catefit {precmed}

Estimation of the conditional average treatment effect (CATE) score for count, survival and continuous data

Description

Provides singly robust and doubly robust estimation of CATE score for count, survival and continuous data with up the following scoring methods among the following: Random forest (survival, continuous only), boosting, poisson regression (count, survival only), two regressions, contrast regression, negative binomial regression (count only), linear regression (continuous only), and generalized additive model (continuous only).

Usage

catefit(
  response,
  data,
  score.method,
  cate.model,
  ps.model,
  ps.method = "glm",
  init.model = NULL,
  initial.predictor.method = NULL,
  ipcw.model = NULL,
  ipcw.method = "breslow",
  minPS = 0.01,
  maxPS = 0.99,
  followup.time = NULL,
  tau0 = NULL,
  higher.y = TRUE,
  prop.cutoff = seq(0.5, 1, length = 6),
  surv.min = 0.025,
  xvar.smooth.score = NULL,
  xvar.smooth.init = NULL,
  tree.depth = 2,
  n.trees.rf = 1000,
  n.trees.boosting = 200,
  B = 3,
  Kfold = 5,
  error.maxNR = 0.001,
  max.iterNR = 150,
  tune = c(0.5, 2),
  seed = NULL,
  plot.gbmperf = TRUE,
  verbose = 0,
  ...
)

Arguments

response

A string describing the type of outcome in the data. Allowed values include "count" (see catecvcount()), "survival" (see catecvsurv()) and "continuous" (see catecvmean()).

data

A data frame containing the variables in the outcome, propensity score, and inverse probability of censoring models (if specified); a data frame with n rows (1 row per observation).

score.method

A vector of one or multiple methods to estimate the CATE score. Allowed values are: 'boosting', 'twoReg', 'contrastReg', 'poisson' (count and survival outcomes only), 'randomForest' (survival, continuous outcomes only), negBin (count outcomes only), 'gam' (continuous outcomes only), 'gaussian' (continuous outcomes only).

cate.model

A formula describing the outcome model to be fitted. The outcome must appear on the left-hand side. For survival outcomes, a Surv object must be used to describe the outcome.

ps.model

A formula describing the propensity score (PS) model to be fitted. The treatment must appear on the left-hand side. The treatment must be a numeric vector coded as 0/1. If data are from a randomized controlled trial, specify ps.model = ~1 as an intercept-only model.

ps.method

A character value for the method to estimate the propensity score. Allowed values include one of: 'glm' for logistic regression with main effects only (default), or 'lasso' for a logistic regression with main effects and LASSO penalization on two-way interactions (added to the model if interactions are not specified in ps.model). Relevant only when ps.model has more than one variable.

init.model

A formula describing the initial predictor model. The outcome must appear on the left-hand side. It must be specified when score.method = contrastReg or twoReg.

initial.predictor.method

A character vector for the method used to get initial outcome predictions conditional on the covariates specified in cate.model. Only applies when score.method includes 'twoReg' or 'contrastReg'.Allowed values include one of 'randomForest' (survival outcomes only), 'boosting', 'logistic' (survival outcomes only, fast), 'poisson' (count outcomes only, fast), 'gaussian' (continuous outcomes only) and 'gam' (count and continuous outcomes only). Default is NULL, which assigns 'boosting' for count outcomes and 'randomForest' for survival outcomes.

ipcw.model

A formula describing the inverse probability of censoring weighting (IPCW) model to be fitted. The left-hand side must be empty. Only applies for survival outcomes. Default is NULL, which corresponds to specifying the IPCW with the same covariates as the outcome model cate.model, plus the treatment.

ipcw.method

A character value for the censoring model. Only applies for survival outcomes. Allowed values are: 'breslow' (Cox regression with Breslow estimator of t he baseline survivor function), 'aft (exponential)', 'aft (weibull)', 'aft (lognormal)' or 'aft (loglogistic)' (accelerated failure time model with different distributions for y variable). Default is 'breslow'.

minPS

A numerical value (in [0, 1]) below which estimated propensity scores should be truncated. Default is 0.01.

maxPS

A numerical value (in (0, 1]) above which estimated propensity scores should be truncated. Must be strictly greater than minPS. Default is 0.99.

followup.time

A column name in data specifying the maximum follow-up time, interpreted as the potential censoring time. Only applies for survival outcomes. Default is NULL, which corresponds to unknown potential censoring time.

tau0

The truncation time for defining restricted mean time lost. Only applies for survival outcomes. Default is NULL, which corresponds to setting the truncation time as the maximum survival time in the data.

higher.y

A logical value indicating whether higher (TRUE) or lower (FALSE) values of the outcome are more desirable. Default is TRUE.

