Application of Cox Model to predict the survival of patients with Chronic Heart Failure: A latent class regression approach

John Mbotwa; Marc de Kamps; Mark S. Gilthorpe; Paul D. Baxter

arxiv: 1907.07957 · v1 · pith:BF5GBZGAnew · submitted 2019-07-18 · 📊 stat.ME

Application of Cox Model to predict the survival of patients with Chronic Heart Failure: A latent class regression approach

John Mbotwa , Marc de Kamps , Paul D. Baxter , Mark S. Gilthorpe This is my paper

Pith reviewed 2026-05-24 19:54 UTC · model grok-4.3

classification 📊 stat.ME

keywords latent class analysisCox proportional hazardschronic heart failuresurvival predictionmixture modelsrisk stratificationBayesian information criterion

0 comments

The pith

A latent class version of the Cox model improves survival predictions for chronic heart failure patients compared to the standard single-class Cox model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper explores using a Cox proportional hazard model inside a latent class framework to predict survival for chronic heart failure patients using routinely collected data. Patients are divided into subgroups based on covariates, with each subgroup having its own risk model. The optimal number of classes is chosen by the Bayesian information criterion. Model performance is checked with area under the ROC curve on cross-validated and bootstrapped samples, and a simulation study confirms better results than the usual single-class Cox model. This approach addresses the common failure of prediction models to account for patient heterogeneity in medical outcomes.

Core claim

Using a latent class regression approach with the Cox model, subgroups of patients are identified from covariates and each is assigned its own hazard function; the resulting multi-class model shows superior predictive performance to the standard one-class Cox PH model in both patient data and simulations.

What carries the argument

The latent class Cox proportional hazards model that assigns patients to unobserved classes and estimates class-specific hazard functions from observed covariates.

If this is right

The model identifies distinct risk subgroups among chronic heart failure patients.
It achieves higher discriminative ability as measured by AUC in cross-validated samples.
An optimal number of classes is selected using the Bayesian information criterion.
Simulation studies demonstrate outperformance over the standard Cox model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method may extend to survival prediction in other diseases with heterogeneous populations.
Subgroup-specific predictions could inform more targeted clinical interventions.
External validation on independent datasets would test the stability of the identified classes.

Load-bearing premise

The observed covariates are sufficient to identify and separate latent classes with distinct hazard functions that improve out-of-sample prediction.

What would settle it

Finding a patient cohort or simulation setting in which the latent class model's AUC does not exceed that of the standard Cox model on held-out data would challenge the outperformance claim.

read the original abstract

Most prediction models that are used in medical research fail to accurately predict health outcomes due to methodological limitations. Using routinely collected patient data, we explore the use of a Cox proportional hazard (PH) model within a latent class framework to model survival of patients with chronic heart failure (CHF). We identify subgroups of patients based on their risk with the aid of available covariates. We allow each subgroup to have its own risk model.We choose an optimum number of classes based on the reported Bayesian information criteria (BIC). We assess the discriminative ability of the chosen model using an area under the receiver operating characteristic curve (AUC) for all the cross-validated and bootstrapped samples.We conduct a simulation study to compare the predictive performance of our models. Our proposed latent class model outperforms the standard one class Cox PH model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This applies an existing latent class Cox model to CHF data with CV and bootstrap AUC plus a simulation, but class selection on the full data before resampling likely inflates the reported gains over standard Cox.

read the letter

The paper fits a latent class version of the Cox model to chronic heart failure survival records, lets each class have its own hazard function, picks the number of classes by BIC, and then reports AUC from cross-validation and bootstrap on the selected model. A simulation study is included to compare predictive performance against the usual single-class Cox. That is the main content: an application plus standard validation steps rather than any new methodological development. Latent class Cox extensions already exist in the literature, so the novelty is limited to the CHF dataset and the simulation exercise. The resampling approach for AUC is a plus because it avoids simple in-sample reporting. The simulation adds a controlled check that the mixture can improve prediction under some conditions. The soft spot is exactly the one flagged in the stress-test note. BIC is run once on the full data to choose the class count, after which AUC is computed on resamples of that fixed model. This sequence can capitalize on sampling variability in the number of classes and produce optimistic outperformance numbers relative to a properly nested procedure where selection happens inside each training fold. The abstract gives no sample size, no covariate list, and no check on the proportional hazards assumption within classes, which makes it hard to judge whether the classes are meaningful or just fitting noise. The simulation description is too high-level to confirm it avoids the same selection issue. This work is aimed at applied statisticians and clinicians who build risk models for heterogeneous conditions like heart failure. A reader looking for a concrete example of mixture survival modeling on real data could extract some practical points from the validation steps and the simulation. It deserves peer review because the clinical question is relevant and the authors have attempted proper out-of-sample checks, even though the method is not new. The referee would need to press on nesting the class selection and on supplying the missing data and assumption details.

