Contents

1 Pancreatic Cancer Overall Survival Predictor

As an example of the utility of the PDATK package, we provide code replicating the analysis published in Sandhu et al. (2019). While the code presented here is run on a subset of the original data to ensure that the PDATK installation size is not too large, the full data from that study can is available via the MetaGxPancreas Bioconductor data package.

data(sampleCohortList)
sampleCohortList
## CohortList of length 11
## names(11): ICGCMICRO ICGCSEQ PCSI TCGA KIRBY UNC CHEN COLLISON ZHANG OUH WINTER

1.1 Split Training and Validation Data

To get started using PDATK, place each of your patient cohorts into SurvivalExperiment objects and then assemble those into a master CohortList, which holds the training and validation data for use with the various SurvivalModels in this package.

commonGenes <- findCommonGenes(sampleCohortList)
# Subsets all list items, with subset for specifying rows and select for
# specifying columns
cohortList <- subset(sampleCohortList, subset=commonGenes)

ICGCcohortList <- cohortList[grepl('ICGC', names(cohortList), ignore.case=TRUE)]
validationCohortList <- cohortList[!grepl('icgc', names(cohortList),
    ignore.case=TRUE)]

Since we are interested in predicting survival, it is necessary to remove patients with insufficient data to be useful. In general, we want to remove patients who did not have an event in our period of interest. As such we remove samples who dropped out of a study, but did not pass away before the first year.

validationCohortList <- dropNotCensored(validationCohortList)
ICGCcohortList <- dropNotCensored(ICGCcohortList)

We have now split our patient cohorts into training and validation data. For this analysis we will be training using the ICGC cohorts, which includes one cohort with RNA micro-array data and another with RNA sequencing data. When using multiple cohorts to train a model, it is required that those cohorts share samples. As a result we will take as training data all patients shared between the two cohorts and leave the remainder of patients as part of our validationData.

# find common samples between our training cohorts in a cohort list
commonSamples <- findCommonSamples(ICGCcohortList)

# split into shared samples for training, the rest for testing
ICGCtrainCohorts <- subset(ICGCcohortList, select=commonSamples)
ICGCtestCohorts <- subset(ICGCcohortList, select=commonSamples, invert=TRUE)

# merge our training cohort test data into the rest of the validation data
validationCohortList <- c(ICGCtestCohorts, validationCohortList)

# drop ICGCSEQ from the validation data, because it only has 7 patients
validationCohortList <- 
    validationCohortList[names(validationCohortList) != 'ICGCSEQ']

1.2 Setup A PCOSP Model Object

We now have patient molecular data, annotated with the number of days survived since treatment and the survival status and are ready to apply a SurvivalModel to this data. In this example, we are applying a Pancreatic Cancer Overall Survival Model, as described in . This class uses the switchBox package to create an ensemble of binary classifiers, whos votes are then tallied into a PCOSP score. A PCOSP score is simply the proportion of models predicting good survival out of the total number of models in the ensemble.

set.seed(1987)
PCOSPmodel <- PCOSP(ICGCtrainCohorts, minDaysSurvived=365, randomSeed=1987)

# view the model parameters; these make your model run reproducible
metadata(PCOSPmodel)$modelParams
## $randomSeed
## [1] 1987
## 
## $RNGkind
## [1] "Mersenne-Twister" "Inversion"        "Rejection"       
## 
## $minDaysSurvived
## [1] 365

1.3 Training a PCOSP Model

To simplify working with different SurvivalModel sub-classes, we have implemented a standard work-flow that is valid for all SurvivalModels. This involves first training the model, then using it to predict risk/risk-classes for a set of validation cohorts and finally assessing performance on the validation data.

To train a model, the trainModel method is used. This function abstracts away the implementation of model training, allowing end-users to focus on applying the SurvivalModel to make predictions without a need to understand the model internals. We hope this will make the package useful for those unfamiliar or uninterested in the details of survival prediction methods.

