reject: Result of unadjusted one-by-one global test of interaction. Null is no effect modification for K subgroups, the alternative is at least one K is an effect modifier.
obo.adjust: Same as obo.reject but with Bonferroni-correction for K comparisons
uim.reject: Result of UIM global test of interaction. Null is no effect modification for K subgroups, the alternative is at least one K is an effect modifier.
pim.exact.reject: Result of PIM exact global test of interaction. Null is no proportional effect modification (theta responsiveness parameter = 1) against the alternative that the treatment responsiveness parameter theta is not equal to 1.
pim.approx.reject: Same as pim.exact.reject but using approximate method.
pim.obo: Two-stage global test. First stage tests PIM using an exact method at level/2 significance. If not rejected, the second stage is a test of adjusted OBO with a second-stage global level/2 significance.
pim.uim: Same as pim.obo but with UIM at the second stage.

Components of pvalues on which the global tests are based:

obo.p: p-value for the maximum LRT of the one-by-one testing
uim.p: p-value for the global LRT of any interaction base on UIM
pim.exact.p: p-value for the test of proportional interaction using the PIM exact method
pim.approx.p: p-value for the test of proportional interaction using the PIM approximate method

Components of fits are the models underlying the global interaction tests:

obo: Univariate interaction regression models of each subgroup.
uim: Full regression model with all pairwise treatment-covariate interactionns
pim.exact: Proportional interactions model with exact fit
pim.approx: Proportional interactions model with asymptotic approximate estimation

Methods

show: signature(object = "anoint.fit"): Display table of results of global test of interaction.
print: signature(x = "anoint.fit",...): Display table of results of global test of interaction.
summary: signature(object = "anoint.fit",...): Display results of global test of interaction and p-values. Returns list with tests and pvalues.
fits: signature(object = "anoint.fit",type=c("obo","uim","pim.exact","pim.approx"): Extracts the specified fitted object from a anoint.fit.

Author(s)

S. Kovalchik [email protected]

Examples


# NO INTERACTION CONDITION, LOGISTIC MODEL

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(c(1.5,2)),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival", n = 500
                             )

object <- anoint(Surv(y, event)~(V1+V2)*trt,data=null.interaction,family="coxph")

fit <- anoint.fit(object)

summary(fit)

fits(fit,type="obo")
# NO INTERACTION CONDITION, LOGISTIC MODEL

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(c(1.5,2)),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival", n = 500
                             )

object <- anoint(Surv(y, event)~(V1+V2)*trt,data=null.interaction,family="coxph")

fit <- anoint.fit(object)

summary(fit)

fits(fit,type="obo")

Create a `formula.anoint` object

Description

Create formula for use with anoint.

Usage

anoint.formula(formula=y~(a+b)*trt,family="binomial")
anoint.formula(formula=y~(a+b)*trt,family="binomial")

Arguments

formula

formula specifying analysis of interaction model

family

string indicating model family, should be one of glm families or coxph

Details

The formula should have all subgroups enclosed in parantheses and the treatment variable as an interaction, as shown in default.

Value

Returns instance of formula.anoint class.

Author(s)

Stephanie Kovalchik <[email protected]>

Examples


anoint.formula()

anoint.formula()

Perform one-by-one subgroup analyses

Description

Computes all interaction effects one variable at a time.

Usage

anoint.subgroups(formula,trt,data,family="binomial",na.action=na.omit,fwer=0.05,...)
anoint.subgroups(formula,trt,data,family="binomial",na.action=na.omit,fwer=0.05,...)

Arguments

formula

formula for covariate model as given in glm or coxph, i.e. y~x1+x2

trt

character name of treatment assignment indicator

data

data.frame containing the variables of formula and trt

family

character specifying family of glm or character "coxph" if coxph model is fit

na.action

function, na.action to perform for handling observations with missing variables among variables in formula. Default is na.omit

fwer

numeric value for the desired familywise error rate, should be between 0 and 1.