Referee Report

3 major / 1 minor

Summary. The manuscript proposes applying a Cox proportional hazards model within a latent class framework to predict survival among chronic heart failure patients. Covariates are used to identify patient subgroups, each assigned its own class-specific hazard model. The number of classes is selected by BIC; discriminative performance is then evaluated by AUC on cross-validated and bootstrapped samples, and a simulation study is reported to demonstrate that the latent-class model outperforms the standard single-class Cox PH model.

Significance. If the reported outperformance survives properly nested validation, the method could improve risk stratification by explicitly modeling unobserved heterogeneity in heart-failure survival. The manuscript already incorporates cross-validation, bootstrapping, and an independent simulation study, which are positive features for assessing predictive utility.

major comments (3)

[Abstract] Abstract: BIC-based selection of the number of latent classes is performed on the full data set before AUC is computed on cross-validated and bootstrapped samples. Because the model-selection step is not nested inside each training fold, the reported superiority over the one-class Cox model may be optimistically biased by capitalizing on sampling variability in the chosen number of classes.
[Abstract] Abstract: The simulation study is described only as comparing predictive performance; it is not stated whether the BIC class-selection step was itself nested inside the simulation replicates. Without this detail the simulation cannot confirm that the claimed advantage is robust to the same selection procedure used on real data.
[Abstract] Abstract: No sample size, covariate list, or within-class proportional-hazards diagnostics are reported. These omissions make it impossible to assess whether the latent classes are identified by the observed covariates or whether the class-specific models satisfy the central modeling assumption.

minor comments (1)

[Abstract] The phrase 'reported Bayesian information criteria (BIC)' is ambiguous; clarify whether the standard BIC or a latent-class-specific variant is used.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thoughtful and constructive comments. We address each major point below and indicate the changes we will make to strengthen the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: BIC-based selection of the number of latent classes is performed on the full data set before AUC is computed on cross-validated and bootstrapped samples. Because the model-selection step is not nested inside each training fold, the reported superiority over the one-class Cox model may be optimistically biased by capitalizing on sampling variability in the chosen number of classes.

Authors: We agree that selecting the number of classes on the full dataset before performing cross-validation and bootstrapping can lead to optimistic bias in the reported AUC values. In the revised manuscript we will re-implement the entire procedure so that BIC-based class selection is performed independently inside each training fold of the cross-validation (and inside each bootstrap replicate). The AUC comparisons will then be recomputed under this nested protocol. revision: yes
Referee: [Abstract] Abstract: The simulation study is described only as comparing predictive performance; it is not stated whether the BIC class-selection step was itself nested inside the simulation replicates. Without this detail the simulation cannot confirm that the claimed advantage is robust to the same selection procedure used on real data.

Authors: The original simulation description omitted this detail. In the revised manuscript we will explicitly state whether (and how) the BIC selection was nested within each simulation replicate. If the original simulation did not nest the selection, we will rerun the simulation study with proper nesting and report the updated results. revision: yes
Referee: [Abstract] Abstract: No sample size, covariate list, or within-class proportional-hazards diagnostics are reported. These omissions make it impossible to assess whether the latent classes are identified by the observed covariates or whether the class-specific models satisfy the central modeling assumption.

Authors: We will add the requested information to the revised manuscript: the total sample size and number of events, the complete list of covariates used for class membership and for the class-specific hazard models, and the results of within-class proportional-hazards diagnostics (e.g., Schoenfeld residuals or log-cumulative-hazard plots) for each retained class. revision: yes

Circularity Check

0 steps flagged

No significant circularity; validation uses independent CV, bootstrap and simulation

full rationale

The paper selects class number via BIC then reports AUC from cross-validated and bootstrapped samples plus a separate simulation study. These are external validation procedures rather than in-sample statistics renamed as predictions. No equations reduce a claimed out-of-sample result to a fitted parameter by construction, no self-citation chain is load-bearing, and no ansatz or uniqueness claim is smuggled in. The derivation chain for the performance comparison therefore remains self-contained against the stated benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim depends on the standard Cox proportional hazards assumption holding separately within each latent class and on the ability of the chosen covariates to recover meaningful class structure; the number of classes is treated as a data-driven choice via BIC.

