The R package BioPred offers a suite of tools for subgroup and biomarker analysis in precision medicine. Leveraging Extreme Gradient Boosting (XGBoost) along with propensity score weighting and A-learning methods, BioPred facilitates the optimization of individualized treatment rules (ITR) to streamline sub-group identification. BioPred also enables the identification of predictive biomarkers and obtaining their importance rankings. Moreover, the package provides graphical plots tailored for biomarker analysis. This tool enables clinical researchers seeking to enhance their understanding of biomarkers and patient population in drug development.
install_github(“deeplearner0731/BioPred”)
install.packages(“BioPred”)
The ‘tutorial_data’ dataset is included with the package. Let’s load and inspect it:
library(BioPred)
kable_styling(kable(x=head(tutorial_data), format="html", caption = "The first 6 subjects"),
bootstrap_options="striped",font_size=16)
x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | y.con | y.bin | y.time | y.event | treatment | subgroup_label | risk_category | treatment_categorical |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
-2.3744988 | 0.0167914 | -2.5412961 | -2.0901502 | -2.6896868 | -1.3455564 | -2.4931001 | -0.3483110 | -1.5673804 | 0.4836952 | 0.0992838 | 0 | 0.0874949 | 0 | 0 | 1 | High Risk | Placebo |
-0.1838847 | 1.8222234 | 0.4601912 | 0.5497404 | 1.6449981 | 0.5433581 | 0.2364084 | -2.7868360 | -0.4006381 | 0.6874968 | 0.0711574 | 0 | 0.9534603 | 0 | 0 | 0 | Intermediate Risk | Placebo |
0.0539828 | -1.9142628 | 1.3112035 | 0.6543154 | -0.0653439 | 0.5491687 | 1.8201585 | 2.5079087 | -0.4686039 | 1.1696815 | -1.2151804 | 0 | 0.0005331 | 0 | 1 | 1 | High Risk | Treatment |
1.1048102 | 0.8346022 | -1.9808589 | -0.5632687 | 0.3344664 | 1.4275303 | 0.1324287 | 2.1463655 | 1.3107915 | 0.4411784 | 0.2773950 | 0 | 0.0435684 | 0 | 1 | 0 | High Risk | Treatment |
-0.4179985 | -2.2484687 | 3.3396929 | 3.1896045 | -0.5779621 | -1.4963500 | 0.4454772 | 0.1323151 | 1.4211205 | -1.5240744 | -2.0069643 | 0 | 0.1050067 | 0 | 1 | 1 | High Risk | Treatment |
1.0177850 | 0.1045029 | 1.4632138 | 1.0294900 | 2.0912418 | 2.2324576 | 0.5073059 | -1.4397678 | 1.5456243 | 0.4183628 | 1.4521578 | 1 | 0.1018182 | 0 | 0 | 0 | High Risk | Placebo |
rownames(tutorial_data)=NULL
The tutorial_data dataset contains the following columns:
We will begin by training the XGBoostSub_con
model for a continuous outcome. This involves using the A-learning or Weight-learning loss function. Note that the treatment variable must be converted to (1, -1). If your treatment variable is (1, 0), you will need to convert it accordingly.
=tutorial_data[,c("x1", "x2" ,"x3" ,"x4","x5","x6","x7","x8","x9","x10")]
X_feature=tutorial_data$y.con
y_label# Convert treatment variable to (1 -1) format (1 for treatment, -1 for control)
=ifelse(tutorial_data$treatment==1, 1, -1)
trt=tutorial_data$subgroup_label
true_label# Estimate the propensity score using logistic regression
=tutorial_data[,c("treatment","x1", "x2" ,"x3" ,"x4" , "x5", "x6" , "x7","x8","x9","x10")]
data_logit<- glm(treatment~ ., data = data_logit, family = binomial)
logit_model <- predict(logit_model, type = "response")
pi # Train the XGBoostSub_con model using the specified parameters
<- XGBoostSub_con(X_feature, y_label, trt ,pi,Loss_type = "A_learning", params = list(learning_rate = 0.005, max_depth = 1, lambda = 5, tree_method = 'hist'), nrounds = 200, disable_default_eval_metric = 0, verbose = FALSE) model
After training the model, you can print the loss value at each epoch using the following code:
cat("Evaluation loss:\n")
#> Evaluation loss:
print(model$evaluation_log)
#> iter train_A_loss
#> <num> <num>
#> 1: 1 1.375787
#> 2: 2 1.375424
#> 3: 3 1.375065
#> 4: 4 1.374708
#> 5: 5 1.374355
#> ---
#> 196: 196 1.339571
#> 197: 197 1.339486
#> 198: 198 1.339402
#> 199: 199 1.339319
#> 200: 200 1.339236
You can also evaluate the loss on independent datasets using the eval_metric_con function
. In this example, we’ll use the training data as test data for illustration purposes. However, you may use a new dataset to see the loss based on the trained model.