...

additional arguments passed to glm or coxph

Value

Returns a list with

subset: indicator of the covariates included in the fitted model
interaction: value of the of treatment-covariate interaction effect (using model with treatment-covariate product term)
LRT: value of likelihood ratio test of treatment-covariate interaction
lower: lower endpoints of 95 percent confidence interval for interaction parameter
upper: upper endpoints of 95 percent confidence interval for interaction parameter
pvalue: pvalue for 1-df chi-squared test
include.exclude.matrix: matrix of same rows as covariates and columns as covariates with logical entries indicating which covariates (columns) were include in the fitted model (row)
covariates: vector of covariate names as in formula
reject: indicator of rejected hypotheses using a Bonferroni multiple testing correction such that familywise error is controlled at level fwer

Author(s)

Stephanie Kovalchik <[email protected]>

Examples


set.seed(11903)

# NO INTERACTION CONDITION, LOGISTIC MODEL

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(c(1.5,2)),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival", n = 500
                             )

head(null.interaction)

anoint.subgroups(Surv(y, event)~V1+V2,trt="trt",data=null.interaction,family="coxph")


# PROPORTIONAL INTERACTION WITH THREE COVARIATES AND BINARY OUTCOME

pim.interaction <- data.anoint(
			     n = 5000,
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = rep(log(.8),3),
                             gamma = rep(1.5,3),
                             mean = c(0,0,0),
                             vcov = diag(3),
                             type="binomial"
                             )

anoint.subgroups(y~V1+V2+V3,trt="trt",data=pim.interaction,family="binomial")
set.seed(11903)

# NO INTERACTION CONDITION, LOGISTIC MODEL

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(c(1.5,2)),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival", n = 500
                             )

head(null.interaction)

anoint.subgroups(Surv(y, event)~V1+V2,trt="trt",data=null.interaction,family="coxph")


# PROPORTIONAL INTERACTION WITH THREE COVARIATES AND BINARY OUTCOME

pim.interaction <- data.anoint(
			     n = 5000,
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = rep(log(.8),3),
                             gamma = rep(1.5,3),
                             mean = c(0,0,0),
                             vcov = diag(3),
                             type="binomial"
                             )

anoint.subgroups(y~V1+V2+V3,trt="trt",data=pim.interaction,family="binomial")

Get coefs from `pim` object.

Description

Extract vector of coefs of the fit of a pim model.

Methods

coef: signature(object = "pim"): Extractor for MLEs returned as a matrix with one column.

Author(s)

S. Kovalchik [email protected]

Compute confindence intervals of `pim` model terms.

Description

Computes Wald-based confidence intervals for the terms of a PIM model.

Methods

confint: signature(object = "pim", parm,level =0.95,...): Returns estimate and confidence intervals for specified parm. Default is to return all params of the model.

Author(s)

S. Kovalchik [email protected]

Generate a clinical trial data set under a specified multiple interaction model

Description

Returns a simulated equal-allocation, parallel-group clinical trial with possibly multiple interactions among prognostic factors.

Usage

data.anoint(alpha, beta, gamma, mean, vcov, n=100, event=.8,
type = c("binomial","survival"))
data.anoint(alpha, beta, gamma, mean, vcov, n=100, event=.8,
type = c("binomial","survival"))

Arguments

alpha

vector specifying control and treatment group intercept

beta

vector specifying prognostic factor main effects

gamma

vector specifying modification of prognostic effects in the presence of treatment

mean

vector of covariate mean to be supplied to mvrnorm of the MASS package.

vcov

matrix of variance-covariance matrix of prognostic covariates to be supplied to mvrnorm

n

number of subjects in each treatment arm

event

proportion of observed events when type is "survival"

type

string indicating type of response variable

Details

When type is "survival", the parameters specify the log-rate for an exponentially distributed random variable. Censored times are non-informatively right-censored. When type is "binomial", the parameters specify a log-odds model.

Value

Data frame with y, trt, and V1,...,VK prognostic factors. The data frame also has event with a time-to-event reponse, which is an indicator for an observed event.

Author(s)

S. Kovalchik [email protected]

Examples


null.interaction <- data.anoint(
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = c(1.5,2),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="binomial"
                             )

fit <- glm(y~(.)*trt,data=null.interaction,family="binomial")

summary(fit)


null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = c(1.5,2),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival",
                             event = .7
                             )

fit <- coxph(Surv(y, event)~(.)*trt,data=null.interaction)

summary(fit)
null.interaction <- data.anoint(
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = c(1.5,2),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="binomial"
                             )

fit <- glm(y~(.)*trt,data=null.interaction,family="binomial")

summary(fit)


null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = c(1.5,2),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival",
                             event = .7
                             )

fit <- coxph(Surv(y, event)~(.)*trt,data=null.interaction)

summary(fit)

Extract fits from `anoint.fit` object

Description

Extract the specified anoint model from a anoint.fit object.