free parameters (1)

Number of latent classes
Selected by minimizing BIC on the observed data, making the final model structure dependent on the specific sample.

axioms (2)

domain assumption Proportional hazards assumption holds within each latent class
Core modeling assumption of the Cox PH model, extended without additional justification to the class-specific models.
domain assumption Finite mixture of Cox models can capture relevant patient heterogeneity
Fundamental premise of the latent class regression framework invoked to justify the multi-class approach.

pith-pipeline@v0.9.0 · 5677 in / 1370 out tokens · 40434 ms · 2026-05-24T19:54:58.476071+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Management of chronic heart failure in the older population.Journal of Geriatric Cardiology2014;11: 329-337

Azad N, Lemay G. Management of chronic heart failure in the older population.Journal of Geriatric Cardiology2014;11: 329-337

work page

[2] [2]

Risk prediction models: II

Moons KG, Kengne AP, Grobbee DE, et al. Risk prediction models: II. External validation, model updating, and impact assessment .Heart 2012; 98: 691-698

work page 2012

[3] [3]

MoonsKG,KengneAP,WoodwardM,etal.Riskpredictionmodels:I.Development,internalvalidation,andassessingthe incremental value of a new (bio)marker.Heart 2012; 98: 683-690

work page 2012

[4] [4]

Cardiovascular risk prediction: basic concepts, current status, and future directions.Circulation 2010; 121: 1768-1777

Lloyd-Jones DM. Cardiovascular risk prediction: basic concepts, current status, and future directions.Circulation 2010; 121: 1768-1777

work page 2010

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DowningA,TwelvesC,FormanD,etal.TimetoBeginAdjuvantChemotherapyandSurvivalinBreastCancerPatientsâ/uni0102/uni0155: A Retrospective Observational Study Using Latent Class Analysis.The Breast Journal2014; 20: 29-36

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Erratum toâ/uni0102/uni0155: A Prospective Study of Psychological Distress and Weight Status in Adolescents / Young Adults.Annals of Behavioral Medicine2014; 48(2): 284-285

Kubzansky, LD., Gilthorpe, MS, Goodman E. Erratum toâ/uni0102/uni0155: A Prospective Study of Psychological Distress and Weight Status in Adolescents / Young Adults.Annals of Behavioral Medicine2014; 48(2): 284-285

work page

[7] [7]

Harrison WJ, Gilthorpe MS, Downing A, et al. Multilevel Latent Class Modelling of Colorectal Cancer Survival Status at Three Years and Socio-economic Background Whilst Incorporating Stage of Disease.International Journal of Statistics and Probability2013; 2(3): 85-95

work page

[8] [8]

Multilevel latent class casemix modellingâ/uni0102/uni0155: a novel approach to accommodate patient casemix.BMC Health Services Research2011; 11(1):53

Gilthorpe MS, Harrison WJ, Downing A, et al. Multilevel latent class casemix modellingâ/uni0102/uni0155: a novel approach to accommodate patient casemix.BMC Health Services Research2011; 11(1):53

work page

[9] [9]

Socio economic deprivation and mode-speciﬁc outcomes in patients with chronic heart failure.Heart 2018; 104:993-998

Witte KK, Patel PA, Walker AMN, et al. Socio economic deprivation and mode-speciﬁc outcomes in patients with chronic heart failure.Heart 2018; 104:993-998

work page 2018

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Changing Characteristics and Mode of Death Associated With Chronic Heart FailureCausedbyLeftVentricularSystolicDysfunction:AStudyAcrossTherapeuticEras

Cubbon RM, Gale CP, Kearney LC, et al. Changing Characteristics and Mode of Death Associated With Chronic Heart FailureCausedbyLeftVentricularSystolicDysfunction:AStudyAcrossTherapeuticEras. CirculationHeartFailure 2011; 4: 396-403

work page 2011

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Mortality Reduction Associated With b-Adrenoceptor Inhibition in Chronic Heart Failure Is Greater in Patients With Diabetes.Diabetes Care2018; 41: 136-142

Witte KK, Drozd M, Walker AMN, Patel PA , et al. Mortality Reduction Associated With b-Adrenoceptor Inhibition in Chronic Heart Failure Is Greater in Patients With Diabetes.Diabetes Care2018; 41: 136-142

work page

[12] [12]

