Chapter Four · failure evidence
What Survival & Proportional Hazards Modeling got wrong, from 47 dissertations
The records evaluate various survival and proportional hazards modeling techniques across biomedical, engineering, and predictive maintenance applications. While standard Cox proportional hazards models frequently encountered assumption violations and data constraints, they also regularly outperformed complex machine learning and neural network alternatives. These records come from PhD theses at 18 institutions, 2021 to 2026. Each links to its thesis. They were extracted by language models reading the full text, so treat each as a lead to read, not a verdict.
Violations of the proportional hazards assumption across time and covariates
The constant proportional hazards assumption repeatedly broke down due to time-varying effects, crossing survival curves, change points, and non-proportional categorical or continuous predictors. Researchers addressed these failures by abandoning standard Cox models or log-rank tests in favor of stratified models, accelerated failure time models, and parametric alternatives.
Tried and failed
Cox proportional hazards survival analysis applied to longitudinal surgical reintervention rate comparison. Reason: Proportional hazards assumption was violated over time in log-log plots
Tried and failed
Cox proportional hazards multivariable regression applied to time-to-event epidemiological cohort data. Reason: proportional hazards assumption was violated for specific categorical predictor variables
Late or missed childhood vaccination in the United Kingdom: Identifying the determinants · Imperial
Tried and failed
Cox proportional hazards survival modeling applied to time to medication discontinuation. Reason: proportional hazards assumption was violated between treatment groups
Tried and failed
standard Cox proportional hazards modeling applied to cost overrun risk estimation. Reason: violated the proportional hazards assumption across key covariates without interaction terms
Enhanced Construction Cost Estimation of Highway Projects using Emerging Statistical and Machine Learning Techniques · Georgia Tech
Considered and rejected
Considered and rejected: Rejected Cox proportional hazards regression for reintervention analysis because the proportional hazards assumption was violated, adopting Poisson regression with robust standard errors instead.
Considered and rejected
Considered and rejected: Rejected standard Cox proportional hazards modeling because proportional hazards assumptions are invalid and misleading in the presence of change points / U-shaped curves.
Semiparametric Change Point Model for Survival Outcomes in the Presence of a U-Shaped Risk · JScholarship
Considered and rejected
Considered and rejected: Rejected Cox semi-parametric hazard modeling for meal duration because the data violated the proportional hazards assumption
Empirical Essays in The Entertainment and Hospitality industries · Penn
Considered and rejected
Considered and rejected: Rejected conventional stratification methods to resolve Cox proportional hazards violations due to heavy reliance on continuous rather than categorical covariates.
Governing open spaces: rules, goals, and metrics in innovation communities · OpenBU
Considered and rejected
Considered and rejected: Rejected Cox proportional hazards event-history model because time-varying covariates violated the constant proportional hazards assumption over time.
Essays in Labor Economics and Applied Microeconomics · Texas Tech
Considered and rejected
Considered and rejected: Rejected unstratified Cox proportional hazards model for LnPCR because LnPCR violated the proportional hazards assumption (p = 0.002), adopting a stratified Cox model instead
Considered and rejected
Considered and rejected: Cox Proportional Hazards (CPH) modeling was rejected due to its assumption of proportional hazards across covariate values failing on the large military datasets.
Considered and rejected
Considered and rejected: Rejected traditional Cox proportional hazards survival modeling due to unrealistic assumptions regarding proportional hazards and inability to accommodate treatment grace periods without survival bias.
Comparative Safety and Effectiveness of Anticonvulsants Among Older Adults · Harvard
Considered and rejected
Considered and rejected: Rejected Cox Proportional Hazards and Mantel-Haenszel log-rank tests because the proportional hazards assumption was violated (p < 0.01 on weighted-residuals score test), selecting parametric Weibull modeling and Peto-Peto-Prentice test instead.
Measuring Distributed Mentoring in an Online Fanfiction Community · ResearchWorks
Considered and rejected
Considered and rejected: Rejected traditional log-rank test splitting criterion because it relies on the proportional hazards assumption and fails when hazard curves cross.
Risk-Adjusted Time-to-Event Modeling: Integrating Absolute Risk and Biomarker-Driven Splitting · JScholarship
Considered and rejected
Considered and rejected: Rejected standard Cox proportional hazards models because treatment intervention/transplant changes the relative hazard of death over time, violating constant relative hazards
Considered and rejected
Considered and rejected: Rejected Cox Proportional Hazards (PH) modeling in favor of Log-logistic Accelerated Failure Time (AFT) because the proportional hazards assumption did not hold and AFT directly models duration deceleration.
Ridehail and Commercial Vehicles Access in Urban Areas: Implications for Public Infrastructure Management · ResearchWorks
Considered and rejected
Considered and rejected: Rejected the log-rank split statistic used in standard RSF because it relies on the proportional hazards assumption and loses power when hazard curves cross
Machine Learning for Individualized Clinical Risk Prediction and Prevention · JScholarship
Machine learning and neural survival methods failing to outperform standard baselines
Complex methods including random survival forests, neural survival architectures, and learning classifier systems repeatedly failed to outperform classical Cox proportional hazards and regression models. These complex approaches suffered from optimization difficulties caused by doubled parameter counts, rule definition issues, or higher prediction error than correctly specified simpler models.