For training a PCOSP model there are two parameters. First, numModels is the number of models to train for use in the ensemble classifier to predict PCOSP scores. To keep computation brief, we are only training 25 models. However, it is recommended to use a minimum of 1000 for real world applications. The second parameter is minAccuracy, which is the minimum model accuracy for a trained model to included in the final model ensemble. Paradoxically, increasing this too high can actually decrease the overall performance of the PCOSP model. We recommend 0.6 as a sweet spot between random chance and over-fitting but encourage experimentation to see what works best with your data.

trainedPCOSPmodel <- trainModel(PCOSPmodel, numModels=15, minAccuracy=0.6)

metadata(trainedPCOSPmodel)$modelParams
## $randomSeed
## [1] 1987
## 
## $RNGkind
## [1] "Mersenne-Twister" "Inversion"        "Rejection"       
## 
## $minDaysSurvived
## [1] 365
## 
## $numModels
## [1] 15
## 
## $minAccuracy
## [1] 0.6

We can see that after training, the additional model parameters are added to the modelParams item in the model metadata. The goal is to ensure that your model training, prediction and validation are fully reproducible by capturing the parameters relevant to a specific model.

1.4 Risk Prediction with a PCOSP Model

After training, a model can now be used with new data to make risk predictions and classify samples into ‘good’ or ‘bad’ survival groups. To do this, the standard predictClasses method is used. Similar to trainData, we have abstracted away the implementation details to provide users with a simple, consistent interface for using SurvivalModel sub-classes to make patient risk predictions.

PCOSPpredValCohorts <- predictClasses(validationCohortList,
    model=trainedPCOSPmodel)

The returned CohortList object now indicates that each of the cohorts have predictions. This information is available in the elementMetadata slot of the cohort list and can be accessed with the mcols function from S4Vectors.

mcols(PCOSPpredValCohorts)
## DataFrame with 10 rows and 2 columns
##             mDataType hasPredictions
##           <character>      <logical>
## ICGCMICRO   rna_micro           TRUE
## PCSI          rna_seq           TRUE
## TCGA          rna_seq           TRUE
## KIRBY         rna_seq           TRUE
## UNC         rna_micro           TRUE
## CHEN        rna_micro           TRUE
## COLLISON    rna_micro           TRUE
## ZHANG       rna_micro           TRUE
## OUH         rna_micro           TRUE
## WINTER      rna_micro           TRUE

Predicting risk with a specific model adds a corresponding metadata column to the object colData. In the case of a PCOSP model, the new column is called PCOSP_prob_good and represents the proportion of models in the ensemble which predicted good survival for a given sample.

knitr::kable(head(colData(PCOSPpredValCohorts[[1]])))
unique_patient_ID grade sex age T N M sample_type sample_name survival_time event_occurred prognosis PCOSP_prob_good
ICGC_0001 ICGC_0001 G1 M 59 T2 N0 M0 tumour ICGC_0001 522 1 good 0.6666667
ICGC_0002 ICGC_0002 G2 F 77 T2 N1a MX tumour ICGC_0002 2848 1 good 0.4666667
ICGC_0003 ICGC_0003 G2 F 58 T3 N1a MX tumour ICGC_0003 1778 0 good 0.9333333
ICGC_0004 ICGC_0004 G2 F 78 T2 N0 MX tumour ICGC_0004 1874 1 good 1.0000000
ICGC_0005 ICGC_0005 G3 M 63 T3 N1b MX tumour ICGC_0005 641 1 good 0.5333333
ICGC_0008 ICGC_0008 G2 M 72 T3 N1b MX tumour ICGC_0008 1209 1 good 0.8000000

Additionally, binary predictions of good or bad survival can be found in the PCOSPpredictions item of each SurvivalExperiments metadata. This contains the raw predictions from the model for each classifier in the ensemble, ordered by classifier accuracy. This data is not important for end users, but is used internally when calculating validation statistics for the model. For users wishing to classify samples rather than estimate risks, we recommend a PCOSP cut-off of >0.5 for good survival prognosis.

knitr::kable(metadata(PCOSPpredValCohorts[[1]])$PCOSPpredictions[1:5, 1:5])
ICGC_0001 ICGC_0002 ICGC_0003 ICGC_0004 ICGC_0005
rank1 bad bad good good good
rank2 good good good good bad
rank3 good good good good good
rank4 bad good good good good
rank5 good bad good good bad

1.5 Validating A PCOSP Model

The final step in the standard SurvivalModel work-flow is to compute model performance statistics for the model on the validation data. This can be accomplished using the validateModel method, which will add statistics to the validationStats slot of a SurvivalModel object and the data to the validationData slot.

