rlt_reg: Fit a RLT model and compute predictions of expectations for...

In YohannLeFaou/sword: Random forest with IPC weights for survival analysis

Description

rlt_reg is a benchmark model we use in [Gerber et al. (2018)]. To model the variable phi(T), where T is a right censored time and phi is a given function, we first fit a RLT (Reinforcement Learning Trees) model to the data to estimate the survival function of T given the covariates. Then, we deduce an estimator of phi(T) by integration of the function phi with respect to the estimated survival function. Different methods are available to assess the quality of fit of rlt_reg. rlt_reg is a wrapper for the RLT function

The notations we use are :

• C : Censoring variable

• Y = min(T, C)

• δ = 1_{T ≤ C} (delta)

Usage

rlt_reg(y_var, delta_var, x_vars, train, test = NULL, phi = function(x) {   
   x }, phi.args = list(), max_time = NULL, rlt_obj = T,
  ev_methods = c("concordance", "weighted"), bandwidths = NULL,
  types_w_ev = c("KM"), max_w_ev = 20, mat_w = NULL,
  y_no_cens_var = NULL, ntree = 100, minleaf = 5, maxdepth = 6,
  mtry = NULL, reinforcement = T, ...)

Arguments

y_var	A character string which gives the name of the Y variable
delta_var	A character string which gives the name of the δ variable (this variable should be binary : 1 = non censored, 0 = censored)
x_vars	A vector of character strings which gives the names of the explanatory variables
train	A data.frame of training observations. It must contain the column names y_var, delta_var and x_vars
test	A data.frame of testing observations (default = NULL)
phi	A function to be applied to y_var
phi.args	A list of additional parameters for the function phi (default = NULL). See Examples for a use case
max_time	A real number giving a threshold for y_var (default = NULL). If NULL, then max_time is set to the maximum non censored observation of y_var among the training set. We note T' = min(T, max_time)
rlt_obj	A boolean which indicates if the RLT model fitted to the training data should be returned (default = TRUE)
ev_methods	A vector of character strings which gives the methods that should be used for the evaluation of the model (default = c("concordance","weighted")). Possible choices are "concordance", "weighted" and "group". Multiple choices are possible. See Details - Evaluation criteria for more information
bandwidths	A vector of real numbers for the bandwidths to use for the model evaluation if "group" is used as an ev_methods (default = NULL : set to 50 if "group" in ev_methods). Only used if "group" is used as ev_methods. See Details - Evaluation criteria for more information
types_w_ev	A vector of character strings which gives the types of weights to be used for IPCW (Inverse Probability of Censoring Weighting) in the model evaluation (default = c("KM") (Kaplan Meier)). Possible choices are "KM", "Cox", "RSF" and "unif". Set to colnames(mat_w) if mat_w is provided. See Details - Evaluation criteria for more information
max_w_ev	A real number which gives the maximum admissible ratio for the IPC weights (default = 1000). See Details - Evaluation criteria for more information
mat_w	A matrix to provide handmade IPC weights for the model evaluation (default = NULL). mat_w should satisfied nrow(mat_w) = nrow(train) + nrow(test) and a column should correspond to a type of weights (multiple columns are possible). Column names of mat_w may be used to specify names for the provided weights (by default names will be "w1", "w2", ...)
y_no_cens_var	A character string which gives the name of the non censored y_var (default = NULL). To be used only in the context of simulated data where full about is available.
ntree	A positive integer which gives the number of trees to grow in the forest (default = 100).
minleaf	A positive integer indicating the minimum number of observations that must be present in a (terminal) leaf (default = 5).
maxdepth	A positive integer indicating the maximum number of layers in individual trees (default = 6).
mtry	A positive integer indicating the number of random variables to draw at each node for the split selection (default = NULL). If NULL, mtry is set to floor(sqrt(length(x_vars))) by default.
reinforcement	A boolean which specifies if reinforcement in RLT shloud be used for split selection
...	Additional parameter that may be pass to the RLT function (package RLT)

Details

• Evaluation criteria

  The quality of fit may be assess throught three different criteria. There are two main criteria : "weighted" and "concordance", and one criteria that is expimental : "group".

  • "weighted" : the weighed criteria is described in <c2><a7>? of [Gerb. et al.]. This criteria aims to estimate the quadratic error of the model in the context of right censoring. It has the form ∑_i W_i (y_i - \hat{y}_i)^2 where (y_i)i are the censored targets of the model, (W_i)i are the IPC weights, and (\hat{y}_i)i are the predictions made.

