Event Distribution

Before performing any survival analysis, it is relevant to understand the structure of the time-to-event data. A key preliminary step is examining how events (e.g., deaths, failures) and censored observations (e.g., lost to follow-up, study termination) are distributed across the dataset, as this exploration helps identify potential biases, assess data quality, and guide appropriate modeling choices.

The plot_events() function in this package provides a straightforward way to visualize this distribution. It displays event occurrences and censoring times, allowing users to:

• Detect imbalances between events and censored cases that may affect statistical power.
• Identify unusual patterns (e.g., clustered censoring) that could indicate informative dropout.
• Compare distributions across groups to reveal differential follow-up rates.
• Validate whether the observed event timing aligns with expected biological or clinical processes.

This visualization serves as an exploratory tool, ensuring that subsequent survival analysis rests on reliable data patterns. The function’s output can highlight the need for extended follow-up or careful interpretation of results in contexts with heavy censoring.

The plot_events() function requires the Y matrix and optionally accepts the following arguments among others:

• categories: the names of each category (a character vector of length two).
• y.text: the label for the y-axis.
• roundTo: the smallest numeric unit to which break times will be rounded. For example, if set to 0.25, a value of 1.32 will be rounded to 1.25.
• max.breaks: the number of breaks for the histogram.

ggp_density.event <- plot_events(Y = Y, 
                                 categories = c("Censored","Event"),
                                 y.text = "Number of observations", 
                                 roundTo = 0.5, 
                                 max.breaks = 15, 
                                 txt.x.angle = 90)

C:1BfP43083d9d5ab9-MO-pipeline.R

ggp_density.event$plot

C:1BfP43083d9d5ab9-MO-pipeline.R

Event Per Variable (EVP)

Before fitting survival models, it is important to ensure that there is sufficient statistical power to avoid overfitting. The Events Per Variable (EPV) metric supports this evaluation by indicating how many outcome events are available per predictor in the model.

According to literature, the higher values the better. As a recommendation, values greater than 10 should be used to obtain models with good predictions, but this value should not be lower than 5.

A low EPV value (typically <10) increases the risk of:

• Overfitting: the model may capture noise rather than true associations
• Unstable estimates: the variability of coefficient estimates increases, reducing reproducibility
• Optimistic performance metrics: apparent model accuracy may not generalize to new data

The getEPV.mb() function calculates and reports the EPV for a given dataset. This helps to:

• Assess whether the sample size is adequate for multivariable modeling
• Guide variable selection to maintain an EPV ≥10 or support justification for deviations
• Compare EPV values across subgroups when conducting stratified analyses

Additionally, working with low EPV values often indicates the presence of high-dimensional datasets, where the number of predictors is large relative to the number of events. In such cases, it is advisable to use survival models specifically designed to handle high-dimensional settings, such as Coxmos methods.

EPV <- getEPV.mb(X, Y)

C:1BfP43083d9d5ab9-MO-pipeline.R

EPV
#> $mirna
#> [1] 0.1121495
#> 
#> $proteomic
#> [1] 0.195122

C:1BfP43083d9d5ab9-MO-pipeline.R

In this case, the EPV has a value of 0.1121495 and 0.195122 for each block, which indicates that the number of predictors is high relative to the number of observed events. This makes it unreliable to apply classical survival algorithms, as they are prone to overfitting under these conditions.

Preprocessing Categorical Variables for Dimensionality Reduction

When working with datasets (i.e., X matrices) that include qualitative or categorical variables, proper encoding is essential prior to applying dimensionality reduction techniques such as Principal Component Analysis (PCA) or Partial Least Squares (PLS). Most of these algorithms require purely numerical input, so categorical variables (e.g., sex = {Male, Female}, tumor_stage = {I, II, III}) must be transformed into a suitable format that retains their informational content without introducing artificial ordinality.

The factorToBinary() function automates the transformation of categorical variables into dummy variables using one-hot encoding. This process addresses several important issues:

• Avoiding misinterpretation: Prevents algorithms from mistakenly interpreting categorical values as ordinal or numeric (e.g., assigning sex Male = 1, Female = 2, etc.).

• Compatibility: Ensures that categorical features are represented numerically, which is required by linear algebra-based techniques such as PCA or PLS.

• Dimensionality control: Allows flexibility in the encoding format:

  • K dummy variables (one for each category) for full representation.
  • K - 1 dummy variables to avoid perfect multicollinearity in regression-based models.

• Easy integration: The resulting matrix preserves original column names with appended suffixes (e.g., sex_Male, tumor_stage_II), enabling straightforward traceability in downstream processes.

It accepts the following arguments:

• X: numeric matrix or data frame. Only qualitative variables (class factor) will be transformed into binary variables.

• all: logical. If TRUE, one binary variable will be generated for each level of the factor (k dummies). If FALSE, only k - 1 variables will be returned, using the first level as the reference category (default: TRUE).

• sep: character. Symbol used to concatenate the original variable name and the level name in the new column names. For example, if the variable is "sex" and sep = "_", the resulting dummy variables will be named "sex_male", "sex_female", etc.

This function ensures compatibility with numerical algorithms while keeping variable names interpretable and traceable.

X$mirna <- factorToBinary(X = X$mirna, all = TRUE, sep = "_")

C:1BfP43083d9d5ab9-MO-pipeline.R

Training/Test Split for Survival Model Validation

Proper validation of survival models requires thoughtful partitioning of the dataset into training and test subsets. The getTrainTest() function provides a consistent and event-aware approach to splitting survival data, ensuring that the characteristics of time-to-event outcomes are preserved during validation.