Methods

fits: signature(object = "anoint.fit",type=c("obo","uim","pim.exact","pim.approx"): Extracts the specified fitted object from a anoint.fit.

Author(s)

S. Kovalchik [email protected]

Construct a forestplot from a `anoint` object

Description

Constructs a forestplot displaying the treatment effect within subgroups for each set of specified categorical variables. Provides a visual comparison of subgroup treatment effect to overall treatment effect, without adjustment for confounding factors or multiplicity.

Includes unadjusted p-values for each subgroup's treatment-covariate interaction test for glm or Cox regression models.

Usage


forest(object,terms=NULL,x.axis=NULL,labels=NULL,fun=exp,...)
forest(object,terms=NULL,x.axis=NULL,labels=NULL,fun=exp,...)

Arguments

object

object of anoint class

terms

numeric index indicating which terms in prognostic model to include in plot

x.axis

Points for tick marks of the bottom axis

labels

Matrix of labels of the same rows as onebyone, columns printed from left to right

fun

functional transformation applied to treatment effects and confidence intervals

...

additional arguments passed to foresplot (see details)

Details

Additional arguments that can be specified include:

pch.size: one number of a vector of two elements indicating the (min, max) for the relative plotting symbols. These reflect the relative precision of the symbol estimates
x.axis: Points for tick marks of the bottom axis
header: Vector of names for the columns of labels
main: String of the title of plot

If no values are specifed for the x.axis, eight values over the range of the CIs is used.

If no values are specified for labels, the row names are used.

Value

A labeled forestplot of subgroup treatment effects.

Author(s)

Stephanie Kovalchik <[email protected]>

Examples

data(simsolvd)

obj <- anoint(Surv(ttodthorchfhosp, censor==0)~(nyha+cardratio+current)*trt,data=simsolvd,
       		       family="coxph")

forest(obj)

grid.newpage()

forest(obj,x.axis=seq(0.7,1.5,by=.2))


data(simsolvd)

obj <- anoint(Surv(ttodthorchfhosp, censor==0)~(nyha+cardratio+current)*trt,data=simsolvd,
       		       family="coxph")

forest(obj)

grid.newpage()

forest(obj,x.axis=seq(0.7,1.5,by=.2))

Subsets forest plot for proportional interactions models

Description

Plot of interaction effects for all possible proportional interactions models.

Usage

forest.subsets(object, index = 1:(min(length(object$interaction), 
    30)), labels = NULL, exclude.fill = "white", include.fill = "grey30", 
    signif.fill = "red", percent.inner = 0.9, xlimits = NULL, 
    legend = TRUE, subgroup.text = NULL, subgroup.axis = NULL, 
    subgroup.title = "Included Covariates", 
    effects.text = NULL, effects.axis = NULL, confint = TRUE, 
    segments.gpar = NULL, subgroup = FALSE)
forest.subsets(object, index = 1:(min(length(object$interaction), 
    30)), labels = NULL, exclude.fill = "white", include.fill = "grey30", 
    signif.fill = "red", percent.inner = 0.9, xlimits = NULL, 
    legend = TRUE, subgroup.text = NULL, subgroup.axis = NULL, 
    subgroup.title = "Included Covariates", 
    effects.text = NULL, effects.axis = NULL, confint = TRUE, 
    segments.gpar = NULL, subgroup = FALSE)

Arguments

object

result of pim.subsets

index

vector indicating which subset models to include in plot, maximum of 30 of the best subsets if not specified.

labels

vector of names for subgroups. If NULL, covariates of pim.subsets is used.

exclude.fill

color for grid squares of excluded covariates

include.fill

color for grid squares of included covariates

signif.fill

color for plot circles indicating multiplicity-corrected significance

percent.inner

percentage of graphic device window for plot region

xlimits

vector of two elements indicating minimum and maximum value for effects plot. Values and confidence intervals outside xlimits will be clipped.

legend

logical value indicating whether legend for significant values should be included

subgroup.text

gpar list for modifying title of subgroup grid

subgroup.axis

gpar list for modifying text of subgroup grid labels

subgroup.title

character for title over inclusion/exclusion grid

effects.text

gpar list for modifying title of effects plot

effects.axis

gpar list for modifying text of effects plot axis

confint

logical indicating whether to include 95 percent confidence intervals on effects plot

segments.gpar

gpar list for rendering of confidence interval segments

subgroup

logical indicator of whether fitted object is the result of anoint.subgroups

Details

The significance level is the multiplicity corrected criterion with fwer control as specified by pim.subsets.