Lost to a baseline
Random Survival Forest with Brier-score gradient splitting (C-index = 0.659 / error rate = 0.341) and log-rank score splitting (C-index = 0.605 / error rate = 0.395) were beaten by the Cox proportional hazards model (C-index = 0.698 / error rate = 0.302)
Lost to a baseline
Random Survival Forest (C-index=0.665 / error rate=0.335) was beaten by Cox proportional hazards regression (C-index=0.698 / error rate=0.302)
Lost to a baseline
Correctly specified main-terms Cox model with Breslow estimator beat machine learning methods across MISE and MSE in proportional hazards simulations (Scenario 4).
Nonparametric methods for integration of survival analysis and machine learning · ResearchWorks
Tried and failed
random forest classification and survival modeling applied to clinical tabular outcome prediction. Outcome: worse than baseline. Reason: complex machine learning models failed to outperform classical logistic regression and Cox proportional hazards baselines
Tried and failed
Bayes by Backprop variational inference applied to survival analysis neural networks. Outcome: worse than baseline. Reason: doubling parameter count impaired optimization compared to Monte Carlo Dropout and frequentist models
Tried and failed
non-proportional hazard neural survival modeling applied to time series sensor predictive maintenance. Reason: abandoned during evaluation in favor of standard Cox proportional hazards with neural feature extraction
Tried and failed
learning classifier systems for survival analysis applied to germline genomic cancer prognosis. Outcome: worse than baseline. Reason: missing somatic features and restrictive rule interval bound definitions
Structural limitations and performance trade-offs among alternative hazard formulations
Standard Cox proportional hazards formulations underperformed random survival forests, lacked defined baseline hazards required for reproducibility, or struggled with continuous interval censoring. Conversely, parametric, discrete-time, and accelerated failure time alternatives were rejected due to unrealistic constant hazard assumptions, discretized hazard approximations, or nuisance baseline parameters distorting mixture clusters.
Lost to a baseline
Cox proportional hazards (CoxPH) model achieved lower mean C-index (0.665 ± 0.046) and AUROC (0.707 ± 0.281) than Random Survival Forest (C-index 0.798 ± 0.114, AUROC 0.748 ± 0.096) on PET data.
Considered and rejected
Considered and rejected: Rejected Cox proportional hazards models in favor of parametric Weibull survival models because undefined baseline hazard functions hinder reproducibility with new data.
Forest Elephant Group Dynamics, Social Interactions, and Population Monitoring · DukeSpace
Considered and rejected
Considered and rejected: Rejected accelerated failure time (AFT) formulation in favor of proportional hazards (PH) to prevent baseline risk nuisance parameters from influencing EDP mixture clusters.
Bayesian Nonparametric Models For Causal Inference And Clustering Under Dirichlet Process Priors · Penn
Considered and rejected
Considered and rejected: Rejected parametric event history models (exponential and Weibull models) in favor of the semi-parametric Cox Proportional Hazards model due to unrealistic assumptions of constant hazard rates and restrictive functional form requirements.
International diffusion of national security policy : the case of civil aviation security policies · UT Austin
Considered and rejected
Considered and rejected: Rejected standard discrete-time hazard models because they directly model discretized hazards rather than the underlying continuous-time hazard function of interest.
Considered and rejected
Considered and rejected: Rejected continuous-time Cox proportional hazards modeling in favor of discrete-time survival analysis using Poisson regression to improve predictive performance and handle interval censoring.
Barriers and Facilitators to Mental Health Service Utilization Among Refugees in Sweden · JScholarship
Data sparsity, high dimensionality, and missing values hindering model estimation
Standard Cox models failed to execute and converge when applied to high-dimensional datasets containing thousands of features. In other settings, extremely low event counts caused severe overfitting, while coarse temporal resolution and missing or poorly normalized inputs prevented models from generalizing or capturing critical relationships.
Tried and failed
standard Cox proportional hazards model applied to high-dimensional survival datasets. Outcome: did not converge. Reason: failed to complete execution on datasets with 1,000 to 10,000 features
Tried and failed
survival analysis models applied to rare event duration prediction. Outcome: overfit. Reason: severe overfitting caused by extremely low observed event counts
Tried and failed
survival analysis model coupled to finite element simulation applied to tissue thermal and pressure damage prediction. Outcome: did not generalise. Reason: training data had coarse temporal resolution and lacked uncoupled baseline parameter regimes
New tissue damage model for pressure and thermal injuries and its practical application · UT Austin
Tried and failed
deterministic regression and survival analysis applied to infrastructure asset renewal prioritization. Outcome: data insufficient. Reason: failed to capture critical parameter relationships when input data was missing or poorly normalized
Fuzzy Logic-based Economic Model for Water Main Renewal · Virginia Tech
Inadequate handling of competing terminal risks and dependent censoring
Standard Cox regression and Poisson models failed by treating competing terminal events such as death as standard right-censored observations, conflating healthy and fatal outcomes. In semi-competing risk settings, log-normal accelerated failure time specifications uniformly underperformed compared to Weibull and Truncated Bernstein Polynomial baseline models.