This function performs event-balanced splits by default, maintaining a similar proportion of events and censored cases across both training and test sets. This is essential to avoid biased performance estimates and to ensure that the test set contains a sufficient number of events for evaluation.

In datasets composed of multiple data blocks (e.g., omics and clinical data), getTrainTest() synchronizes the partitioning across all blocks, preserving sample alignment and ensuring integrity during downstream analysis. Whether working with simple matrices or multiblock structures, the function guarantees that each block is split consistently.

It also supports flexible validation schemes. By setting the times argument, users can perform a single data split (times = 1) or repeated random splits for cross-validation (times > 1), allowing for evaluation of model stability and robustness across different partitions. A fixed random seed ensures reproducibility of the results.

split_data <- getTrainTest(X, Y, p = 0.7)

X_train <- split_data$X_train #106x642 and 106x369
Y_train <- split_data$Y_train

X_test <- split_data$X_test #44x642 and 44x369
Y_test <- split_data$Y_test

C:1BfP43083d9d5ab9-MO-pipeline.R

This splitting strategy is especially relevant in survival analysis, where event sparsity and censoring can lead to unreliable validation if not properly addressed. By incorporating stratified sampling and support for complex data structures, getTrainTest() serves as a reliable bridge between preprocessing and model development. It enables performance assessment that reflects real-world behavior while preserving the temporal dynamics of time-to-event data.

MB methods for Survival Analyses

In order to perform survival analysis with our multi-block high-dimensional data, we have implemented a series of methods that utilize techniques such as partial least squares (PLS) methodology in order to reduce the dimensionality of the input data.

To evaluate the performance of these methods, we have implemented cross-validation, which allows us to estimate the optimal parameters for future predictions based on prediction metrics such as: AIC, C-INDEX, I.BRIER and Area Under the Curve (AUC). By default AUC metric is used with the "cenROC" evaluator as it has provided the best results in our tests. However, multiple AUC evaluators could be used: "risksetROC", "survivalROC", "cenROC", "nsROC", "smoothROCtime_C" and "smoothROCtime_I".

Furthermore, a mix of multiple metrics could be used to obtain the optimal model. The user has to establish different weights for each metric and all of them will be considered to compute the optimal model (the total weight must sum 1).

In addition, we have included options for normalizing data, filtering variables, and setting the minimum EPV, as well as specific parameters for each method, such as the alpha value for Cox Elastic Net and the number of components for sPLS models. Overall, our cross-validation methodology allows us to effectively analyze high-dimensional survival data and optimize our model parameters.

cv.sb.splsicox_res <- cv.mb.coxmos(method = "sb.splsicox",
                                   X = X_train, Y = Y_train,
                                   max.ncomp = 2, penalty.list = c(0.5,0.9),
                                   n_run = 1, k_folds = 5)

cv.sb.splsicox_res

cv.sb.splsicox_res$plot_AUC

sb.splsicox_model <- mb.coxmos(method = "sb.splsicox",
                               X = X_train, Y = Y_train,
                               n.comp = 2, #cv.sb.splsicox_res$opt.comp
                               penalty = 0.9) #cv.sb.splsicox_res$opt.penalty
#> As we are working with a multiblock approach with 2 blocks, a maximum of 5 components can be used.

sb.splsicox_model
#> The method used is SB.sPLS-ICOX.
#> Survival model:
#>                        coef exp(coef)    se(coef)  robust se         z
#> comp_1_mirna     0.08136291  1.084765 0.023122035 0.02795461 2.9105362
#> comp_2_mirna     0.02298943  1.023256 0.008282689 0.01137970 2.0202130
#> comp_1_proteomic 0.04192283  1.042814 0.282275072 0.33317483 0.1258283
#> comp_2_proteomic 0.72828143  2.071517 0.381966688 0.37589925 1.9374378
#>                     Pr(>|z|)
#> comp_1_mirna     0.003608091
#> comp_2_mirna     0.043361296
#> comp_1_proteomic 0.899867825
#> comp_2_proteomic 0.052691844

sb.splsicox_model <- mb.coxmos(method = "sb.splsicox",
                               X = X_train, Y = Y_train,
                               n.comp = 2, #cv.sb.splsicox_res$opt.comp
                               penalty = 0.9, #cv.sb.splsicox_res$opt.penalty
                               remove_non_significant = TRUE)
#> As we are working with a multiblock approach with 2 blocks, a maximum of 5 components can be used.

sb.splsicox_model
#> The method used is SB.sPLS-ICOX.
#> A total of 1 variables have been removed due to non-significance filter inside cox model.
#> Survival model:
#>                        coef exp(coef)    se(coef)  robust se        z
#> comp_1_mirna     0.08401369  1.087644 0.014683553 0.01827697 4.596696
#> comp_2_mirna     0.02253909  1.022795 0.007657962 0.01017298 2.215583
#> comp_2_proteomic 0.72600739  2.066812 0.381060467 0.36841663 1.970615
#>                      Pr(>|z|)
#> comp_1_mirna     4.292437e-06
#> comp_2_mirna     2.672004e-02
#> comp_2_proteomic 4.876791e-02

cv.isb.splsicox_res <- cv.mb.coxmos(method = "isb.splsicox", 
                                    X = X_train, Y = Y_train,
                                    max.ncomp = 2, penalty.list = c(0.5,0.9),
                                    n_run = 1, k_folds = 5,
                                    remove_non_significant = TRUE)

