dipm {dipm}

Depth Importance in Precision Medicine (DIPM)

Description

This function creates a classification tree designed to identify subgroups in which subjects perform especially well or especially poorly in a given treatment group.

Usage

dipm(
  formula,
  data,
  types = NULL,
  nmin = 5,
  nmin2 = 5,
  ntree = NULL,
  mtry = Inf,
  maxdepth = Inf,
  maxdepth2 = Inf,
  print = TRUE,
  dataframe = FALSE,
  prune = FALSE
)

Arguments

formula

A description of the model to be fit with format Y ~ treatment | X1 + X2 for data with a continuous outcome variable Y and Surv(Y, delta) ~ treatment | X1 + X2 for data with a right-censored survival outcome variable Y and a status indicator delta

data

A matrix or data frame of the data

types

A vector, data frame, or matrix of the types of each variable in the data; if left blank, the default is to assume all of the candidate split variables are ordinal; otherwise, all variables in the data must be specified, and the possible variable types are: "response", "treatment", "status", "binary", "ordinal", and "nominal" for outcome variable Y, the treatment variable, the status indicator (if applicable), binary candidate split variables, ordinal candidate split variables, and nominal candidate split variables respectively

nmin

An integer specifying the minimum node size of the overall classification tree

nmin2

An integer specifying the minimum node size of embedded trees

ntree

An integer specifying the number of embedded trees to construct at each node of the overall classification tree; if left blank, the default value of ceiling(min(max(sqrt(n), sqrt(nc)), 1000)) will be used if mtry = Inf below and ceiling(min(max(n, nc), 1000)) otherwise; n is the total sample size of the data, and nc is the total number of candidate split variables

mtry

An integer specifying the number of candidate split variables to randomly select at each node of embedded trees; if mtry is set equal to the default value of Inf, then all possible splits of all candidate split variables are considered at the nodes of the embedded trees; otherwise, a recommended value of mtry to use is the square root of the total number of candidate split variables rounded up to the nearest integer

maxdepth

An integer specifying the maximum depth of the overall classification tree; this argument is optional but useful for shortening computation time; if left blank, the default is to grow the full tree until the minimum node size nmin is reached

maxdepth2

An integer specifying the maximum depth of embedded trees; this argument is optional but useful for shortening computation time; if left blank, the default is to grow each full, embedded tree until the minimum node size nmin2 is reached

print

A boolean (TRUE/FALSE) value, where TRUE prints a more readable version of the final tree to the screen

dataframe

A boolean (TRUE/FALSE) value, where TRUE returns the final tree as a dataframe

prune

A boolean (TRUE/FALSE) value, where TRUE prunes the final tree using pmprune function

Details

This function creates a classification tree to identify subgroups relevant to the precision medicine setting. At each node of the classification tree, a random forest of so-called embedded trees are fit and used to calculate a depth variable importance score for each candidate split variable in the data. The candidate split variable with the largest variable importance score is identified as the best split variable of the node. Then, all possible splits of the selected split variable are considered, and the split with the greatest split criteria value is finally selected as the best split of the best variable.

The depth variable importance score was originally proposed by Chen et al. (2007), and the score has been adapted to the precision medicine setting here. The depth variable importance score is a relatively simple measure that takes into account two components: the depth of a split in a tree and the strength of the split. The strength of the split is captured with a G test statistic that may be modified depending on the type of analysis at hand. When the outcome variable is continuous, G is the test statistic that tests the significance of the split by treatment interaction term in a linear regression model. When the outcome variable is a right-censored survival time, G is the test statistic that tests the significance of the split by interaction term in a Cox proportional hazards model.

When using dipm, note the following requirements for the supplied data. First, the dataset must contain an outcome variable Y and a treatment variable. If Y is a right-censored survival time outcome, then there must also be a status indicator delta, where values of 1 denote the occurrence of the (harmful) event of interest, and values of 0 denote censoring. If there are only two treatment groups, then the two possible values must be 0 or 1. If there are more than two treatment groups, then the possible values must be integers starting from 1 to the total number of treatment assignments. In regard to the candidate split variables, if a variable is binary, then the variable must take values of 0 or 1. If a variable is nominal, then the values must be integers starting from 1 to the total number of categories. There cannot be any missing values in the dataset. For candidate split variables with missing values, the missings together (MT) method proposed by Zhang et al. (1996) is helpful.