<- eval_metric_con(model, X_feature, y_label, pi, trt, Loss_type = "A_learning")
eval_metric_test cat("Testing Evaluation Result:\n")
#> Testing Evaluation Result:
print(eval_metric_test$value)
#> [1] 1.339236
Next, we evaluate the importance of predictive biomarkers using the predictive_biomarker_imp
function.
=predictive_biomarker_imp(model) biomarker_imp
kable_styling(kable(x=biomarker_imp, format="html", caption = "Biomarker importance table"),
bootstrap_options="striped",font_size=16)
Biomarker | Importance |
---|---|
x2 | 0.4904407 |
x1 | 0.4793201 |
x10 | 0.0302392 |
From the results, we observe that the most important predictive biomarker is x2
.
You can obtain the subgroup results using the get_subgroup_results
function.
=get_subgroup_results(model, X_feature, subgroup_label=true_label, cutoff = 0.5)
subgroup_resultskable_styling(kable(x=head(subgroup_results$assignment), format="html", caption = "The first 6 subjects subgroup assigentment"),
bootstrap_options="striped",font_size=16)
Patient_ID | Treatment_Assignment |
---|---|
1 | 1 |
2 | 1 |
3 | 1 |
4 | 0 |
5 | 1 |
6 | 1 |
cat("Prediction accuracy of true subgroup label:\n")
#> Prediction accuracy of true subgroup label:
cat(subgroup_results$acc)
#> 0.634
Note that when using the get_subgroup_results
function with real data, the true subgroup label is typically unknown. In such cases, set subgroup_label = NULL. This will return only the subgroup assignment without the prediction accuracy of the subgroup.
Given that x2
was identified as the most important predictive biomarker by XGBoostSub_con
, we will use the cdf_plot
function to evaluate the distribution of this biomarker by assessing the percentage of subjects falling within different cutoff values.
cdf_plot (xvar="x2", data=tutorial_data, y.int=5, xlim=NULL, xvar.display="Biomarker_X2", group=NULL)
We will also evaluate x2
prognostic capability. To determine if this biomarker is prognostic, we can assess the association between the response variable y.con
and the biomarker x2
using the scat_cont_plot
function.
scat_cont_plot(
yvar='y.con',
xvar='x2',
data=tutorial_data,
ybreaks = NULL,
xbreaks = NULL,
yvar.display = 'y',
xvar.display = "Biomarker_X2"
)#> $Cor.Pearson
#> [1] -0.12
#>
#> $Cor.Spearman
#> [1] -0.12
#>
#> $fig
#>
#> $slope
#> [1] -0.1013384
#>
#> $intercept
#> [1] 0.6769244
Selecting the cutoff value for a predictive biomarker is important in clinical practice, as it can, for example, help enrich responders. We select the optimal cutoff for the identified biomarker x2
from a list of candidate cutoff values using the fixcut_con
function.
=fixcut_con(yvar='y.con', xvar="x2", dir=">", cutoffs=c(-0.1,-0.3,-0.5,0.1,0.3,0.5), data=tutorial_data, method="t.test", yvar.display='y.con', xvar.display='biomarker x2', vert.x=F)
cutoff_result_con
$fig cutoff_result_con
From the results, the optimal cutoff value is 0.5. Next, we define the biomarker positive group using a cutoff of 0.5. The biomarker positive group includes subjects with x2
values less than or equal to 0.5, while the biomarker negative group includes subjects with x2 values greater than 0.5. We first use the cut_perf()
function to evaluate the performance between the biomarker positive and negative groups.
