Fig 1.
Survival prediction training and performance tasks.
Training-Task: Historical data with event times and censor-status along with covariates are used to train a model—top-to-bottom. Performance-Task: new patient covariates are input to the learned model to produce a prediction of survival time—bottom, left-to-right. (Included picture designed by Freepik.).
Table 1.
Characteristics of METABRIC and KIPAN cohorts.
Fig 2.
The dashed line is the Kaplan-Meier plot for this dataset.
Each of the other 5 curves is a patient-specific survival curve, for 5 different METABRIC patients, from a learned MTLR model. The curves show that there are very different prognoses for the different patients, even though they all are breast cancer patients from the same cohort: here, the patient with the orange survival curve (near the top) has a very good prognosis, especially compared to the patient with the blue survival curve.
Fig 3.
LSM = LearnSurvivalModel Uses Ψ ∈ {MTLR, Cox, RCox} for type of learner; ρ ∈ {dLDA, PCA} for the type of basis; XGE are the gene expression values, XCF are clinical features for a set of patients, “Lbl” is the set of their (survival prediction) labels, is the basis, of type ρ based on the instance XGE; W is the learned survival model, of type Ψ; and Ω is information about the preprocessing. Each (unrounded) box corresponds to data, whose dimensions appear around it. Each row is a patient, and each column, a feature. Each rounded box is a subroutine; here we show the input and output of each.
Fig 4.
Histogram of the normalized Gene Expression values , from METABRIC, showing how we descretized them into essentially equal-width bins.
Note the heights are on a log-scale. The material under the histogram—involving x and y—compare two ways to compute the discretized Gene Expression Values (dGEV): The top Enc_A discretizes the GEVs into a single count-feature A(⋅), and the bottom Enc_B discretizes the GEVs into two count-features B(⋅) representing over-expression and under-expression, respectively.
Fig 5.
The ComputeBasis[ρ=dLDA] process (shown top-to-bottom, on left) uses a set of high-dimensional gene expression vectors from many patients, to produce a set of basis vectors (corresponding the parameters of the LDA)
.
The UseBasis[ρ=dLDA] process (shown left-to-right horizontally) uses the set of dLDA “basis vectors” to transform a gene expression vector
from a novel patient, into a low-dimensional description
. (Note ComputeBasis[ρ=dLDA] also uses other information,
and Lbl, to determine the number K of basis vectors; to simplify the figure, we did not show this.).
Fig 6.
Overview of performance process, USM = UseSurvivalModel.
xGE and xCF are the gene expression values and clinical feature values, for a single patient; see also terms ρ, Ψ, Ω, , W from Fig 3.
Fig 7.
Test CI: METABRIC (left) and KIPAN (right).
Note higher values are better. The labels on the x-axis correspond to Table 2.
Table 2.
Concordance results of various models from METABRIC (over 395 test instances) and KIPAN (over 176 test instances).
+ = used these features and − = did not use these features As PAM50 is specific to breast cancer, it is not applicable to the kidney (KIPAN) data. The first row, with the ID “A(*)”, is the baseline.
Table 3.
D-calibration results from METABRIC, KIPAN, and BRCA, on the held-out test data.
p-values greater than 0.05 suggest the model is good (“D-calibrated”). Note that Cox models fail D-calibration test for all feature combinations, for BRCA dataset.
Fig 8.
Simplified flow diagram describing the overall prediction process, including both the learning task and the performance task.
Fig 9.
Kaplan–Meier survival function from METABRIC (training) data.
(We only use the quartiles for pedagogic purposes.).