Value

dipm returns the final classification tree as a party object by default or a data frame. See Hothorn and Zeileis (2015) for details. The data frame contains the following columns of information:

node

Unique integer values that identify each node in the tree, where all of the nodes are indexed starting from 1

splitvar

Integers that represent the candidate split variable used to split each node, where all of the variables are indexed starting from 1; for terminal nodes, i.e., nodes without child nodes, the value is set equal to NA

splitvar_name

The names of the candidate split variables used to split each node obtained from the column names of the supplied data; for terminal nodes, the value is set equal to NA

type

Characters that denote the type of each candidate split variable; "bin" is for binary variables, "ord" for ordinal, and "nom" for nominal; for terminal nodes, the value is set equal to NA

splitval

Values of the left child node of the current split/node; for binary variables, a value of 0 is printed, and subjects with values of 0 for the current splitvar are in the left child node, while subjects with values of 1 are in the right child node; for ordinal variables, splitval is numeric and implies that subjects with values of the current splitvar less than or equal to splitval are in the left child node, while the remaining subjects with values greater than splitval are in the right child node; for nominal variables, the splitval is a set of integers separated by commas, and subjects in that set of categories are in the left child node, while the remaining subjects are in the right child node; for terminal nodes, the value is set equal to NA

lchild

Integers that represent the index (i.e., node value) of each node's left child node; for terminal nodes, the value is set equal to NA

rchild

Integers that represent the index (i.e., node value) of each node's right child node; for terminal nodes, the value is set equal to NA

depth

Integers that specify the depth of each node; the root node has depth 1, its children have depth 2, etc.

nsubj

Integers that count the total number of subjects within each node

besttrt

Integers that denote the identified best treatment assignment of each node

References

Chen, V., Li, C., and Zhang, H. (2022). dipm: an R package implementing the Depth Importance in Precision Medicine (DIPM) tree and Forest-based method. Bioinformatics Advances, 2(1), vbac041.

Chen, V. and Zhang, H. (2022). Depth importance in precision medicine (DIPM): A tree-and forest-based method for right-censored survival outcomes. Biostatistics 23(1), 157-172.

Chen, V. and Zhang, H. (2020). Depth importance in precision medicine (DIPM): a tree and forest based method. In Contemporary Experimental Design, Multivariate Analysis and Data Mining, 243-259.

Chen, X., Liu, C.-T., Zhang, M., and Zhang, H. (2007). A forest-based approach to identifying gene and gene-gene interactions. Proceedings of the National Academy of Sciences of the United States of America 204, 19199-19203.

Zhang, H., Holford, T., and Bracken, M.B. (1996). A tree-based method of analysis for prospective studies. Statistics in Medicine 15, 37-49.

Hothorn, T. and Zeileis, A. (2015). partykit: a modular toolkit for recursive partytioning in R. The Journal of Machine Learning Research 16(1), 3905-3909.

See Also

spmtree

Examples

#
# ... an example with a continuous outcome variable
#     and two treatment groups
#

N = 100
set.seed(123)

# generate binary treatments
treatment = rbinom(N, 1, 0.5)

# generate candidate split variables
X1 = rnorm(n = N, mean = 0, sd = 1)
X2 = rnorm(n = N, mean = 0, sd = 1)
X3 = rnorm(n = N, mean = 0, sd = 1)
X4 = rnorm(n = N, mean = 0, sd = 1)
X5 = rnorm(n = N, mean = 0, sd = 1)
X = cbind(X1, X2, X3, X4, X5)
colnames(X) = paste0("X", 1:5)

# generate continuous outcome variable
calculateLink = function(X, treatment){

    ((X[, 1] <= 0) & (X[, 2] <= 0)) *
        (25 * (1 - treatment) + 8 * treatment) + 

    ((X[, 1] <= 0) & (X[, 2] > 0)) *
        (18 * (1 - treatment) + 20 * treatment) +

    ((X[, 1] > 0) & (X[, 3] <= 0)) *
        (20 * (1 - treatment) + 18 * treatment) + 

    ((X[, 1] > 0) & (X[, 3] > 0)) *
        (8 * (1 - treatment) + 25 * treatment)
}

Link = calculateLink(X, treatment)
Y = rnorm(N, mean = Link, sd = 1)

# combine variables in a data frame
data = data.frame(X, Y, treatment)

# fit a dipm classification tree 
tree1 = dipm(Y ~ treatment | ., data, mtry = 1, maxdepth = 3)
# predict optimal treatment for new subjects
predict(tree1, newdata = head(data), 
FUN = function(n)  as.numeric(n$info$opt_trt))


#
# ... an example with a continuous outcome variable
#     and three treatment groups
#

N = 600
set.seed(123)