=cut_perf (yvar="y.con", censorvar=NULL, xvar="x2", cutoff=c(0.5), dir="<=", xvars.adj=NULL, data=tutorial_data, type='c', yvar.display='y.con', xvar.display="biomarker x2")
reskable_styling(kable(x=res$comp.res.display[,-2:-4], format="html", caption = "Performace at optimal cutoff"),
bootstrap_options="striped",font_size=16)
Response | Median.Diff | Mean.Diff.CI | t.pvalue | WRS.pvalue |
---|---|---|---|---|
y.con | -0.3 | -0.38 (NA , NA) | NA | NA |
Next, we will further assess the predictive model performance by examining the differences between the treatment and control groups within both the biomarker positive and negative groups.
$biogroup=ifelse(tutorial_data$x2<=0.5,'biomarker_positive','biomarker_negative')
tutorial_data
= subgrp_perf_pred(yvar="y.time", censorvar="y.event", grpvar="biogroup", grpname=c("biomarker_positive",'biomarker_negative'),trtvar="treatment_categorical", trtname=c("Placebo" , "Treatment"), xvars.adj=NULL,data=tutorial_data, type="s")
res kable_styling(kable(x=res$group.res.display, format="html", caption = "BioSubgroup Stat"),
bootstrap_options="striped",font_size=16)
Response | N | Events | Mean.Surv.CI | Med.Surv.CI | |
---|---|---|---|---|---|
treatment_categorical=Placebo,biogroup=biomarker_positive | y.time | 321 | 127 | 3.7 (2.49 , 4.92) | 1.99 (1.65 , 2.7) |
treatment_categorical=Placebo,biogroup=biomarker_negative | y.time | 192 | 76 | 4.49 (2.37 , 6.61) | 1.83 (1.58 , 2.27) |
treatment_categorical=Treatment,biogroup=biomarker_positive | y.time | 321 | 133 | 4.84 (3.66 , 6.02) | 2.85 (2.11 , 3.52) |
treatment_categorical=Treatment,biogroup=biomarker_negative | y.time | 166 | 75 | 2.63 (1.93 , 3.32) | 1.51 (0.84 , 2.14) |
$fig res
From the Kaplan-Meier (KM) curve, a difference between the treatment and control groups is observed in the biomarker positive group. This difference is not observed in the biomarker negative group, validating that biomarker x2
identified by XGBoostSub_con is predictive.
Similar to training the XGBoostSub_con
model for continuous outcomes, we can also train the XGBoostSub_bin
model for binary outcomes.
=tutorial_data$y.bin
y_label<- XGBoostSub_bin(X_feature, y_label, trt ,pi,Loss_type = "A_learning", params = list(learning_rate = 0.01, max_depth = 1, lambda = 5, tree_method = 'hist'), nrounds = 300, disable_default_eval_metric = 0, verbose = FALSE) model
=predictive_biomarker_imp(model) biomarker_imp
kable_styling(kable(x=biomarker_imp, format="html", caption = "Biomarker importance table"),
bootstrap_options="striped",font_size=16)
Biomarker | Importance |
---|---|
x10 | 0.6100485 |
x2 | 0.1428244 |
x8 | 0.1083907 |
x5 | 0.0805473 |
x1 | 0.0581890 |
Based on the results, biomarker x10
emerges as the most important biomarker.
=get_subgroup_results(model, X_feature, subgroup_label=true_label, cutoff = 0.5)
subgroup_resultskable_styling(kable(x=head(subgroup_results$assignment), format="html", caption = "The first 6 subjects subgroup assigentment"),
bootstrap_options="striped",font_size=16)
Patient_ID | Treatment_Assignment |
---|---|
1 | 0 |
2 | 0 |
3 | 0 |
4 | 0 |
5 | 1 |
6 | 0 |
cat("Prediction accuracy of true subgroup label:\n")
#> Prediction accuracy of true subgroup label:
cat(subgroup_results$acc)
#> 0.535
Users can freely tune the parameters in the XGBoostSub-based models to enhance the performance of identifying true subgroups. In this example, we provide a random parameter setting for illustration purposes. However, when applying this model to real data, the ground truth labels are unknown, which means you may not be able to tune the parameters based on prediction accuracy.