cv.isb.splsicox_res

cv.isb.splsicox_res$list_cv_spls_models$mirna$plot_AUC
cv.isb.splsicox_res$list_cv_spls_models$proteomic$plot_AUC

isb.splsicox_model <- mb.coxmos(method = "isb.splsicox",
                                X = X_train, Y = Y_train, cv.isb = cv.isb.splsicox_res,
                                remove_non_significant = FALSE)

isb.splsicox_model

cv.sb.splsdrcox_res <- cv.mb.coxmos(method = "sb.splsdrcox", 
                                    X = X_train, Y = Y_train,
                                    max.ncomp = 2, vector = NULL,
                                    n_run = 1, k_folds = 5)

cv.sb.splsdrcox_res

sb.splsdrcox_model <- mb.coxmos(method = "sb.splsdrcox", 
                                X = X_train, Y = Y_train, 
                                n.comp = 2, #cv.sb.splsdrcox_res$opt.comp, 
                                vector = list("mirna" = 161, "proteomic" = 185), #cv.sb.splsdrcox_res$opt.nvar,
                                remove_non_significant = T)
#> As we are working with a multiblock approach with 2 blocks, a maximum of 5 components can be used.

sb.splsdrcox_model
#> The method used is SB.sPLS-DRCOX-Dynamic.
#> Survival model:
#>                          coef exp(coef)     se(coef)    robust se        z
#> comp_2_mirna     1.026886e-06  1.000001 5.316507e-07 4.398692e-07 2.334525
#> comp_1_proteomic 7.072923e-01  2.028491 1.031619e-01 9.865372e-02 7.169444
#> comp_2_proteomic 2.752298e-01  1.316833 6.880221e-02 6.227886e-02 4.419313
#>                      Pr(>|z|)
#> comp_2_mirna     1.956824e-02
#> comp_1_proteomic 7.530320e-13
#> comp_2_proteomic 9.901509e-06

cv.isb.splsdrcox_res <- cv.mb.coxmos(method = "isb.splsdrcox", 
                                     X = X_train, Y = Y_train,
                                     max.ncomp = 2, vector = NULL,
                                     n_run = 1, k_folds = 5)

cv.isb.splsdrcox_res

cv.isb.splsdrcox_res$list_cv_spls_models$mirna$plot_AUC
cv.isb.splsdrcox_res$list_cv_spls_models$proteomic$plot_AUC

isb.splsdrcox_model <- mb.coxmos(method = "isb.splsdrcox", 
                                 X = X_train, Y = Y_train, cv.isb = cv.isb.splsdrcox_res,
                                 remove_non_significant = TRUE)

isb.splsdrcox_model

cv.sb.splsdacox_res <- cv.mb.coxmos(method = "sb.splsdacox", 
                                    X = X_train, Y = Y_train,
                                    max.ncomp = 2, vector = NULL,
                                    n_run = 1, k_folds = 5)

cv.sb.splsdacox_res

sb.splsdacox_model <- mb.coxmos(method = "sb.splsdacox", 
                                X = X_train, Y = Y_train, 
                                n.comp = 1, #cv.sb.splsdacox_res$opt.comp, 
                                vector = list("mirna" = 321, "proteomic" = 369), #cv.sb.splsdacox_res$opt.nvar,
                                remove_non_significant = T)
#> As we are working with a multiblock approach with 2 blocks, a maximum of 5 components can be used.

sb.splsdacox_model
#> The method used is SB.sPLS-DACOX-Dynamic.
#> A total of 1 variables have been removed due to non-significance filter inside cox model.
#> Survival model:
#>                       coef exp(coef)  se(coef)  robust se        z     Pr(>|z|)
#> comp_1_proteomic 0.4428919  1.557204 0.1065671 0.09343293 4.740212 2.134948e-06

cv.isb.splsdacox_res <- cv.mb.coxmos(method = "isb.splsdacox", 
                                     X = X_train, Y = Y_train,
                                     max.ncomp = 2, vector = NULL,
                                     n_run = 1, k_folds = 5)

cv.isb.splsdacox_res

cv.isb.splsdacox_res$list_cv_spls_models$mirna$plot_AUC
cv.isb.splsdacox_res$list_cv_spls_models$proteomic$plot_AUC

isb.splsdacox_model <- mb.coxmos(method = "isb.splsdacox", 
                                 X = X_train, Y = Y_train, cv.isb = cv.isb.splsdacox_res,
                                 remove_non_significant = TRUE)

isb.splsdacox_model

cv.mb.splsdrcox_res <- cv.mb.coxmos(method = "mb.splsdrcox", 
                                    X = X_train, Y = Y_train, 
                                    max.ncomp = 2, vector = NULL,
                                    MIN_NVAR = 10, MAX_NVAR = NULL, n.cut_points = 10, EVAL_METHOD = "AUC",
                                    n_run = 1, k_folds = 5)

cv.mb.splsdrcox_res

mb.splsdrcox_model <- mb.coxmos(method = "mb.splsdrcox", 
                                X = X_train, Y = Y_train, 
                                n.comp = 1, #cv.mb.splsdrcox_res$opt.comp,
                                vector = list("mirna" = 10, "proteomic" = 369)) #cv.mb.splsdrcox_res$opt.nvar
#> As we are working with a multiblock approach with 2 blocks, a maximum of 5 components can be used.
#> Design matrix has changed to include Y; each block will be
#>             linked to Y.
mb.splsdrcox_model
#> The method used is MB.sPLS-DRCOX-Dynamic.
#> Survival model:
#>                           coef exp(coef)     se(coef)    robust se          z
#> comp_1_mirna      2.336609e-07 1.0000002 3.622335e-07 3.462225e-07  0.6748866
#> comp_1_proteomic -5.074908e-02 0.9505171 5.972778e-02 6.766230e-02 -0.7500348
#>                   Pr(>|z|)
#> comp_1_mirna     0.4997478
#> comp_1_proteomic 0.4532338