validatedPCOSPmodel <- validateModel(trainedPCOSPmodel,
    valData=PCOSPpredValCohorts)
knitr::kable(head(validationStats(validatedPCOSPmodel)))
statistic estimate se lower upper p_value n cohort isSummary mDataType
AUC 0.7070000 0.0470000 0.6150000 0.7990000 0.0000142 158 ICGCMICRO FALSE rna_micro
log_D_index 0.5956475 0.1592665 0.4882238 0.7030711 0.0001668 158 ICGCMICRO FALSE rna_micro
concordance_index 0.6434057 0.0321350 0.5804223 0.7063892 0.0000081 158 ICGCMICRO FALSE rna_micro
AUC 0.6400000 0.0570000 0.5280000 0.7530000 0.0088634 107 PCSI FALSE rna_seq
log_D_index 0.4697159 0.1838308 0.3457239 0.5937078 0.0105421 107 PCSI FALSE rna_seq
concordance_index 0.6212825 0.0387126 0.5454073 0.6971577 0.0017309 107 PCSI FALSE rna_seq

Examining the data.table from the validationStats slot we can see that three model performance statistics have been calculated for all of the validation cohorts. Additionally, aggregate statistics have been calculated by molecular data type and for all cohorts combined. This table can be used to generate model performance plots. We have included several functions for examining model performance.

1.6 Plotting Model Performance

PCOSPdIndexForestPlot <- forestPlot(validatedPCOSPmodel, stat='log_D_index')
PCOSPdIndexForestPlot

PCOSPconcIndexForestPlot <- forestPlot(validatedPCOSPmodel, stat='concordance_index')
PCOSPconcIndexForestPlot

cohortROCplots <- plotROC(validatedPCOSPmodel, alpha=0.05)
## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.
cohortROCplots

2 Permutations Testing for a PCOSP Model

To compare the performance of a PCOSP model to random chance, we have included two model classes which permute either patient prognosis labels or the feature names. These models can be used to evaluate if a PCOSP model performs better than random chance.

2.1 Random Label Shuffling Model

The RLSModel class is a SurvivalModel using the same risk prediction algorithm as a PCOSP model, but randomizing the patient prognosis labels in each of the individual KTSP classifiers used in the classification ensemble. Given this random prognosis label shuffling, we expect the classification results for this model to be no better than random chance.

The work-flow for this model follows the standard SurvivalModel sub-class work-flow.

2.1.1 Construct the Model Object

# Merge to a single SurvivalExperiment
ICGCtrainCohorts <- merge(ICGCtrainCohorts[[1]], ICGCtrainCohorts[[2]], 
    cohortNames=names(ICGCtrainCohorts))
RLSmodel <- RLSModel(ICGCtrainCohorts, minDaysSurvived=365, randomSeed=1987)

2.1.2 Train the Model

trainedRLSmodel <- trainModel(RLSmodel, numModels=15)

2.1.3 Predict the Classes

RLSpredCohortList <- predictClasses(validationCohortList, model=trainedRLSmodel)
## Warning in FUN(X[[i]], ...): 
## [PDATK::predictClasses] Dropped samples with NA survival data!

## Warning in FUN(X[[i]], ...): 
## [PDATK::predictClasses] Dropped samples with NA survival data!

## Warning in FUN(X[[i]], ...): 
## [PDATK::predictClasses] Dropped samples with NA survival data!

2.1.4 Validate Model Performance

validatedRLSmodel <- validateModel(trainedRLSmodel, RLSpredCohortList)

2.1.5 Compare with a PCOSP Model

To compare the performance of a permuted model to that of a PCOSP model, we have included the densityPlotModelComparion method, which plots a density plot of model AUCs per molecular data type and overall. The dotted line represents the mean AUC of the PCOSP model. From this plot we can see that the PCOSP model performs significantly better than the random label shuffling model.

RLSmodelComparisonPlot <- densityPlotModelComparison(validatedRLSmodel,
    validatedPCOSPmodel, title='Random Label Shuffling vs PCOSP',
    mDataTypeLabels=c(rna_seq='Sequencing-based', rna_micro='Array-based',
        combined='Overall'))
RLSmodelComparisonPlot

2.2 Random Gene Assignment Model

A RandomGeneAssignmentModel (aliased as RGAModel for user convenience) is similar to a RLSModel except that the gene labels are randomized for each KTSP classifier in the ensemble. In this case, we also expect this model to perform no better than random chance.

2.2.1 Construct the Model Object

RGAmodel <- RGAModel(ICGCtrainCohorts, randomSeed=1987)

2.2.2 Train the Model

trainedRGAmodel <- trainModel(RGAmodel, numModels=15)

2.2.3 Predict the Classes

RGApredCohortList <- predictClasses(validationCohortList,
    model=trainedRGAmodel)
## Warning in FUN(X[[i]], ...): 
## [PDATK::predictClasses] Dropped samples with NA survival data!