Value

Returns a plot of the results of all subsets of proportional interactions models. On the lefthand side we plot a grid describing the subsets models. This is a grid showing the included and exclude covariates of each proportional interactions model. Each row corresponds to a particular model. Colored squares in each row indicate the covariates given a proportional interaction effect, while unfilled (exclude.fill) indicate covariates left out of the model. The righthand side shows the interaction effect estimates (effects) for the corresponding subset model.

Author(s)

Stephanie Kovalchik <[email protected]>

Examples


set.seed(11903)

# NO INTERACTION CONDITION, LOGISTIC MODEL
# SUPPOSE 5 HYPOTHESIZED EFFECT MODIFIERS

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(rep(1.5,5)),
                             gamma = rep(1,5),
                             mean = rep(0,5),
                             vcov = diag(5),
                             type="survival", n = 500
                             )

head(null.interaction)

fit <- pim.subsets(Surv(y, event)~V1+V2+V3+V4+V5,trt="trt",
		data=null.interaction,family="coxph")

forest.subsets(fit)
set.seed(11903)

# NO INTERACTION CONDITION, LOGISTIC MODEL
# SUPPOSE 5 HYPOTHESIZED EFFECT MODIFIERS

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(rep(1.5,5)),
                             gamma = rep(1,5),
                             mean = rep(0,5),
                             vcov = diag(5),
                             type="survival", n = 500
                             )

head(null.interaction)

fit <- pim.subsets(Surv(y, event)~V1+V2+V3+V4+V5,trt="trt",
		data=null.interaction,family="coxph")

forest.subsets(fit)

Class "formula.anoint"

Description

Formula class for anoint objects

Objects from the Class

Objects can be created by calls of the form new("formula.anoint", ...).

Slots

formula:: formula supplied to anoint
uni:: list of all univariate interaction model formulas
prognostic:: formula of subgroup main effects
prognostic.trt:: formula of subgroup and treatment main effects model (no interactions)
trt:: character string of treatment variable
family:: character string describing model family

Methods

show: signature(object = "formula.anoint"): Display main formula of formula.anoint object.
print: signature(x = "formula.anoint",...): Display main formula of formula.anoint object.
update: signature(object = "formula.anoint",...): Updates formula with same syntax as supplied to anoint function.

Author(s)

Stephanie Kovalchik [email protected]

Perform one-by-one (OBO) estimates of treatment-covariate interaction

Description

Fits GLM of Cox regression models with a treatment-covariate interaction separately for each covariate specified in anoint object.

Usage

obo(anoint,...)
obo(anoint,...)

Arguments

anoint

object of class anoint

...

other arguments passed to glm or coxph

Value

A list of model fits (fit), interaction likelihood-ratio statistics (LRT), and pvalues per interaction test (pvalue).

Author(s)

Stephanie Kovalchik [email protected]

Examples

data(simsolvd)

obj <- anoint(Surv(ttodthorchfhosp,censor==0)~(age+beat+lvef)*trt,
				data = simsolvd, family = "coxph")

fits <- obo(obj)

fits

lapply(fits$fit, summary)
data(simsolvd)

obj <- anoint(Surv(ttodthorchfhosp,censor==0)~(age+beat+lvef)*trt,
				data = simsolvd, family = "coxph")

fits <- obo(obj)

fits

lapply(fits$fit, summary)

Fit proportional interaction model

Description

Fits a proportional interactions model from parallel-group clinical trial.

Usage

pim(object,exact=TRUE,interval=c(-3,3),n.boot=NULL,...)
pim(object,exact=TRUE,interval=c(-3,3),n.boot=NULL,...)

Arguments

object

object of class anoint

exact

logical indicator whether exact or approximate fit is performed

interval

interval passed to optimize if exact is TRUE

n.boot

number of bootstrap resamples for variance calculations

...

other arguments passed to optimize if exact is TRUE

Details

When exact is FALSE the method of Follmann and Proschan (1999) is used to estimate the PIM coefficients and perform a likelihood-ratio test on the responsiveness parameter theta.