cv.mb.splsdacox_res <- cv.mb.coxmos(method = "mb.splsdacox", 
                                    X = X_train, Y = Y_train, 
                                    max.ncomp = 2, vector = NULL,
                                    n_run = 1, k_folds = 5)

cv.mb.splsdacox_res

mb.splsdacox_model <- mb.coxmos(method = "mb.splsdacox", 
                                X = X_train, Y = Y_train, 
                                n.comp = 2, #cv.mb.splsdacox_res$opt.comp,
                                vector = list("mirna" = 1, "proteomic" = 93)) #cv.mb.splsdacox_res$opt.nvar
#> As we are working with a multiblock approach with 2 blocks, a maximum of 5 components can be used.
#> Design matrix has changed to include Y; each block will be
#>             linked to Y.

mb.splsdacox_model
#> The method used is MB.sPLS-DACOX-Dynamic.
#> Survival model:
#>                           coef exp(coef)     se(coef)    robust se          z
#> comp_1_mirna      2.219494e-07 1.0000002 3.652928e-07 3.802056e-07  0.5837614
#> comp_2_mirna      3.117680e-07 1.0000003 3.664796e-07 3.303379e-07  0.9437851
#> comp_1_proteomic -5.026128e-02 0.9509809 6.575603e-02 7.353506e-02 -0.6835009
#> comp_2_proteomic  2.382137e-02 1.0241074 5.125087e-02 4.843720e-02  0.4917991
#>                   Pr(>|z|)
#> comp_1_mirna     0.5593808
#> comp_2_mirna     0.3452795
#> comp_1_proteomic 0.4942904
#> comp_2_proteomic 0.6228614

Survival Models’ Comparison

Next, we will analyze the results obtained from the multiple models to see which one provides the best predictions based on our data. To do this, we will use the test set that has not been used to train any model. However, in case that test data are not available, the train data can also be used.

Initially, we will compare the results for each of the methods according to the evaluator we desire. Additionaly, we must provide a list of the different models as well as the X and Y evaluation set.

When evaluating survival model results, we must indicate at which temporal points we want to perform the evaluation. As we already specified a NULL value for the times parameter in the cross-validation, we are going to let the algorithm compute them again.

lst_models <- list("SB.sPLS-ICOX" = sb.splsicox_model,
                   #"iSB.sPLS-ICOX" = isb.splsicox_model,
                   "SB.sPLS-DRCOX-Dynamic" = sb.splsdrcox_model,
                   #"iSB.sPLS-DRCOX-Dynamic" = isb.splsdrcox_model,
                   "SB.sPLS-DACOX-Dynamic" = sb.splsdacox_model,
                   #"iSB.sPLS-DACOX-Dynamic" = isb.splsdacox_model,
                   "MB.sPLS-DRCOX" = mb.splsdrcox_model,
                   "MB.sPLS-DACOX" = mb.splsdacox_model)

eval_results <- eval_Coxmos_models(lst_models = lst_models,
                                  X_test = X_test, Y_test = Y_test, 
                                  times = NULL)

C:1BfP43083d9d5ab9-MO-pipeline.R

We can print the results obtained in the console where we can see, for each of the selected methods, the training time and the time it took to be evaluated, as well as their AIC, C-Index and AUC metrics and at which time points it was evaluated.

