How to use DynForest with
continuous outcome?
Introduction to data_simu1 and data_simu2
datasets
In this vignette, we present an illustration of
DynForest with a continuous outcome. DynForest
was used on a simulated dataset with 200 subjects and 10 predictors (6
time-dependent and 4 time-fixed predictors). The 6 longitudinal
predictors were generated using a linear mixed model with linear
trajectory according to time. We considered 6 measurements by subject
(at baseline and then randomly drawn around theoretical annual visits up
to 5 years). Then, we generated the continuous outcome using a linear
regression with the baseline random-effect of marker 1 and slope
random-effect of marker 2 as linear predictors. We generated two
datasets (data_simu1} and data_simu2), one for
each step (training and prediction).
The aim of this illustration is to predict the continuous outcome
using time-dependent and time-fixed predictors.
Managing data
First of all, we load the data and we build the mandatory objects
needed to execute DynForest() function. We specify the
model for the longitudinal predictors. For the illustration, we consider
linear trajectories over time for the 6 longitudinal predictors.
timeData_train <- data_simu1[,c("id","time",
paste0("marker",seq(6)))]
timeVarModel <- lapply(paste0("marker",seq(6)),
FUN = function(x){
fixed <- reformulate(termlabels = "time",
response = x)
random <- ~ time
return(list(fixed = fixed, random = random))
})
fixedData_train <- unique(data_simu1[,c("id",
"cont_covar1","cont_covar2",
"bin_covar1","bin_covar2")])
To define the object for a continuous outcome, the type
argument should be chosen to numeric to set up the random
forest in regression mode. The dataframe Y should include
two columns with the unique identifier id and the
continuous outcome Y_res.
Y <- list(type = "numeric",
Y = unique(data_simu1[,c("id","Y_res")]))
Build the random forest
To build the random forest, we chose default hyperparameters
(i.e. ntree = 200 and nodesize = 1), except
for mtry which was fixed to 10. We ran
DynForest() function with the following code:
res_dyn <- DynForest(timeData = timeData_train,
fixedData = fixedData_train,
timeVar = "time", idVar = "id",
timeVarModel = timeVarModel,
mtry = 10,
Y = Y, seed = 1234)
Out-Of-Bag error
For continuous outcome, the OOB prediction error is evaluated using
mean square error (MSE). We used compute_OOBerror()
function to compute the OOB prediction error and we provided overall
results with summary() function as below:
res_dyn_OOB <- compute_OOBerror(DynForest_obj = res_dyn)
summary(res_dyn_OOB)
DynForest executed with regression mode
Splitting rule: Minimize weighted within-group variance
Out-of-bag error type: Mean square error
Leaf statistic: Mean
----------------
Input
Number of subjects: 200
Longitudinal: 6 predictor(s)
Numeric: 2 predictor(s)
Factor: 2 predictor(s)
----------------
Tuning parameters
mtry: 10
nodesize: 1
ntree: 200
----------------
----------------
DynForest summary
Average depth by tree: 9.06
Average number of leaves by tree: 126.47
Average number of subjects by leaf: 3.03
----------------
Out-of-bag error based on Mean square error
Out-of-bag error: 4.3663
----------------
Time to build the random forest
Time difference of 4.74484 mins
----------------
The random forest was executed in regression mode (for a continuous
outcome). The splitting rule aimed to minimize the weighted within-group
variance. We built the random forest using 200 subjects and 10
predictors (6 time-dependent and 4 time-fixed predictors) with
hyperparameters ntree = 200, mtry = 10 and
nodesize = 1. As we can see, nodesize = 1
leads to deeper trees (the average depth by tree is 9.1) and few
subjects by leaf (3 on average). We obtained 4.4 for the MSE. This
quantity needs to be minimized using hyperparameters mtry
and nodesize.
Predict the outcome
In regression mode, the tree-specific predictions are averaged across
the trees to get an unique prediction over the random forest.
predict() function provides the individual predictions. We
first created the objects with the same predictors used to build the
random forest. We then predicted the continuous outcome by using the
data.
timeData_pred <- data_simu2[,c("id","time",
paste0("marker",seq(6)))]
fixedData_pred <- unique(data_simu2[,c("id","cont_covar1","cont_covar2",
"bin_covar1","bin_covar2")])
pred_dyn <- predict(object = res_dyn,
timeData = timeData_pred,
fixedData = fixedData_pred,
idVar = "id", timeVar = "time")
predict() function provides several results for the new
subjects. We can extract from its returning object the individual
predictions using the following code:
head(pred_dyn$pred_indiv)
1 2 3 4 5 6
5.2117462 -1.2899651 0.8591368 1.5115133 5.2957749 7.9194240
For instance, we predicted 5.21 for subject 1, -1.29 for subject 2
and 0.86 for subject 3.
Explore the most predictive variables
In this illustration, we want to evaluate if DynForest
can identify the true predictors (i.e. baseline random-effect of marker1
and slope random-effect of marker2). To do this, we used the minimal
depth which allows to understand the random forest at feature level.
This information about the minimal depth can be extracted using
var_depth() function and can be displayed with
plot() function. For the purpose of this illustration, we
displayed the minimal depth in figure 1 by predictor and by feature.
depth_dyn <- var_depth(DynForest_obj = res_dyn)
plot(x = depth_dyn, plot_level = "predictor")
plot(x = depth_dyn, plot_level = "feature")
We observe in figure 1A that marker2 and marker1 have the lowest
minimal depth, as expected. To go further, we also looked into the
minimal depth computed on features. We perfectly identified the slope
random-effect of marker2 (i.e. marker2.bi1) and the baseline
random-effect of marker1 (i.e. marker1.bi0) as predictors in our
simulation.