Continuing our assessment, we aim to determine whether the identified biomarker is prognostic or not. To do so, we examine the association between the binary response variable y.bin
and biomarker x10
.
roc_bin_plot (yvar='y.bin', xvars="x10", dirs="auto", data=tutorial_data, yvar.display='y.bin', xvars.display="Biomarker x10")
The association between the binary response variable y.bin
and biomarker x2
, identified as the second most important biomarker by the XGBoostSub_bin
model, is shown below.
roc_bin_plot (yvar='y.bin', xvars="x2", dirs="auto", data=tutorial_data, yvar.display='y.bin', xvars.display="Biomarker x2")
We select the optimal cutoff of identified biomarker x10
from a candidate list of cutoff values This capability is particularly valuable for companion diagnostics (CDx) development when working with a limited set of candidate cutoffs (e.g., IHC).
=fixcut_bin (yvar='y.bin', xvar="x10", dir=">", cutoffs=c(-0.1,-0.3,-0.5,0.1,0.3,0.5), data=tutorial_data, method="Fisher", yvar.display='Response_Y', xvar.display='Biomarker_X10', vert.x=F)
cutoff_result_bin$fig cutoff_result_bin
Here, users can select the optimal cutoff based on various metrics such as sensitivity, specificity, PPV (Positive Predictive Value), and NPV (Negative Predictive Value). The choice of metric depends on the specific research context. For instance, if the goal is to enrich responders, focusing on PPV might be more appropriate. Based on the highest PPV value, users can then select the optimal cutoff.
If accuracy is our primary concern, the optimal cutoff value is 0.5. In this case, we define the biomarker positive group using a cutoff of 0.5. This group comprises subjects with x10
values greater than or equal to 0.5, while the biomarker negative group consists of subjects with x10
values less than 0.5. To assess the performance between the biomarker positive and negative groups, we initially employ the cut_perf
function.
=cut_perf (yvar="y.con", censorvar=NULL, xvar="x10", cutoff=c(0.5), dir=">", xvars.adj=NULL, data=tutorial_data, type='c', yvar.display='y.con', xvar.display="biomarker x2")
reskable_styling(kable(x=res$comp.res.display[,-2:-4], format="html", caption = "caption"),
bootstrap_options="striped",font_size=16)
Response | Median.Diff | Mean.Diff.CI | t.pvalue | WRS.pvalue |
---|---|---|---|---|
y.con | 0.22 | 0.2 (NA , NA) | NA | NA |
Next, the subgrp_perf_pred
function will provide the predictive model performance based on the defined subgroup.
$biogroup=ifelse(tutorial_data$x10>0.5,'biomarker_positive','biomarker_negative')
tutorial_data
= subgrp_perf_pred(yvar="y.time", censorvar="y.event", grpvar="biogroup", grpname=c("biomarker_positive",'biomarker_negative'),trtvar="treatment_categorical", trtname=c("Placebo" , "Treatment"), xvars.adj=NULL,data=tutorial_data, type="s")
res kable_styling(kable(x=res$group.res.display, format="html", caption = "BioSubgroup Stat"),
bootstrap_options="striped",font_size=16)
Response | N | Events | Mean.Surv.CI | Med.Surv.CI | |
---|---|---|---|---|---|
treatment_categorical=Placebo,biogroup=biomarker_positive | y.time | 191 | 73 | 3.94 (2.27 , 5.6) | 1.83 (1.46 , 2.47) |
treatment_categorical=Placebo,biogroup=biomarker_negative | y.time | 322 | 130 | 3.98 (2.52 , 5.43) | 2.03 (1.74 , 2.44) |
treatment_categorical=Treatment,biogroup=biomarker_positive | y.time | 181 | 79 | 3.19 (2.35 , 4.04) | 1.71 (1.16 , 2.14) |
treatment_categorical=Treatment,biogroup=biomarker_negative | y.time | 306 | 129 | 4.68 (3.46 , 5.89) | 2.96 (2.12 , 3.73) |
$fig res
From the KM curve, it appears that 0.5 for X10
may not be the optimal cutoff. Further evaluation using the fixcut_bin
function with different candidate optimal cutoffs is suggested.