Considered and rejected
Considered and rejected: Rejected Cox proportional hazards regression in favor of competing risk analysis because Cox regression inappropriately treats competing terminal events as standard censored observations.
Ergebnisse einer dosisreduzierten Konditionierung mit Fludarabin/Treosulfan zur allogenen Stammzelltransplantation bei Patienten mit hämatologischen Neoplasien · Publikationssystem UB Tuebingen
Considered and rejected
Considered and rejected: Rejected standard Cox proportional hazards regression and Poisson models for primary hospitalisation analyses because censoring deaths conflates healthy non-admissions with fatal non-admissions and violates distribution assumptions.
Tried and failed
log-normal accelerated failure time modeling applied to survival analysis with semi-competing risks. Outcome: worse than baseline. Reason: uniformly underperformed compared to Weibull and Truncated Bernstein Polynomial baseline models
Methods for Flexible Survival Analysis and Prediction of Semi-Competing Risks · Harvard
Mismatch between survival modeling requirements and study designs or outcomes
Investigators rejected Cox proportional hazards modeling when clinical research objectives focused on binary in-hospital mortality rather than time-to-event outcomes, or when event times were completely unavailable in curated files. Survival analysis was also set aside for customer churn prediction because the dataset had complete campaign tracking with no right-censoring.
Considered and rejected
Considered and rejected: Rejected Cox proportional hazards regression because the clinical question focused on in-hospital mortality rather than time-to-event.
Considered and rejected
Considered and rejected: Rejected Cox proportional hazards regression in favor of logistic regression because specific time-to-event data were not accessible in the curated analysis files.
Considered and rejected
Considered and rejected: Decided against using survival analysis for churn prediction because the dataset contained no censored data (full campaign duration was recorded).
Alone with Company: Studying Individual and Social Players' In-game Behaviors in Adaptive Gamification · IRIS - UNITN - prod
Excess variance and uncertainty underestimation in complex or non-parametric estimators
Nonparametric survival estimators exhibited higher standard deviations and variance across biomarker values compared to correctly specified Cox models. Similarly, adding nuisance parameters to adjust for dependent truncation increased variance noise more than it reduced bias, while variational inference underestimated variance and degraded credible interval coverage compared to MCMC.
Lost to a baseline
When the Cox proportional hazards model is correctly specified, the nonparametric estimator exhibited higher standard deviation / variance across all biomarker values than the basic Cox model.
Statistical tools for immune correlates analysis of vaccine clinical trial data · ResearchWorks
Tried and failed
adding nuisance parameters for dependent truncation correction applied to survival analysis with missing covariates. Outcome: worse than baseline. Reason: estimating additional nuisance parameters introduced more variance noise than the bias reduction gained
Missing Data and Measurement Error Methods for Left-Truncated Survival Data · Penn
Lost to a baseline
SVB marginal credible interval coverage for non-zero coefficients (0.770) was lower than MCMC (0.928) on survival analysis setting 1 with c=0.25 due to variational variance underestimation.
Variational bayes for high-dimensional linear models · Imperial
Left open by the authors
Problems the authors named and did not get to.
Left open
Evaluate how violating the proportional hazards assumption affects the generalizability and performance of deep survival analysis models. Blocker: None
Scalable and Deep Bayesian Nonparametric Survival Analysis for Large-Scale Data · Texas Tech
Left open
Investigate alternative survival models beyond proportional hazards and proportional reversed hazards for left-truncated interval-censored data. Blocker: Lacks specific target models, mathematical formulations, or concrete test construction approaches
Analyzing Cohort Studies with Left-truncated and Interval-censored Data: A New Model-based Linear Rank-type Test · TXST Digital Repository
Left open
Evaluate alternative survival models including log-logistic, Cox proportional hazards, frailty, and cure rate models for object persistence modeling. Blocker: None
Spatio-temporal object persistence modeling and semantics for long-term robot navigation · UT Austin
Left open
Revisit Cox proportional hazards simulation studies using martingale-based score equations dM_i(t) to improve sandwich variance performance in unified estimation. Blocker: None
Improving applicability of the non-monotone unified estimate for missing data · oURspace
Left open
Implement Cox proportional hazards models with Breslow estimator-derived weights instead of pooled logistic regressions for validation set risk prediction. Blocker: None
Left open
Extend interval-censored measurement error estimation methods from discrete proportional hazards to continuous failure time models. Blocker: None
Left open
Extend the Bayesian project portfolio model using survival analysis and proportional hazards models to evaluate budget, time, and cost failure mechanisms. Blocker: None
A Bayesian learning approach to advance the reliability of LeAgile project portfolio management · Texas Tech
Left open
Extend the discrete proportional hazards measurement error model to allow outcome errors dependent on covariates or previous responses. Blocker: None
Left open
Implement and evaluate LSTM or Transformer architectures for Cox proportional hazards survival analysis on sequential time series sensor data. Blocker: None
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