If exact method is specified, then optimize is used to maximize the profile-likelihood alternating between fixing theta and fixing all other PIM parameters. The arguments interval and additional arguments to ... control the optimization with respect to theta.

When n.boot is NULL no bootstrap resamples are taken. In this case, when using the exact method the variance-covariance for the main effects is based on the model likelihood treating the responsiveness parameter as fixed. To include uncertainty measures for the responsiveness parameter, bootstrap resampling can be used. For the approximate method, only the bootstrap resampling variance is provided for the vcov and confint methods, which is invoked by specifying a positive integer number of samples or n.boot.

Value

Returns instance of pim class.

Author(s)

Stephanie Kovalchik <[email protected]>

References

Follmann DA, Proschan MA. A multivariate test of interaction for use in clinical trials. Biometrics 1999; 55(4):1151-1155

Examples


set.seed(1115)

pim.interaction <- data.anoint(
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = log(c(1.25,1.5)),
                             gamma = rep(1.2,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="binomial", n = 500
                             )


object <- anoint(y~(V1+V2)*trt,data=pim.interaction,family="binomial")

object

fit <- pim(object)

fit

summary(fit)

# EXAMPLE WITH BOOTSTRAP 
fit <- pim(object, n=50)
summary(fit)
confint(fit)
set.seed(1115)

pim.interaction <- data.anoint(
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = log(c(1.25,1.5)),
                             gamma = rep(1.2,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="binomial", n = 500
                             )


object <- anoint(y~(V1+V2)*trt,data=pim.interaction,family="binomial")

object

fit <- pim(object)

fit

summary(fit)

# EXAMPLE WITH BOOTSTRAP 
fit <- pim(object, n=50)
summary(fit)
confint(fit)

Class "pim"

Description

Class for proportional interactions model (PIM).

Objects from the Class

Objects can be created by calls of the form new("pim", ...).

Slots

formula:: object of anoint class
coef:: list of baseline (alpha), control prognostic effects (beta), and responsiveness parameter (theta)
exact:: logical indicator whether exact fit used
LRT:: likelihood ratio test statistic of responsiveness parameter
interval:: numeric vector supplied to optimize if exact fit is used
boot.pim:: matrix of bootstrap estimates of PIM coefficients
vcov:: matrix of bootstrap variance-covariance

Methods

show: signature(object = "pim"): Display point estimates of pim object.
print: signature(x = "pim",...): Display point estimates of pim object.
summary: signature(object = "pim",...): List of estimates and convergence information.
coef: signature(object = "pim"): Extractor for MLEs.
confint: signature(object = "pim",parm,level=0.95,...): Computes confidence interval for specified parameters and level. Intervals are based on bootstrap resamples of PIM model.
predict: signature(object = "pim"): Returns linear predictor for each subject.
vcov: signature(object = "pim"): Extractor for variance-covariance matrix which is estimated with bootstrap resampling.

Author(s)

Stephanie Kovalchik [email protected]

Fit proportional interactions model

Description

Fits a single proportional interactions model for generalized linear or Cox regression model.

Usage

pim.fit(formula, trt, data, family="binomial", na.action=na.omit, ...)
pim.fit(formula, trt, data, family="binomial", na.action=na.omit, ...)

Arguments

formula

formula for covariate model as given in glm or coxph, i.e. y~x1+x2

trt

character name of treatment assignment indicator

data

data.frame containing the variables of formula and trt

family

character specifying family of glm or character "coxph" if coxph model is fit

na.action

function, na.action to perform for handling observations with missing variables among variables in formula. Default is na.omit

...

additional arguments passed to glm or coxph

Details

Under the proportional interaction model the coef of the main covariate effects in the control arm are multiplied by the interaction effect to get the covariate effects for the treatment group.

Value

Returns a list with

interaction: value of the interaction effect of the proportional interaction model, see details
LRT: value of likelihood ratio test of proportional interaction
lower: lower endpoint of 95 percent confidence interval for interaction parameter
upper: upper endpoint of 95 percent confidence interval for interaction parameter
pvalue: pvalue for 1-df chi-squared test
model0: model object for control group
model1: model object for treatment group

Author(s)

Stephanie Kovalchik <[email protected]>

References

Follmann DA, Proschan MA. A multivariate test of interaction for use in clinical trials. Biometrics 1999; 55(4):1151-1155

Examples


set.seed(11903)