    The types_w_ev argument allows the use of four kinds of IPC weights : "KM", "Cox", "RSF" and "unif". The first three types of weights correspond to different ways to estimate the survival function of the censoring. On the other hand, "unif" corresponds to W_i = 1 for all i.

    Since the IPC weights may take too large values in some situation, max_w_ev allows to threshold the weights (W_i)i so that the ratio between the largest and the smallest weights doesn't exceed max_w_ev. If W_max is the maximum weight, considered weights are then min(W_i, W_max) / ( ∑_i min(W_i, W_max) )

    You can also manually provide weights to be used for IPCW with the argument mat_w (those weights will also be threshold w.r.t. max_ration_weights_eval). mat_w should be a matrix satisfying nrow(mat_w) = nrow(train) + nrow(test), any numbers of columns may be provided and then each column of the matrix corresponds to a type of weights. Columns name of the matrix are taken as names for the different types of weights. If there is no column name, then default names are "w1", "w2', ...

  • "concordance" : The concordance is a classical measure of performance when modelling censored variables. It indicates if the order of the predicted values of the model is similar to the order of the observed values. The concordance generalizes the Kendall tau to the censored case.

  • "group" : This is an experimental criteria that we didn't mention in [Gerb. et al.]. Here, the idea to take the censoring into account is to measure errors given groups of observations and not single observations. First, the test sample is ordered w.r.t. the predicted values of the model. Second, respecting this order the test sample is splited into groups of size v_bandwidht[1], or v_bandwidht[2], etc ... (each bandwidth in v_bandwidht corresponds to a different score "group").

    Then, inside a group, an estimator of the survival function of T may be obtained by Kaplan Meier, and we can deduce an estimator of phi(T) by integration. This estimator of phi(T) may be viewed as an "empirical" value of phi(T) inside the group.

    On the other other hand, each observation of a group is associated to a prediction of phi(T). The prediction for the group may be defined as the mean of the predictions of the observations inside the group.

    The resulting group scores correspond to the classical quality of fit criteria (e.g. quadratic error, Kendall tau, Gini index) but taken on groups and not on single observations.

    The "group" criteria is interesting in the context of big database, in which sufficient number of groups are available. This criteria has a high variance if applied to small test sample.

Value

A list with the following elements :

pred_train	The vector of the predicted values for phi(T') (with T' = min(T, max_time)) for the observations of the train set
pred_test	The vector of the predicted values for phi(T') for the observations of the test set (require test != NULL)
perf_train	The list with the values for the evaluation criteria computed on the train set
perf_test	The list with the values for the evaluation criteria computed on the test set (require test != NULL))
surv_train	The matrix which contains the estimated values of the survival curves at time_points (with the Cox model), for the observations of the train set
surv_test	The matrix which contains the estimated values of the survival curves at time_points, for the observations of the test set (require test != NULL)
time_points	The vector of the time points where the survival curves are evaluated
mat_w_train	The matrix which contains the values of the weights used for the "weighted" criteria, for the observations of the train set
mat_w_test	The matrix which contains the values of the weights used for the "weighted" criteria, for the observations of the test set
n_w_ev_modif_train	The vector giving the number of train weights modified due to max_w_ev
n_w_ev_modif_test	The vector giving the number of test weights modified due to max_w_ev
rlt_obj	The obj returned by the RLT function
max_time	The real number giving the threshold used by the model
cens_rate	The real number giving the rate of censoring of T', computed on the concatenation of train and test
train	The data.frame of the train data provided as arguments, plus columns : Y' = min(Y, max_time ), δ' = 1_{T' ≤ C} and phi(T')
test	The data.frame of the test data provided as arguments, plus columns : Y' = min(Y, max_time ), δ' = 1_{T' ≤ C} and phi(T')
phi	See Argument
phi.args	See Argument
x_vars	See Argument
max_w_ev	See Argument

References

Gerber, G., Le Faou, Y., Lopez, O., & Trupin, M. (2018). The impact of churn on prospect value in health insurance, evaluation using a random forest under random censoring. https://hal.archives-ouvertes.fr/hal-01807623/

See Also

RLT, predict_rlt_reg

YohannLeFaou/sword documentation built on May 28, 2019, 3:21 p.m.