eval_results
#> Evaluation performed for methods: SB.sPLS-ICOX, SB.sPLS-DRCOX-Dynamic, SB.sPLS-DACOX-Dynamic, MB.sPLS-DRCOX, MB.sPLS-DACOX.
#> SB.sPLS-ICOX:
#>  training.time: 0.1713
#>  evaluating.time: 0.0088
#>  AIC: 301.8495
#>  C.Index: 0.8538
#>  time: 377, 554.786, 732.572, 910.358, 1088.143, 1265.929, 1443.715, 1621.5, 1799.286, 1977.072, 2154.858, 2332.643, 2510.429, 2688.215, 2866
#>  AUC: 0.62239
#>  brier_time: 116, 186, 322, 377, 385, 454, 477, 489, 506, 518, 522, 606, 614, 616, 678, 703, 723, 747, 759, 825, 847, 904, 1015, 1048, 1150, 1174, 1189, 1233, 1275, 1324, 1508, 1528, 1611, 1694, 1742, 1793, 1935, 1972, 2632, 2854, 2866, 3001, 3472, 3669
#>  I. Brier: 0.2003
#> 
#> SB.sPLS-DRCOX-Dynamic:
#>  training.time: 0.0361
#>  evaluating.time: 0.0086
#>  AIC: 318.2304
#>  C.Index: 0.817
#>  time: 377, 554.786, 732.572, 910.358, 1088.143, 1265.929, 1443.715, 1621.5, 1799.286, 1977.072, 2154.858, 2332.643, 2510.429, 2688.215, 2866
#>  AUC: 0.57529
#>  brier_time: 116, 186, 322, 377, 385, 454, 477, 489, 506, 518, 522, 606, 614, 616, 678, 703, 723, 747, 759, 825, 847, 904, 1015, 1048, 1150, 1174, 1189, 1233, 1275, 1324, 1508, 1528, 1611, 1694, 1742, 1793, 1935, 1972, 2632, 2854, 2866, 3001, 3472, 3669
#>  I. Brier: 0.19103
#> 
#> SB.sPLS-DACOX-Dynamic:
#>  training.time: 0.0368
#>  evaluating.time: 0.0087
#>  AIC: 351.6075
#>  C.Index: 0.6749
#>  time: 377, 554.786, 732.572, 910.358, 1088.143, 1265.929, 1443.715, 1621.5, 1799.286, 1977.072, 2154.858, 2332.643, 2510.429, 2688.215, 2866
#>  AUC: 0.5214
#>  brier_time: 116, 186, 322, 377, 385, 454, 477, 489, 506, 518, 522, 606, 614, 616, 678, 703, 723, 747, 759, 825, 847, 904, 1015, 1048, 1150, 1174, 1189, 1233, 1275, 1324, 1508, 1528, 1611, 1694, 1742, 1793, 1935, 1972, 2632, 2854, 2866, 3001, 3472, 3669
#>  I. Brier: 0.20821
#> 
#> MB.sPLS-DRCOX:
#>  training.time: 0.0262
#>  evaluating.time: 0.0078
#>  AIC: 371.5634
#>  C.Index: 0.5335
#>  time: 377, 554.786, 732.572, 910.358, 1088.143, 1265.929, 1443.715, 1621.5, 1799.286, 1977.072, 2154.858, 2332.643, 2510.429, 2688.215, 2866
#>  AUC: 0.63332
#>  brier_time: 116, 186, 322, 377, 385, 454, 477, 489, 506, 518, 522, 606, 614, 616, 678, 703, 723, 747, 759, 825, 847, 904, 1015, 1048, 1150, 1174, 1189, 1233, 1275, 1324, 1508, 1528, 1611, 1694, 1742, 1793, 1935, 1972, 2632, 2854, 2866, 3001, 3472, 3669
#>  I. Brier: 0.17193
#> 
#> MB.sPLS-DACOX:
#>  training.time: 0.0337
#>  evaluating.time: 0.0138
#>  AIC: 373.6803
#>  C.Index: 0.5287
#>  time: 377, 554.786, 732.572, 910.358, 1088.143, 1265.929, 1443.715, 1621.5, 1799.286, 1977.072, 2154.858, 2332.643, 2510.429, 2688.215, 2866
#>  AUC: 0.61615
#>  brier_time: 116, 186, 322, 377, 385, 454, 477, 489, 506, 518, 522, 606, 614, 616, 678, 703, 723, 747, 759, 825, 847, 904, 1015, 1048, 1150, 1174, 1189, 1233, 1275, 1324, 1508, 1528, 1611, 1694, 1742, 1793, 1935, 1972, 2632, 2854, 2866, 3001, 3472, 3669
#>  I. Brier: 0.17102
#> 

C:1BfP43083d9d5ab9-MO-pipeline.R

However, we can also obtain graphical results where we can compare each method over time, as well as their average scores using the function plot_evaluation() or plot_evaluation.list() if multiple evaluators have been tested. The user can choose to plot the AUC for time prediction points or the Brier Score.

lst_eval_results_auc <- plot_evaluation(eval_results, evaluation = "AUC", pred.attr = "mean")
lst_eval_results_brier <- plot_evaluation(eval_results, evaluation = "IBS", pred.attr = "mean")

C:1BfP43083d9d5ab9-MO-pipeline.R

After generating the evaluation plot with Coxmos, an R object is returned containing two sublists. The first sublist contains time-dependent evaluation results for each method, along with a variant that includes the average performance values. The second sublist enables comparison of the mean performance across methods using statistical tests such as the T-test, Wilcoxon test, ANOVA, or Kruskal–Wallis test.

lst_eval_results_auc$lst_plots$lineplot.mean

lst_eval_results_auc$lst_plot_comparisons$anova

C:1BfP43083d9d5ab9-MO-pipeline.R

lst_models_time <- list(#cv.sb.splsicox_res,
                        sb.splsicox_model,
                        #isb.splsicox_model,
                        #cv.sb.splsdrcox_res,
                        sb.splsdrcox_model,
                        #isb.splsdrcox_model,
                        #cv.sb.splsdacox_res,
                        sb.splsdacox_model,
                        #isb.splsdacox_model,
                        #cv.mb.splsdrcox_res,
                        mb.splsdrcox_model,
                        #cv.mb.splsdrcox_res,
                        mb.splsdacox_model,
                        eval_results)

ggp_time <- plot_time.list(lst_models_time, txt.x.angle = 90)

ggp_time

Evaluating the Proportional Hazards Assumption

A critical diagnostic step when using Cox models is evaluating whether the Proportional Hazards (PH) assumption holds for each predictor or component. This assumption underpins the validity of Cox regression results, and violations can lead to misleading inferences.

So the function plot_proportionalHazard() tries to answer the question: “Does my Cox model violate the fundamental proportional hazards assumption, and if so, which specific variables or components show time-dependent effects that could invalidate my results?”

The plot_proportionalHazard() function provides a visual and statistical assessment of this assumption. It leverages Schoenfeld residuals to test whether the hazard ratio associated with each variable remains constant over time. If patterns in the Schoenfeld residuals are systematic or show statistically significant deviations, it indicates that the effect of a variable changes over time during the follow-up period.

This is particularly important when working with dimension-reduced components, such as those generated from sPLS models. Because these components aggregate the effects of multiple variables, subtle time-dependent behavior from individual features may be masked, and only detectable through residual diagnostics.