# Prepare the data for training the XGBoostSub_sur
=tutorial_data$y.time
y_label=tutorial_data$y.event
delta
# Train the XGBoostSub_sur model using the specified parameters
<- XGBoostSub_sur(X_feature, y_label, trt ,pi,delta,Loss_type = "A_learning", params=list(learning_rate = 0.005, max_depth = 1,lambda = 9, gamma=1, min_child_weight=1,
model max_bin=128, tree_method = 'exact',subsample=0.8), nrounds = 250, disable_default_eval_metric = 1, verbose = FALSE)
=predictive_biomarker_imp(model) biomarker_imp
kable_styling(kable(x=biomarker_imp, format="html", caption = "Biomarker importance table"),
bootstrap_options="striped",font_size=16)
Biomarker | Importance |
---|---|
x6 | 0.7034638 |
x2 | 0.2382198 |
x1 | 0.0250257 |
x10 | 0.0117930 |
x9 | 0.0071005 |
x5 | 0.0055363 |
x8 | 0.0034420 |
x3 | 0.0027360 |
x4 | 0.0026829 |
=get_subgroup_results(model, X_feature, subgroup_label=true_label, cutoff = 0.5)
subgroup_resultskable_styling(kable(x=head(subgroup_results$assignment), format="html", caption = "The first 6 subjects subgroup assigentment"),
bootstrap_options="striped",font_size=16)
Patient_ID | Treatment_Assignment |
---|---|
1 | 1 |
2 | 0 |
3 | 0 |
4 | 0 |
5 | 1 |
6 | 0 |
cat("Prediction accuracy of true subgroup label:\n")
#> Prediction accuracy of true subgroup label:
cat(subgroup_results$acc)
#> 0.54
Subgroup analysis often involves dividing subjects into different groups based on categorical variables, such as baseline characteristics or genetic mutation variables. In this package, we provide the cat_summary function to summarize these categorical variables. For example, in the tutorial dataset, there is a variable called risk_category
, which takes values like High Risk, Intermediate Risk, and Low Risk. First, we use this function to determine the distribution of subjects in each subgroup.
= cat_summary(yvar="risk_category", yname=c("High Risk","Intermediate Risk" ,"Low Risk"), xvars="treatment_categorical", xname.list=list(c("Placebo" , "Treatment")), data=tutorial_data)
res
kable_styling(kable(x=res$cont.display, format="html", caption = "Contingency Table"),
bootstrap_options="striped",font_size=16)
treatment_categorical | risk_category = High Risk | risk_category = Intermediate Risk | risk_category = Low Risk |
---|---|---|---|
Placebo | 128 (25%) | 263 (51.3%) | 122 (23.8%) |
Treatment | 122 (25.1%) | 237 (48.7%) | 128 (26.3%) |
Then, we can also visualize the KM curves based on predefined risk groups and treatment/control groups using the subgrp_perf_pred
function.
= subgrp_perf_pred(yvar="y.time", censorvar="y.event", grpvar="risk_category", grpname=c("High Risk","Intermediate Risk" ,"Low Risk"),trtvar="treatment_categorical", trtname=c("Placebo" , "Treatment"), xvars.adj=NULL,data=tutorial_data, type="s")
res kable_styling(kable(x=res$group.res.display, format="html", caption = "Subgroup Stat"),
bootstrap_options="striped",font_size=16)
Response | N | Events | Mean.Surv.CI | Med.Surv.CI | |
---|---|---|---|---|---|
treatment_categorical=Placebo,risk_category=High Risk | y.time | 128 | 4 | 22.57 (3.96 , 41.17) | NA (0.13 , NA) |
treatment_categorical=Placebo,risk_category=Intermediate Risk | y.time | 263 | 110 | 2.95 (-0.03 , 5.92) | 1.12 (0.99 , 1.21) |
treatment_categorical=Placebo,risk_category=Low Risk | y.time | 122 | 89 | 6.18 (4.38 , 7.98) | 3.31 (2.87 , 4.33) |
treatment_categorical=Treatment,risk_category=High Risk | y.time | 122 | 4 | 0.12 (0.11 , 0.13) | 0.13 (0.12 , NA) |
treatment_categorical=Treatment,risk_category=Intermediate Risk | y.time | 237 | 108 | 0.96 (0.89 , 1.04) | 0.99 (0.82 , 1.11) |
treatment_categorical=Treatment,risk_category=Low Risk | y.time | 128 | 96 | 6.49 (5.19 , 7.79) | 4.41 (3.86 , 5.2) |
$fig res