# NO INTERACTION CONDITION, LOGISTIC MODEL

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(c(1.5,2)),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival", n = 500
                             )

head(null.interaction)

pim.fit(Surv(y, event)~V1+V2,trt="trt",data=null.interaction,family="coxph")


# PROPORTIONAL INTERACTION WITH THREE COVARIATES AND BINARY OUTCOME

pim.interaction <- data.anoint(
			     n = 5000,
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = rep(log(.8),3),
                             gamma = rep(1.5,3),
                             mean = c(0,0,0),
                             vcov = diag(3),
                             type="binomial"
                             )

pim.fit(y~V1+V2+V3,trt="trt",data=pim.interaction,family="binomial")
set.seed(11903)

# NO INTERACTION CONDITION, LOGISTIC MODEL

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(c(1.5,2)),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival", n = 500
                             )

head(null.interaction)

pim.fit(Surv(y, event)~V1+V2,trt="trt",data=null.interaction,family="coxph")


# PROPORTIONAL INTERACTION WITH THREE COVARIATES AND BINARY OUTCOME

pim.interaction <- data.anoint(
			     n = 5000,
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = rep(log(.8),3),
                             gamma = rep(1.5,3),
                             mean = c(0,0,0),
                             vcov = diag(3),
                             type="binomial"
                             )

pim.fit(y~V1+V2+V3,trt="trt",data=pim.interaction,family="binomial")

Perform all subsets proportional interactions modeling

Description

Computes all possible proportional interactions model among p covariates.

Usage

pim.subsets(formula,trt,data,family="binomial",na.action=na.omit,fwer=0.05,...)
pim.subsets(formula,trt,data,family="binomial",na.action=na.omit,fwer=0.05,...)

Arguments

formula

formula for covariate model as given in glm or coxph, i.e. y~x1+x2

trt

character name of treatment assignment indicator

data

data.frame containing the variables of formula and trt

family

character specifying family of glm or character "coxph" if coxph model is fit

na.action

function, na.action to perform for handling observations with missing variables among variables in formula. Default is na.omit

fwer

numeric value for the desired familywise error rate, should be between 0 and 1.

...

additional arguments passed to glm or coxph

Details

Under the proportional interaction model the coef of the main covariate effects in the control arm are multiplied by the interaction effect to get the covariate effects for the treatment group.

Value

Returns a list with

subset: indicator of the covariates included in the fitted model
interaction: value of the interaction effect of the proportional interaction model, see details
LRT: value of likelihood ratio test of proportional interaction
lower: lower endpoints of 95 percent confidence interval for interaction parameter
upper: upper endpoints of 95 percent confidence interval for interaction parameter
pvalue: pvalue for 1-df chi-squared test
include.exclude.matrix: matrix of same rows as subsets and columns as covariates with logical entries indicating which covariates (columns) were include in which subset model (row)
covariates: vector of covariate names as in formula
reject: indicator of rejected hypotheses using a multiple testing correction such that familywise error is controlled at level fwer

Author(s)

Stephanie Kovalchik <[email protected]>

References

Follmann DA, Proschan MA. A multivariate test of interaction for use in clinical trials. Biometrics 1999; 55(4):1151-1155

Examples


set.seed(11903)

# NO INTERACTION CONDITION, LOGISTIC MODEL

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(c(1.5,2)),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival", n = 500
                             )

head(null.interaction)

pim.subsets(Surv(y, event)~V1+V2,trt="trt",data=null.interaction,family="coxph")


# PROPORTIONAL INTERACTION WITH THREE COVARIATES AND BINARY OUTCOME

pim.interaction <- data.anoint(
			     n = 5000,
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = rep(log(.8),3),
                             gamma = rep(1.5,3),
                             mean = c(0,0,0),
                             vcov = diag(3),
                             type="binomial"
                             )

pim.subsets(y~V1+V2+V3,trt="trt",data=pim.interaction,family="binomial")
set.seed(11903)

# NO INTERACTION CONDITION, LOGISTIC MODEL

null.interaction <- data.anoint(
                             alpha = c(log(.5),log(.5*.75)),
                             beta = log(c(1.5,2)),
                             gamma = rep(1,2),
                             mean = c(0,0),
                             vcov = diag(2),
                             type="survival", n = 500
                             )

head(null.interaction)

pim.subsets(Surv(y, event)~V1+V2,trt="trt",data=null.interaction,family="coxph")


# PROPORTIONAL INTERACTION WITH THREE COVARIATES AND BINARY OUTCOME

pim.interaction <- data.anoint(
			     n = 5000,
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = rep(log(.8),3),
                             gamma = rep(1.5,3),
                             mean = c(0,0,0),
                             vcov = diag(3),
                             type="binomial"
                             )

pim.subsets(y~V1+V2+V3,trt="trt",data=pim.interaction,family="binomial")

Prognostic response plot (PR-plot) for `anoint` class.