Diagnostic methods 2: receiver operating characteristic (ROC) curves.Kidney Int 2009; 76: 252-256

Tripepi G, Jager KJ, Dekker FW et al. Diagnostic methods 2: receiver operating characteristic (ROC) curves.Kidney Int 2009; 76: 252-256

work page 2009

[13] [13]

Model Selection in Finite Mixture Models: A k-Fold Cross-Validation Approach,StructuralEquationModeling: AMultidisciplinaryJournal 2017;24(2):246-256.Availablefrom:http://dx.doi

Grimm KJ, Mazza GL, Davoudzadeh P, et al. Model Selection in Finite Mixture Models: A k-Fold Cross-Validation Approach,StructuralEquationModeling: AMultidisciplinaryJournal 2017;24(2):246-256.Availablefrom:http://dx.doi. org/10.1080/10705511.2016.1250638

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Regression models and life tables.Journal of the Royal Statistical Society1972: 34: 187-220

Cox DR. Regression models and life tables.Journal of the Royal Statistical Society1972: 34: 187-220

work page

[16] [16]

Cox D.R.Partial Likelihood Biometrika1975; 62: 269-276

work page

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and MuthÃ/uni013En BO

MuthÃ/uni013En LK. and MuthÃ/uni013En BO. Mplus User’s Guide. Seventh Edition. 1998-2012

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Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study.Struct Equ Modeling2007; 14:535-569

Nylund KL, Asparoutiov T, Muthen BO. Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study.Struct Equ Modeling2007; 14:535-569

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Basic principles of ROC analysis.Semin NuclMed1978; 8: 283-298

Metz CE. Basic principles of ROC analysis.Semin NuclMed1978; 8: 283-298

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CaspJIntern Med 2013; 4: 627-635

Hajian-TilakiK.Receiveroperatingcharacteristic(ROC)curveanalysisformedicaldiagnostictestevaluation. CaspJIntern Med 2013; 4: 627-635. 12 MBOTWAET AL

work page 2013

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Robust causal inference using Directed Acyclic Graphs: the R package â/uni0102Ÿdagittyâ/uni0102/uni0179.Int J Epidemiol2016; 45: 1887-1894

Textor J, van der Zander B, Gilthorpe MS et al. Robust causal inference using Directed Acyclic Graphs: the R package â/uni0102Ÿdagittyâ/uni0102/uni0179.Int J Epidemiol2016; 45: 1887-1894

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Zupan B, Demstar J, Kattan MW. et al. Machine Learning for survival analysis: A case study on recurrence of prostate Cancer.Artiﬁcial Intelligence in Medicine2000; 20: 59-75

work page

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SongXW,MitnitskiA,CoxJ.etal.Comparisonofmachinelearningtechniqueswithclassicalstatisticalmodelsinpredicting health outcomes.Medinfo2004; 107(1-2): 736-740

work page

[24] [24]

Time dependent ROC curves for censored survival data and a diagnostic marker

Heagerty PJ, Lumley T, Pepe MS. Time dependent ROC curves for censored survival data and a diagnostic marker. Biometrics2000; 56:337-344

work page

[25] [25]

The prevention and handling of the missing data.Korean Journal of Anesthesiology2013; 64(5): 402-406

Kang H. The prevention and handling of the missing data.Korean Journal of Anesthesiology2013; 64(5): 402-406

work page

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Statistics notes: bootstrap resampling methods.BMJ 2015; 350:h2622

Bland JM, Altman DG. Statistics notes: bootstrap resampling methods.BMJ 2015; 350:h2622

work page 2015

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Survival analysis in public health research.Annual Review of Public Health1997; 18:105-134

Lee ET & Go OT. Survival analysis in public health research.Annual Review of Public Health1997; 18:105-134

work page

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IEEETrans

VillanuevaD.,FeijooA.,PazosJL.Simulationofcorrelatedwindspeeddataforeconomicdispatchevaluation. IEEETrans. Sustain. Energy2012; 3(1):142-149

work page

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The theory of path coeﬃcients-A reply to Niles’s criticism.Genetics1923; 8:239-255

Wright S. The theory of path coeﬃcients-A reply to Niles’s criticism.Genetics1923; 8:239-255. How to cite this article:MbotwaJ.,deKampsM.,BaxterPD,andGilthorpeMS(2019),ApplicationofCoxmodeltopredictthe survivalofpatientswithChronicHeartFailure(CHF): AlatentClassregressionapproach,StatisticsinMedicine,2019;00:0–0

work page 2019