# generate treatments
treatment = sample(1:3, N, replace = TRUE)

# generate candidate split variables
X1 = round(rnorm(n = N, mean = 0, sd = 1), 4)
X2 = round(rnorm(n = N, mean = 0, sd = 1), 4)
X3 = sample(1:4, N, replace = TRUE)
X4 = sample(1:5, N, replace = TRUE)
X5 = rbinom(N, 1, 0.5)
X6 = rbinom(N, 1, 0.5)
X7 = rbinom(N, 1, 0.5)
X = cbind(X1, X2, X3, X4, X5, X6, X7)
colnames(X) = paste0("X", 1:7)

# generate continuous outcome variable
calculateLink = function(X,treatment){

    10.2 - 0.3 * (treatment == 1) - 0.1 * X[, 1] + 
    2.1 * (treatment == 1) * X[, 1] +
    1.2 * X[, 2]
}

Link = calculateLink(X, treatment)
Y = rnorm(N, mean = Link, sd = 1)

# combine variables in a data frame
data = data.frame(X, Y, treatment)

# create vector of variable types
types = c(rep("ordinal", 2), rep("nominal", 2), rep("binary", 3),
        "response", "treatment")

# fit a dipm classification tree 
tree2 = dipm(Y ~ treatment | ., data, types = types, maxdepth = 2)

#
# ... an example with a survival outcome variable
#     and two treatment groups
#

N = 300
set.seed(321)

# generate binary treatments
treatment = rbinom(N, 1, 0.5)

# generate candidate split variables
X1 = rnorm(n = N, mean = 0, sd = 1)
X2 = rnorm(n = N, mean = 0, sd = 1)
X3 = rnorm(n = N, mean = 0, sd = 1)
X4 = rnorm(n = N, mean = 0, sd = 1)
X5 = rnorm(n = N, mean = 0, sd = 1)
X = cbind(X1, X2, X3, X4, X5)
colnames(X) = paste0("X", 1:5)

# generate survival outcome variable
calculateLink = function(X, treatment){

    X[, 1] + 0.5 * X[, 3] + (3 * treatment - 1.5) * (abs(X[, 5]) - 0.67)
}

Link = calculateLink(X, treatment)
T = rexp(N, exp(-Link))
C0 = rexp(N, 0.1 * exp(X[, 5] + X[, 2]))
Y = pmin(T, C0)
delta = (T <= C0)

# combine variables in a data frame
data = data.frame(X, Y, delta, treatment)

# fit a dipm classification tree 
tree3 = dipm(Surv(Y, delta) ~ treatment | .,data, ntree = 1, maxdepth = 2,
           maxdepth2 = 6)

#
# ... an example with a survival outcome variable
#     and four treatment groups
#

N = 800
set.seed(321)

# generate treatments
treatment = sample(1:4, N, replace = TRUE)

# generate candidate split variables
X1 = round(rnorm(n = N, mean = 0, sd = 1), 4)
X2 = round(rnorm(n = N, mean = 0, sd = 1), 4)
X3 = sample(1:4, N, replace = TRUE)
X4 = sample(1:5, N, replace = TRUE)
X5 = rbinom(N, 1, 0.5)
X6 = rbinom(N, 1, 0.5)
X7 = rbinom(N, 1, 0.5)
X = cbind(X1, X2, X3, X4, X5, X6, X7)
colnames(X) = paste0("X", 1:7)

# generate survival outcome variable
calculateLink = function(X, treatment, noise){

    -0.2 * (treatment == 1) +
    -1.1 * X[, 1] + 
    1.2 * (treatment == 1) * X[, 1] +
    1.2 * X[, 2]
}

Link = calculateLink(X, treatment)
T = rweibull(N, shape=2, scale = exp(Link))
Cnoise = runif(n = N) + runif(n = N)
C0 = rexp(N, exp(0.3 * -Cnoise))
Y = pmin(T, C0)
delta = (T <= C0)

# combine variables in a data frame
data = data.frame(X, Y, delta, treatment)

# create vector of variable types
types = c(rep("ordinal", 2), rep("nominal", 2), rep("binary", 3), 
        "response", "status", "treatment")

# fit two dipm classification trees 
tree4 = dipm(Surv(Y, delta) ~ treatment | ., data, types = types, ntree = 1, 
           maxdepth = 2, maxdepth2 = 6)
tree5 = dipm(Surv(Y, delta) ~ treatment | X3 + X4, data, types = types, ntree = 1, 
           maxdepth = 2, maxdepth2 = 6)