## Warning in FUN(X[[i]], ...): 
## [PDATK::predictClasses] Dropped samples with NA survival data!

## Warning in FUN(X[[i]], ...): 
## [PDATK::predictClasses] Dropped samples with NA survival data!

2.2.4 Validate Model Performance

validatedRGAmodel <- validateModel(trainedRGAmodel, RGApredCohortList)

2.2.5 Compare RGAModel to PCOSP

The density plot for the RGAModel also shows that the PCOSP model does significantly better than random chance.

RGAmodelComparisonPlot <-  densityPlotModelComparison(validatedRGAmodel,
    validatedPCOSPmodel, title='Random Gene Assignment vs PCOSP',
    mDataTypeLabels=c(rna_seq='Sequencing-based', rna_micro='Array-based',
        combined='Overall'))
RGAmodelComparisonPlot

3 Pathway Analysis of a PCOSP Model

Confident that the PCOSP model is performing better than random chance at prediction patient survival, we can now begin to look into the features that are most relevant to these predictions. Once we have extracted the features, we will use the runGSEA method to evaluate which pathways these genes are representative of.

3.1 Get the Top Predictive Features

We can get the features which are most predictive from a SurvivalModel object using the getTopFeatures method. By default this retrieves the gene names from the top 10% of models in the SurvivalModel. Users can customize the top N models to extract genes from using the numModels parameter.

topFeatures <- getTopFeatures(validatedPCOSPmodel)
topFeatures
##  [1] "ATOX1"    "NAMPT"    "KRT6A"    "FCGRT"    "SERTAD4"  "ZNF792"  
##  [7] "KRT6C"    "BIRC3"    "PKIB"     "SSBP3"    "PPFIBP2"  "FBLIM1"  
## [13] "ZSCAN29"  "KRT15"    "UBE2C"    "C16orf74" "BLNK"     "MARK3"

3.2 Querying Genesets for Enriched Pathways

To perform pathway analysis, which is done internally using the piano::runGSAhyper function we first to pathway data to query against. We recommend using the msigdbr R package to fetch pathways of interest.

Because of the small number of genes included in the sample patient cohorts, this section will not find any enriched pathways and therefore this code is not run.

allHumanGeneSets <- msigdbr()
allGeneSets <- as.data.table(allHumanGeneSets)
geneSets <- allGeneSets[grepl('^GO.*|.*CANONICAL.*|^HALLMARK.*', gs_name),
    .(gene_symbol, gs_name)]
GSEAresultDT <- runGSEA(validatedPCOSPmodel, geneSets)

4 Clinical Model Comparison

Equipped with a risk prediction model performing better than random chance, the next pertinent question is: does it out perform simpler models? To answer this question we have included the ClinicalModel class, which leverages the glm function from the stats package to fit a generalized linear model based on a set of clinical variables in the patient metadata. To do this, we need to specify a model formula based on the column names available in the colData slot of our training data SurvivalExpeiment objects. All formula parameters must be valid column names in the colData of the training cohorts. The same patient metadata must be present in any validation cohorts used to make risk predictions.

4.1 Build the Model

We can see there are a number of clinical variables related to patient survived in the patient metadata. For our model, we will be using patient sex, age and tumour grade along with the TNM staging of the tumour.

knitr::kable(head(colData(ICGCtrainCohorts)))
unique_patient_ID grade sex age T N M sample_type sample_name survival_time event_occurred prognosis
ICGC_0006 ICGC_0006 G2 F 49 T1 N1b MX tumour ICGC_0006 1715 0 good
ICGC_0007 ICGC_0007 G2 F 74 T3 N1b MX tumour ICGC_0007 56 1 bad
ICGC_0009 ICGC_0009 G4 M 34 T3 N0 MX tumour ICGC_0009 399 1 good
ICGC_0020 ICGC_0020 G2 M 57 T3 N1b MX tumour ICGC_0020 1259 1 good
ICGC_0021 ICGC_0021 G3 M 60 T3 N1b MX tumour ICGC_0021 715 1 good
ICGC_0025 ICGC_0025 G3 M 69 T3 N1b MX tumour ICGC_0025 348 1 bad 
clinicalModel <- ClinicalModel(ICGCtrainCohorts,
    formula='prognosis ~ sex + age + T + N + M + grade',
    randomSeed=1987)

