DynTxRegime (version 3.2)

bowl: Backward Outcome Weighted Learning

Description

A statistical learning method for estimating the optimal dynamic treatment regime (DTR) termed backward outcome weighted learning (BOWL). This approach converts individualized treatment selection into a sequential classification problem. The method directly maximizes over all DTRs a nonparametric estimator of the expected long-term outcome. This function implements a single step of a BOWL analysis. A complete BOWL analysis requires repeated calls to this function. Note that this method is limited to binary treatment regimes.

Usage

bowl(..., moPropen, data, reward, txName, regime, BOWLObj = NULL, 
      lambdas = 2.0, cvFolds = 0L, kernel = "linear", kparam = NULL, 
      fSet = NULL, verbose = TRUE)

Arguments

…

ignored. Included to require named input.

moPropen

An object of class "modelObj" or an object of class "list" containing objects of class "modelObjSubset." This input specifies the model(s) for the propensity score regression, Pr(A=a|X), and the R methods to be used to obtain parameter estimates and predictions. The method specified to obtain predictions must return the prediction on the scale of the probability, i.e., returned values must be in the interval (0,1). See moPropen for additional information.

data

An object of class "data.frame." The covariates and treatment history.

reward

An object of class "numeric." The reward for the decision point under analysis.

txName

An object of class "character." The column header of the stage treatment variable in input data. Treatment must be binary and will be recoded to -1/+1 if not provided as such.

regime

An object of class "formula" or an object of class "list" containing objects of class "formula." The formula defines the decision rule, i.e., the covariates to be included in the kernel. If regime is a single "formula," all patients are used to obtain parameter estimates. If regime is a list, subsets of patients are used to fit each decision rule. When using subset models, input fSet must be defined, and the name of each element of the list must correspond to a subset defined by fSet. See fSet for further details.

BOWLObj

An object of class "BOWL" or NULL. For the first step of the BOWL algorithm (the final decision point), this input must be NULL. For all other steps, it is the value object returned by the previous call to bowl().

lambdas

An object of class "numeric." This input is the tuning parameter to avoid over fitting. If more than one value is given and input cvFolds is greater than zero, cross-validation will be used to select an optimal value from among those provided.

cvFolds

An object of class "integer." If cross-validation is to be used to find an optimal lambda and/or kernel parameter, the number of folds to use in the cross-validation procedure.

kernel

An object of class "character." In conjunction with input kparam, this input specifies the kernel function to be used. Must be one of {'linear', 'poly', or 'radial'}. If 'linear,' the linear kernel; kparam is ignored. If 'poly,' the polynomial kernel; kparam must be specified. If 'radial,' the Gaussian radial basis function kernel; kparam must be specified.

kparam

An object of class "numeric." If input kernel = 'linear', this input is ignored. If input kernel = 'poly', this input is the order of the polynomial. If input kernel = 'radial', this input is sigma; i.e., $$K(x,y) = exp(||x-y||^2 / (2*sigma^2)).$$ For kernel = 'radial', a vector of kernel parameters can be provided, and cross-validation will be used to determine the optimal of those provided. Note that input cvFolds must be > 0.

fSet

An object of class "function" or NULL. If a function, fSet defines (i) the conditions under which only a subset of treatment options is available to a patient or (ii) the conditions under which patients are to be subset and the subsets modeled uniquely. The form of this input has been extended from the original release of DynTxRegime. See fSet for additional information.

verbose

An object of class "logical." If FALSE, screen prints will be suppressed.

Value

Returns a "BOWL" object, which inherits directly from class "DynTxRegime."

Methods

coef

signature(object = "BOWL"): Retrieve parameter estimates for all regression steps.

cvInfo

signature(object = "BOWL"): Retrieve cross-validation results.

DTRstep

signature(object = "BOWL"): Retrieve description of method used to create object.

estimator

signature(x = "BOWL"): Retrieve the estimated value of the estimated optimal regime for the training data set.

fitObject

signature(object = "BOWL"): Retrieve value object returned by regression methods.

optimObj

signature(object = "BOWL"): Retrieve value object returned by optimization routine.

optTx

signature(x = "BOWL", newdata = "missing"): Retrieve the estimated optimal treatment regime for training data set.

optTx

signature(x = "BOWL", newdata = "data.frame"): Estimate the optimal treatment regime for newdata.

plot

signature(x = "BOWL"): Generate plots for regression analyses.

print

signature(object = "BOWL"): Print main results of analysis.

propen

signature(x = "BOWL"): Retrieve value object returned by propensity score regression methods.

regimeCoef

signature(object = "BOWL"): Retrieve the estimated decision function parameter estimates.

show

signature(object = "BOWL"): Show main results of analysis.

summary

signature(object = "BOWL"): Retrieve summary information from regression analyses.

References

Zhao, Y-Q., Zeng, D., Laber, E. B., and Kosorok, M. R. (2015). New Statistical Learning Methods for Estimating Optimal Dynamic Treatment Regimes. Journal of the American Statistical Association, 110, 583--598.

Examples

# NOT RUN {
# Load and process data set
data(bmiData)

# define the negative 12 month change in BMI from baseline
y12 <- -100*(bmiData[,6L] - bmiData[,4L])/bmiData[,4L]

# define the negative 4 month change in BMI from baseline
y4 <- -100*(bmiData[,5L] - bmiData[,4L])/bmiData[,4L]

# reward for second stage
rewardSS <- y12 - y4

#### Second-stage regression

# Constant propensity model
moPropen <- buildModelObj(model = ~1,
                          solver.method = 'glm',
                          solver.args = list('family'='binomial'),
                          predict.method = 'predict.glm',
                          predict.args = list(type='response'))

fitSS <- bowl(moPropen = moPropen,
              data = bmiData, reward = rewardSS,  txName = 'A2', 
              regime = ~ parentBMI + month4BMI)

##Available methods

  # Coefficients of the propensity score regression
  coef(fitSS)

  # Description of method used to obtain object
  DTRstep(fitSS)

  # Estimated value of the optimal treatment regime for training set
  estimator(fitSS)

  # Value object returned by propensity score regression method
  fitObject(fitSS)

  # Summary of optimization routine
  optimObj(fitSS)

  # Estimated optimal treatment for training data
  optTx(fitSS)

  # Estimated optimal treatment for new data
  optTx(fitSS, bmiData)

  # Plots if defined by propensity regression method
  dev.new()
  par(mfrow = c(2,4))

  plot(fitSS)
  plot(fitSS, suppress = TRUE)

  # Value object returned by propensity score regression method
  propen(fitSS)

  # Parameter estimates for decision function
  regimeCoef(fitSS)

  # Show main results of method
  show(fitSS)

  # Show summary results of method
  summary(fitSS)
 
#### First-stage regression

# Constant propensity model
fitFS <- bowl(moPropen = moPropen,
              data = bmiData, reward = y4,  txName = 'A1', 
              regime = ~ gender + parentBMI,
              BOWLObj = fitSS)

# }