The function can be applied to a single model using plot_proportionalHazard(), or to a list of models with plot_proportionalHazard.list(). The output plot shows, for each component or variable, the residual pattern and associated p-value from the proportional hazards test.

lst_ph_ggplot <- plot_proportionalHazard(lst_models$`SB.sPLS-ICOX`)

C:1BfP43083d9d5ab9-MO-pipeline.R

Variables or components with a significant p-value (typically p < 0.05) indicate a violation of the PH assumption.

lst_ph_ggplot

C:1BfP43083d9d5ab9-MO-pipeline.R

This visualization helps determine whether model refinement is needed. For instance, if the assumption is violated, one might:

• Introduce time-dependent covariates.
• Apply stratified models.
• Use alternative modeling strategies better suited to non-proportional effects.

Forest Plots for Cox Model Interpretation

The plot_forest() function provides a concise and interpretable summary of the effects estimated by a Cox model. It visualizes Hazard Ratios (HRs) and their confidence intervals for each predictor or component, allowing for rapid identification of statistically significant associations and the directionality of their effects.

Forest plots are especially useful in models derived from Cox, but plot_forest() function was updated to work with all Coxmos approaches, where each component represents a latent combination of variables. The function automatically handles these structures, labeling components appropriately and ensuring that effect sizes can be meaningfully compared across components or even between models.

For each variable or component, the plot displays:

• The hazard ratio (HR), quantifying the strength and direction of association with the event.
• Confidence intervals, which convey the precision of the estimate.
• P-values, to assess statistical significance (typically, p < 0.05 indicates a significant effect).

Interpretation is straightforward: components with HR > 1 are associated with increased risk (right-sided bars), while those with HR < 1 are associated with reduced risk (left-sided bars). If the confidence interval crosses HR = 1, the effect is considered non-significant.

This visualization bridges statistical output and clinical interpretation, helping to prioritize features or components that have both statistical and biological relevance.

lst_forest_plot <- plot_forest(lst_models$`SB.sPLS-ICOX`)

C:1BfP43083d9d5ab9-MO-pipeline.R

lst_forest_plot

C:1BfP43083d9d5ab9-MO-pipeline.R

Predicted Value Distribution by Event Status

Another type of visualization implemented for all supported models, whether classical or sPLS-based, is the distribution of predicted values by event status. These plots are useful for assessing how well the model separates patients who experienced the event from those who did not, based on the model’s output.

The function plot_cox.event() (or plot_cox.event.list() for multiple models) enables the generation of density and histogram plots using predictions derived from the fitted Cox model. Internally, the function leverages the prediction types provided by the coxph function in the survival package. The main types include:

• lp (linear predictors): the log-risk scores for each observation based on the model’s coefficients. These reflect the relative risk associated with an individual’s covariate profile.
• risk: the relative risk of experiencing the event, obtained by exponentiating the linear predictor.
• expected: the expected number of events for each subject over time, given their covariate profile.
• terms: the contribution of each variable to the linear predictor, shown separately.
• survival: the estimated probability of survival at a given time point.

By selecting the appropriate prediction type, the function produces plots that show the distribution of predicted values stratified by event status. These plots allow for visual evaluation of the model’s discriminative ability, indicate that the model is effectively distinguishing between censored and event observations.

density.plots.lp <- plot_cox.event(lst_models$`SB.sPLS-ICOX`, type = "lp")

C:1BfP43083d9d5ab9-MO-pipeline.R

density.plots.lp$plot.density

density.plots.lp$plot.histogram

C:1BfP43083d9d5ab9-MO-pipeline.R

Variable or Component Contributions in Coxmos Models

How much do my components (SB/MB.sPLS-COX) contribute to the full model?

Understanding the internal structure of sPLS-COX models is essential for translating their predictive power into biological insight. The eval_Coxmos_model_per_variable() function enables an evaluation of how individual variables or latent components contribute to model performance.

A central goal of this analysis is to assess component-level predictive performance, both in training and test datasets. The function decomposes the model’s AUC by component, allowing users to determine which components carry the most prognostic information. Comparing individual component AUCs against the full model’s linear predictor helps identify whether some components are particularly dominant or redundant.

From a validation standpoint, the function supports the identification of overfitting risk. Components that perform well in training data but drop in test performance may lack generalizability. Conversely, components that consistently perform across datasets represent robust predictors worthy of further investigation.

The eval_Coxmos_model_per_variable() function provides:

• AUC decomposition by component, for both training and test sets
• Visual comparison between individual component performance and the full linear predictor
• Quantitative indicators of overfitting through cross-dataset validation

In terms of interpretation, components with high AUC values can be considered the primary drivers of the model. If an individual component outperforms the full model (linear predictor), it may represent potential overfitting, and should be considered in model refinement.

variable_auc_results <- eval_Coxmos_model_per_variable(model = lst_models$`SB.sPLS-ICOX`, 
                                                      X_test = lst_models$`SB.sPLS-ICOX`$X_input, 
                                                      Y_test = lst_models$`SB.sPLS-ICOX`$Y_input)

variable_auc_plot_train <- plot_evaluation(variable_auc_results, evaluation = "AUC")

C:1BfP43083d9d5ab9-MO-pipeline.R

variable_auc_plot_train$lst_plots$lineplot.mean

C:1BfP43083d9d5ab9-MO-pipeline.R

Visualizing sPLS Models for Survival Analysis

The plot_sPLS_Coxmos() function provides a visualization framework for exploring sPLS components in the context of survival analysis. One of its capabilities is the visual detection of outliers, which can significantly impact model interpretation and performance.