4.2 Train the Model

trainedClinicalModel <- trainModel(clinicalModel)

4.3 Predict the Classes

Clinical annotations are only available for a subset of our patient cohorts, thus we subset our cohort list to ensure the model works as expected. Variable columns with levels of a model parameter which are not present in the original model will be dropped automatically. To prevent this behavior, it is necessary to add any missing levels to the colData of the training data before training the model. The easiest way to achieve this is by converting the columns in question into factors and ensuring all levels in the training and validation data are set for those columns.

hasModelParamsCohortList <-
    PCOSPpredValCohorts[c('ICGCMICRO', 'TCGA', 'PCSI', 'OUH')]

clinicalPredCohortList <- predictClasses(hasModelParamsCohortList,
    model=trainedClinicalModel)
## Warning in .local(object, model, ...): 
## [PDATK:::.local] Rows 120, 155 have levels that are not in the model, skipping these rows...

4.4 Validate the Model

validatedClinicalModel <- validateModel(trainedClinicalModel,
    clinicalPredCohortList)

4.5 Visualize Comparison with PCOSP Model

To get a general idea of how the ClinicalModel performed relative to the PCOSP model, the barPlotModelComaprison can be used to show the . For this example, we will compare the AUC of the models in each of the validation cohorts. Other statistics in the validationStats slot can be used by changing the stat argument to the plotting function.

clinicalVsPCOSPbarPlot <- barPlotModelComparison(validatedClinicalModel,
    validatedPCOSPmodel, stat='AUC')
clinicalVsPCOSPbarPlot

To reduce the number of plotting functions and simplify meta-analysis of many models of different types, we have included the ModelComparison object. This object aggregates the validation statistics from two models. Plotting methods can then be dispatched on this class, greatly simplifying the process of comparing several SurivalModel sub-classes. You can also compare a model to an existing model comparison, and in this way built up a collection of model performance statistics which can be visualized in a forest plot to enable complex comparisons between many models.

Below, we use this feature to compare the PCOSP and ClinicalModels based on D index and concordance index, as calculated using the survcomp R package.

clinicalVsPCOSP <- compareModels(validatedClinicalModel, validatedPCOSPmodel)
clinVsPCOSPdIndexForestPlot <- forestPlot(clinicalVsPCOSP, stat='log_D_index')
clinVsPCOSPdIndexForestPlot

clinVsPCOSPconcIndexForestPlot <- forestPlot(clinicalVsPCOSP,
    stat='concordance_index')
clinVsPCOSPconcIndexForestPlot

5 Comparing PCOSP Models to Existing Published Classifiers

To get and idea of how our PCOSP model stacks up against other classifiers from the literature, we have included the GeneFuModel class. This SurvivalModel performs risk prediction using a set of genes and corresponding coefficients using the genefu::sig.score function. We have included data for three published classifiers from Chen et al. (2015), Birnbaum et al. (2017) and Haider et al. (2014).

5.1 Make the Models

Since there is no training data for the published classifiers, we create empty GeneFuModel objects, then assign the model predictors to the models slot of each respective object.

chenGeneFuModel <- GeneFuModel(randomSeed=1987)
birnbaumGeneFuModel <- GeneFuModel(randomSeed=1987)
haiderGeneFuModel <- GeneFuModel(randomSeed=1987)

For the Haider model, we were unable to get the genes and coefficients. However, the author provided the risk scores. As a result we need to do a bit of work to get the Haider GeneFuModel to work with the package function.

data(existingClassifierData)

models(chenGeneFuModel) <- SimpleList(list(chen=chen))
models(birnbaumGeneFuModel) <- SimpleList(list(birnbuam=birnbaum))
models(haiderGeneFuModel) <- SimpleList(list(haider=NA))

5.2 Predict the Classes

chenClassPredictions <- predictClasses(PCOSPpredValCohorts[names(haiderSigScores)],
    model=chenGeneFuModel)
birnClassPredictions <- predictClasses(PCOSPpredValCohorts[names(haiderSigScores)],
    model=birnbaumGeneFuModel)
haiderClassPredictions <- PCOSPpredValCohorts[names(haiderSigScores)]
# Manually assign the scores to the prediction cohorts
for (i in seq_along(haiderClassPredictions)) {
  colMData <- colData(haiderClassPredictions[[i]])
  colMData$genefu_score <- NA_real_
  colMData[rownames(colMData) %in% names(haiderSigScores[[i]]), ]$genefu_score <- 
      haiderSigScores[[i]][names(haiderSigScores[[i]]) %in% rownames(colMData)]
  colData(haiderClassPredictions[[i]]) <- colMData
}
# Setup the correct model metadata
mcols(haiderClassPredictions)$hasPredictions <- TRUE
metadata(haiderClassPredictions)$predictionModel <- haiderGeneFuModel