prop.cutoff

A vector of numerical values (in (0, 1]) specifying percentiles of the estimated log CATE scores to define nested subgroups. Each element represents the cutoff to separate observations in nested subgroups (below vs above cutoff). The length of prop.cutoff is the number of nested subgroups. An equally-spaced sequence of proportions ending with 1 is recommended. Default is seq(0.5, 1, length = 6).

surv.min

Lower truncation limit for the probability of being censored. It must be a positive value and should be chosen close to 0. Only applies for survival outcomes. Default is 0.025.

xvar.smooth.score

A vector of characters indicating the name of the variables used as the smooth terms if score.method = 'gam'. The variables must be selected from the variables listed in cate.model.

xvar.smooth.init

A vector of characters indicating the name of the variables used as the smooth terms if initial.predictor.method = 'gam'. The variables must be selected from the variables listed in init.model. Default is NULL, which uses all variables in init.model.

tree.depth

A positive integer specifying the depth of individual trees in boosting (usually 2-3). Used only if score.method = 'boosting' or if initial.predictor.method = 'boosting' with score.method = 'twoReg' or 'contrastReg'. Default is 2.

n.trees.rf

A positive integer specifying the maximum number of trees in random forest. Used if score.method = 'ranfomForest' or if initial.predictor.method = 'randomForest' with score.method = 'twoReg' or 'contrastReg'. Only applies for survival outcomes. Default is 1000.

n.trees.boosting

A positive integer specifying the maximum number of trees in boosting (usually 100-1000). Used if score.method = 'boosting' or if initial.predictor.method = 'boosting' with score.method = 'twoReg' or 'contrastReg'. Default is 200.

B

A positive integer specifying the number of time cross-fitting is repeated in score.method = 'twoReg' and 'contrastReg'. Default is 3.

Kfold

A positive integer specifying the number of folds used in cross-fitting to partition the data in score.method = 'twoReg' and 'contrastReg'. Default is 5.

error.maxNR

A numerical value > 0 indicating the minimum value of the mean absolute error in Newton Raphson algorithm. Used only if score.method = 'contrastReg'. Default is 0.001.

max.iterNR

A positive integer indicating the maximum number of iterations in the Newton Raphson algorithm. Used only if score.method = 'contrastReg'. Default is 150.

tune

A vector of 2 numerical values > 0 specifying tuning parameters for the Newton Raphson algorithm. tune[1] is the step size, tune[2] specifies a quantity to be added to diagonal of the slope matrix to prevent singularity. Used only if score.method = 'contrastReg'. Default is c(0.5, 2).

seed

An optional integer specifying an initial randomization seed for reproducibility. Default is NULL, corresponding to no seed.

plot.gbmperf

A logical value indicating whether to plot the performance measures in boosting. Used only if score.method = 'boosting' or if score.method = 'twoReg' or 'contrastReg' and initial.predictor.method = 'boosting'. Default is TRUE.

verbose

An integer value indicating whether intermediate progress messages and histograms should be printed. 1 indicates messages are printed and 0 otherwise. Default is 0.

...

Additional arguments for gbm()

Details

For count response, see details in catefitcount(). For survival response, see details in catefitsurv().

Value

For count response, see description of outputs in catefitcount(). For survival response, see description of outputs in catefitsurv().

References

Yadlowsky, S., Pellegrini, F., Lionetto, F., Braune, S., & Tian, L. (2020). Estimation and validation of ratio-based conditional average treatment effects using observational data. Journal of the American Statistical Association, 1-18. https://www.tandfonline.com/doi/full/10.1080/01621459.2020.1772080

See Also

catecv()

Examples

# Count outcome
fit_1 <- catefit(response = "count",
                 data = countExample,
                 score.method = "poisson",
                 cate.model = y ~ age + female + previous_treatment +
                                  previous_cost + previous_number_relapses +
                                  offset(log(years)),
                 ps.model = trt ~ age + previous_treatment,
                 higher.y = TRUE,
                 seed = 999)

coef(fit_1)


# Survival outcome
library(survival)
tau0 <- with(survivalExample,
                 min(quantile(y[trt == "drug1"], 0.95), quantile(y[trt == "drug0"], 0.95)))

fit_2 <- catefit(response = "survival",
                 data = survivalExample,
                 score.method = c("poisson", "boosting", "randomForest"),
                 cate.model = Surv(y, d) ~ age + female + previous_cost +
                                           previous_number_relapses,
                 ps.model = trt ~ age + previous_treatment,
                 initial.predictor.method = "logistic",
                 ipcw.model = ~ age + previous_cost + previous_treatment,
                 tau0 = tau0, higher.y = TRUE, seed = 999, n.cores = 1)

coef(fit_2)