Through score plots, users can visually inspect how samples are distributed across the latent component space. Samples that appear distant from the main cluster may indicate potential outliers — observations with unique profiles that could disproportionately influence the model. Identifying such samples early allows for more informed decisions about data quality, potential stratification, or exclusion.

In addition to outlier detection, the score plots also highlight sample clustering patterns. They help determine whether patients group naturally according to event status and whether component axes capture meaningful clinical variation. A clear separation between event groups supports the relevance of the extracted components.

Loading plots complement this view by showing the variables that contribute most to each component. They can reveal which features are driving sample positioning in the score space and whether any variables have excessive influence.

The biplot integrates both sample and variable information, allowing users to examine relationships between extreme samples and specific variables.

The plot_sPLS_Coxmos() function generates graphical representations of sPLS components from any Coxmos sPLS-based survival model. It supports three types of plots depending on the mode selected:

• mode = "scores": displays sample projections onto the latent components (score plot).
• mode = "loadings": shows variable contributions to the selected components (loading plot).
• mode = "biplot": combines both sample and variable information in a single view.

ggp_scores <- plot_sPLS_Coxmos(model = lst_models$`SB.sPLS-ICOX`,
                               comp = c(1,2), mode = "scores")

C:1BfP43083d9d5ab9-MO-pipeline.R

ggp_scores
#> $mirna

#> 
#> $proteomic

C:1BfP43083d9d5ab9-MO-pipeline.R

ggp_loadings <- plot_sPLS_Coxmos(model = lst_models$`SB.sPLS-ICOX`, 
                                 comp = c(1,2), mode = "loadings",
                                 top = 10)

C:1BfP43083d9d5ab9-MO-pipeline.R

ggp_loadings
#> $mirna

#> 
#> $proteomic

C:1BfP43083d9d5ab9-MO-pipeline.R

ggp_biplot <- plot_sPLS_Coxmos(model = lst_models$`SB.sPLS-ICOX`, 
                               comp = c(1,2), mode = "biplot",
                               top = 15,
                               only_top = T,
                               overlaps = 20)

C:1BfP43083d9d5ab9-MO-pipeline.R

ggp_biplot
#> $mirna

#> 
#> $proteomic

C:1BfP43083d9d5ab9-MO-pipeline.R

Interpreting original variables in sPLS Components: Pseudobeta Coefficients

Which original variables drive my sPLS model’s survival predictions, and what direction of effect (protective or risk) do they contribute to each component?

The plot_pseudobeta() function allows for a detailed inspection of how individual variables influence the components of a sPLS-based survival model. This visualization provides a transparent and biologically interpretable summary of variable-level contributions, capturing both the magnitude and direction of effect for each feature.

By decomposing each component into pseudobeta coefficients, it becomes possible to rank variables based on their impact on the linear predictor (LP) and to assess whether their effects are consistent across components. The directionality—whether a variable acts as a protective or risk factor—is visualized through the orientation of the bars, even when components aggregate multiple opposing effects.

This type of analysis is particularly valuable for biological interpretation, as it links abstract components back to measurable variables. It also reveals whether known biomarkers align with expected effects or whether new candidate variables emerge as strong contributors to survival risk.

The function includes several customizable options:

• onlySig = TRUE filters components based on statistical significance (by default at alpha = 0.05), reducing variable noise contribution and emphasizing robust effects.
• top defines the number of top variables to display (e.g., top = 20 for overview; top = NULL for full detail).
• The percentage of total LP explained by the displayed variables is included, providing quantitative context for their contribution to the model.

ggp.simulated_beta <- plot_pseudobeta(model = lst_models$`SB.sPLS-ICOX`, 
                                      error.bar = T, onlySig = F, alpha = 0.05, 
                                      zero.rm = T, auto.limits = T, top = 20,
                                      show_percentage = T, size_percentage = 2)
#> For iSB.sPLS-ICOX and SB.sPLS-ICOX model, pseudobetas are an approximation as predictions are obtained through a deflation process.

C:1BfP43083d9d5ab9-MO-pipeline.R

The iSB.sPLS-DRCOX model was computed using a total of 2 components. Although these components were classified as dangerous for the observations (based on coefficients greater than one), certain variables within the components may still have a protective effect, depending on their individual weights.

The following plot illustrates the pseudo-beta coefficient for the original variables in the iSB.sPLS-DRCOX model. As only the top 20 variables are shown, in some case a percentage of the total linear predictor total value could be shown. To view the complete model, all variables would need to be included in the plot by assigning the value NULL to the “top” parameter.

ggp.simulated_beta$plot
#> $mirna

#> 
#> $proteomic

C:1BfP43083d9d5ab9-MO-pipeline.R

In addition, for MB datasets, all omics are combined into a single plot. In this case, the relative pseudobeta per variable is shown. The user must take into account that each omic has a different survival beta, which influences the relative importance of each original variable. In this case, only proteomic variables are shown.

ggp.simulated_beta$mb_plot$plot

C:1BfP43083d9d5ab9-MO-pipeline.R

Kaplan-Meier Curves for Visualizing Survival Differences

Kaplan-Meier (KM) curves are a fundamental tool in survival analysis. They estimate the probability of survival over time and allow visual comparison between different patient groups. When used in conjunction with a risk prediction model, such as the Cox model, KM curves help assess whether the predicted risk groups truly differ in their survival outcomes. Typically, the survival probability is plotted against time, and differences between curves indicate the effectiveness of the model in stratifying risk.

In this context, the getAutoKM() and getAutoKM.list() functions provide an automated way to generate KM plots from models. These functions can be used to analyze the survival curves based on:

• The model’s linear predictor (type = "LP"),
• Specific sPLS components (type = "COMP"), or
• Original variables (type = "VAR").