Description

Computes the prognostic score (baseline risk) based on the covariates of anoint or a supplied set of predictions. Risk scores are binned into ten groups based on risk deciles and a treatment effect (and confidence interval) is estimated in each group. This is compared to the overall treatment effect which is indicated by the shaded region.

Details

Additional arguments are passed to glm or coxph.

Methods

plot: signature(object = "anoint",predict=NULL,fun=exp,...): Prognostic response plot.

Author(s)

S. Kovalchik [email protected]

Examples

set.seed(11903)

# BINOMIAL EVENT DATA WITH 4 NORMAL PROGNOSTIC FACTORS
pim.interaction <- data.anoint(
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = log(c(1.5,1.1,2,1.3)),
                             gamma = rep(1.5,4),
                             mean = rep(0,4),
                             vcov = diag(4),
                             type="binomial", n = 500
                             )

object <- anoint(y~(V1+V2+V3+V4)*trt,data=pim.interaction)

plot(object,bty="n",las=1)

# PLOT TREATMENT EFFECT ON LINEAR PREDICTOR SCALE
plot(object,fun=function(x)x,bty="n",las=1,ylab="treatment effect (linear predictor)")

set.seed(11903)

# BINOMIAL EVENT DATA WITH 4 NORMAL PROGNOSTIC FACTORS
pim.interaction <- data.anoint(
                             alpha = c(log(.2/.8),log(.2*.75/(1-.2*.75))),
                             beta = log(c(1.5,1.1,2,1.3)),
                             gamma = rep(1.5,4),
                             mean = rep(0,4),
                             vcov = diag(4),
                             type="binomial", n = 500
                             )

object <- anoint(y~(V1+V2+V3+V4)*trt,data=pim.interaction)

plot(object,bty="n",las=1)

# PLOT TREATMENT EFFECT ON LINEAR PREDICTOR SCALE
plot(object,fun=function(x)x,bty="n",las=1,ylab="treatment effect (linear predictor)")

Get risk predictions for `pim` object.

Description

Computes linear predictors for the dataset used to fit the model.

Methods

predict: signature(object = "pim"): Linear predictors for dataset used to fit pim model.

Author(s)

S. Kovalchik [email protected]

Print coefficients of `pim`

Description

Prints the regression coefficients of the fit of a pim.

Methods

print: signature(x = "pim",digits=4,...): Prints call, coefficients, and responsiveness parameter for pim object.

Author(s)

S. Kovalchik [email protected]

Prognostic scores for `pim` object.

Description

Computes prognostic score from pim model, which is the linear predictor for the main effects of the prognostic factors for untreated subjects.

Methods

prognostic.score: signature(object = "pim"): Prognostic score at baseline.

Author(s)

S. Kovalchik [email protected]

Show coefficients of `pim`

Description

Shows the regression coefficients of the fit of a pim.

Methods

show: signature(object = "pim"): Shows call, coefficients, and multiple interaction parameter for pim object.

Author(s)

S. Kovalchik [email protected]

Show table of LRT global test results for `anoint.fit` object

Description

Prints a matrix with logical indicators of whether the given anoint test rejected the null hypothesis for the global test of interaction.

Methods

show: signature(object = "anoint.fit"): Matrix of logical indicators for global LRT test rejection.

Author(s)

S. Kovalchik [email protected]

Show `anoint` object

Description

Shows the formula specification of the anoint object.

Methods

show: signature(object = "anoint"): Shows formula call for anoint object.

Author(s)

S. Kovalchik [email protected]

Show `formula.anoint` object

Description

Returns the formula of the formula.anoint object.

Methods

show: signature(object = "formula.anoint"): Shows formula of the formula.anoint object.

Author(s)

S. Kovalchik [email protected]

Simulated SOLVD-Trial data set

Description

A simulated clinical trial based on the design of the Studies of Left Ventricular Dysfunction Trial (SOLVD-T), a placebo-controlled trial of the angiotensin-converting-enzyme inhibitor enalapril for patients with congestive heart failure.