5.3 Validate the Models

validatedChenModel <- validateModel(chenGeneFuModel, valData=chenClassPredictions)
validatedBirnbaumModel <- validateModel(birnbaumGeneFuModel, 
    valData=birnClassPredictions)
validatedHaiderModel <- validateModel(haiderGeneFuModel, valData=haiderClassPredictions)

5.4 Model Performance Meta-Analysis

genefuModelComparisons <- compareModels(validatedChenModel,
    validatedBirnbaumModel, modelNames=c('Chen', 'Birnbaum'))
genefuModelComparisons <- compareModels(genefuModelComparisons,
    validatedHaiderModel, model2Name='Haider')
allModelComparisons <- compareModels(genefuModelComparisons, validatedPCOSPmodel, 
  model2Name='PCOSP')
# We are only interested in comparing the summaries, so we subset our model comparison
allModelComparisons <- subset(allModelComparisons, isSummary == TRUE)
allDindexComparisonForestPlot <- forestPlot(allModelComparisons,
    stat='log_D_index', colourBy='model', groupBy='mDataType')
allDindexComparisonForestPlot

allConcIndexComparisonForestPlot <- forestPlot(allModelComparisons,
    stat='concordance_index', colourBy='model', groupBy='mDataType')
allConcIndexComparisonForestPlot

From the two forest plots, we can see that the PCOSP model matched our outperformed all of the public classifiers, even when only trained with 100 models. It is likely that using 1000 models, we would see even better separation of the PCOSP model. Indeed, this is was the result in Sandhu et al. (2019).

6 Comparing PCOSP Models By Patient Subtype

data(cohortSubtypeDFs)

# Add the subtypes to the prediction cohort
subtypedPCOSPValCohorts <- assignSubtypes(PCOSPpredValCohorts, cohortSubtypeDFs)
subtypeValidatedPCOSPmodel <- validateModel(trainedPCOSPmodel, valData=subtypedPCOSPValCohorts)
## <simpleError in doTryCatch(return(expr), name, parentenv, handler): report ROC failed>
## <simpleError in wilcox.test.default(pred[obs == 1], pred[obs == 0], alternative = "great"): not enough (non-missing) 'x' observations>
## <simpleError in if (AUC.low > 0.5 & P >= 0.05) {    wilc.t = wilcox.test(predictor[table.gold == 1], predictor[table.gold ==         0], alternative = "less")    P = wilc.t$p.value}: missing value where TRUE/FALSE needed>
forestPlot(subtypeValidatedPCOSPmodel, stat='log_D_index', groupBy='cohort',
    colourBy='subtype')
## Warning: Removed 1 rows containing missing values (geom_pointrange).

forestPlot(subtypeValidatedPCOSPmodel, stat='concordance_index', groupBy='cohort',
    colourBy='subtype')
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Warning: Removed 1 rows containing missing values (geom_segment).

7 References

  1. Sandhu V, Labori KJ, Borgida A, et al. Meta-Analysis of 1,200 Transcriptomic Profiles Identifies a Prognostic Model for Pancreatic Ductal Adenocarcinoma. JCO Clin Cancer Inform. 2019;3:1-16. doi:10.1200/CCI.18.00102

  2. Chen DT, Davis-Yadley AH, Huang PY, et al. Prognostic Fifteen-Gene Signature for Early Stage Pancreatic Ductal Adenocarcinoma. PLoS One. 2015;10(8):e0133562. Published 2015 Aug 6. doi:10.1371/journal.pone.0133562

  3. Birnbaum DJ, Finetti P, Lopresti A, et al. A 25-gene classifier predicts overall survival in resectable pancreatic cancer. BMC Med. 2017;15(1):170. Published 2017 Sep 20. doi:10.1186/s12916-017-0936-z

  4. Haider S, Wang J, Nagano A, et al. A multi-gene signature predicts outcome in patients with pancreatic ductal adenocarcinoma. Genome Med. 2014;6(12):105. Published 2014 Dec 3. doi:10.1186/s13073-014-0105-3