LST_KM_RES_LP <- getAutoKM(type = "LP",
                           model = lst_models$`SB.sPLS-ICOX`)

LST_KM_RES_LP$LST_PLOTS$LP

LST_KM_RES_COMP <- getAutoKM(type = "COMP",
                             model = lst_models$`SB.sPLS-ICOX`,
                             comp = 1:2)

LST_KM_RES_COMP$LST_PLOTS$mirna$comp_1

LST_KM_RES_COMP$LST_PLOTS$proteomic$comp_2

LST_KM_RES_VAR <- getAutoKM(type = "VAR",
                            model = lst_models$`SB.sPLS-ICOX`,
                            top = 10,
                            ori_data = T, #original data selected
                            only_sig = T, alpha = 0.05)

LST_KM_RES_VAR$LST_PLOTS$mirna$hsa.minus.miR.minus.491.minus.3p

LST_KM_RES_VAR$LST_PLOTS$proteomic$var_5080

Single Patient Analysis

To illustrate this functionality, we select a censored observation from the test dataset:

new_pat <- X_test
new_pat$mirna <- new_pat$mirna[1,,drop=F]
new_pat$proteomic <- new_pat$proteomic[1,,drop=F]

C:1BfP43083d9d5ab9-MO-pipeline.R

This observation corresponds to a censored patient with the last follow-up recorded at time :

knitr::kable(Y_test[rownames(new_pat$mirna),])
#> Warning: 'xfun::attr()' is deprecated.
#> Use 'xfun::attr2()' instead.
#> See help("Deprecated")

#> Warning: 'xfun::attr()' is deprecated.
#> Use 'xfun::attr2()' instead.
#> See help("Deprecated")

C:1BfP43083d9d5ab9-MO-pipeline.R

pat_density <- plot_observation.eventDensity(observation = new_pat,
                                             model = lst_models$`SB.sPLS-ICOX`,
                                             type = "lp")

pat_density

pat_histogram <- plot_observation.eventHistogram(observation = new_pat, 
                                                 model = lst_models$`SB.sPLS-ICOX`, 
                                                 type = "lp")

pat_histogram

ggp.simulated_beta_newObs <- plot_observation.pseudobeta(model = lst_models$`SB.sPLS-ICOX`,
                                                         observation = new_pat,
                                                         error.bar = T, onlySig = T, alpha = 0.05,
                                                         zero.rm = T, auto.limits = T, show.betas = T, top = 20,
                                                         txt.x.angle = 90)
#> For iSB.sPLS-ICOX and SB.sPLS-ICOX model, pseudobetas are an approximation as predictions are obtained through a deflation process.

ggp.simulated_beta_newObs$plot
#> $mirna

#> 
#> $proteomic

Multiple new observation comparison

variable_auc_results_test <- eval_Coxmos_model_per_variable(model = lst_models$`SB.sPLS-ICOX`, 
                                                       X_test = X_test, 
                                                       Y_test = Y_test)

variable_auc_plot_test <- plot_evaluation(variable_auc_results_test, evaluation = "AUC")

variable_auc_plot_test$lst_plots$lineplot.mean

lst_observations <- list()
for(b in names(X_test)){
  lst_observations[[b]] <- X_test[[b]][1:5,]
}

knitr::kable(Y_test[rownames(lst_observations$mirna),])
#> Warning: 'xfun::attr()' is deprecated.
#> Use 'xfun::attr2()' instead.
#> See help("Deprecated")

#> Warning: 'xfun::attr()' is deprecated.
#> Use 'xfun::attr2()' instead.
#> See help("Deprecated")

lst_cox.comparison <- plot_multipleObservations.LP(model = lst_models$`SB.sPLS-ICOX`,
                                                   observations = lst_observations,
                                                   top = 10)
#> For iSB.sPLS-ICOX and SB.sPLS-ICOX model, pseudobetas are an approximation as predictions are obtained through a deflation process.

lst_cox.comparison$plot
#> $mirna

#> 
#> $proteomic

lst_cutoff <- getCutoffAutoKM(LST_KM_RES_LP)
LST_KM_TEST_LP <- getTestKM(model = lst_models$`SB.sPLS-ICOX`, 
                            X_test = X_test, Y_test = Y_test, 
                            type = "LP",
                            BREAKTIME = NULL, n.breaks = 20,
                            cutoff = lst_cutoff)

LST_KM_TEST_LP

lst_cutoff <- getCutoffAutoKM(LST_KM_RES_COMP)
LST_KM_TEST_COMP <- getTestKM(model = lst_models$`SB.sPLS-ICOX`, 
                              X_test = X_test, Y_test = Y_test, 
                              type = "COMP",
                              BREAKTIME = NULL, n.breaks = 20,
                              cutoff = lst_cutoff)

LST_KM_TEST_COMP$comp_1_mirna

LST_KM_TEST_COMP$comp_2_proteomic

lst_cutoff <- getCutoffAutoKM(LST_KM_RES_VAR)
LST_KM_TEST_VAR <- getTestKM(model = lst_models$`SB.sPLS-ICOX`, 
                             X_test = X_test, Y_test = Y_test, 
                             type = "VAR", ori_data = T,
                             BREAKTIME = NULL, n.breaks = 20,
                             cutoff = lst_cutoff)

LST_KM_TEST_VAR$mirna$hsa.minus.miR.minus.491.minus.3p

LST_KM_TEST_VAR$proteomic$var_5080