Usage

data(simsolvd)data(simsolvd)

Format

A data frame with 2569 observations on the following 12 variables.

trt: indicator for enalapril group
age: age at baseline (centered and scaled)
beat: pulse at baseline (centered and scaled)
lymphocyte: lymphocyte count at baseline (centered and scaled)
lvef: left ventricular ejection fraction at baseline (centered and scaled)
noise: simulated vector of random uniform variables
nyha: indicator whether New York Heart Association score greater than 2
cardratio: indicator whether cardiothoracic ratio is greater than 0.5
creatinine: creatinine at baseline (centered and scaled)
sodium: sodium at baseline (centered and scaled)
ttodthorchfhosp: time to death or hospitalization in days
censor: indicator whether censored (1) or an event (0)
current: indicator whether current smoker

Source

Simulated data set based on the clinical study reported by: Yusuf, S. et al. (1991). Effect of Enalapril on Survival in Patients with Reduced Left-Ventricular Ejection Fractions and Congestive-Heart-Failure. NEJM 325:293-302.

Examples


data(simsolvd)

obj <- anoint(Surv(ttodthorchfhosp,censor==0)~(age+beat+lvef)*trt,
				data = simsolvd, family = "coxph")

uim(obj)$fit

data(simsolvd)

obj <- anoint(Surv(ttodthorchfhosp,censor==0)~(age+beat+lvef)*trt,
				data = simsolvd, family = "coxph")

uim(obj)$fit

Summary of `anoint` model fit.

Description

A list of estimates and convergence status of a anoint model fit. When exact is TRUE the test statistic is the likelihood ratio test, otherwise the Follmann approximate likelihood ratio test statistic is used.

Methods

summary: signature(x = "anoint",...): Calls summary method of underlying model fit.

Author(s)

S. Kovalchik [email protected]

Perform unrestricted multiple treatment-covariate interaction regression

Description

Fits GLM of Cox regression analysis for model with all pairwise interactions between treatment and covariates specified in anoint object.

Usage

uim(object,...)
uim(object,...)

Arguments

object

object of class anoint

...

other arguments passed to glm or coxph

Value

List of model fit of glm or coxph class (fit), likelihood-ratio test of global test of treatment-covariate interaction (LRT), and LRT p-value for global test of interaction (pvalue).

Author(s)

Stephanie Kovalchik <[email protected]>

Examples

data(simsolvd)

obj <- anoint(Surv(ttodthorchfhosp,censor==0)~(age+beat+lvef)*trt,
				data = simsolvd, family = "coxph")

fit <- uim(obj)

fit 

summary(fit$fit)
data(simsolvd)

obj <- anoint(Surv(ttodthorchfhosp,censor==0)~(age+beat+lvef)*trt,
				data = simsolvd, family = "coxph")

fit <- uim(obj)

fit 

summary(fit$fit)

Get variance-covariance from `pim` object.

Description

Returns Hessian-based variance-covariance matrix of the fit of a pim model.

Methods

vcov: signature(object = "pim"): Extractor for variance-covariance of MLEs.

Author(s)

S. Kovalchik [email protected]

Package 'anoint'

Help Index

Analysis of interactions for generalized linear models (GLM) or Cox proportional hazards regression models.

Description

Details

Author(s)

References

Create analysis of interactions object

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Fits and global tests of analysis of interaction models

Description

Arguments

Details

Objects from the Class

Slots

Methods

Author(s)

See Also

Examples

Create a formula.anoint object

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Perform one-by-one subgroup analyses

Description

Usage

Arguments

Value

Author(s)

Examples

Get coefs from pim object.

Description

Methods

Author(s)

Compute confindence intervals of pim model terms.

Description

Methods

Author(s)

Generate a clinical trial data set under a specified multiple interaction model

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Extract fits from anoint.fit object

Description

Methods

Author(s)

Construct a forestplot from a anoint object

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Subsets forest plot for proportional interactions models

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Create a `formula.anoint` object

Get coefs from `pim` object.

Compute confindence intervals of `pim` model terms.

Extract fits from `anoint.fit` object

Construct a forestplot from a `anoint` object

Prognostic response plot (PR-plot) for `anoint` class.

Get risk predictions for `pim` object.

Print coefficients of `pim`

Prognostic scores for `pim` object.

Show coefficients of `pim`