Advanced survival modelling for consumer credit risk assessment: addressing recurrent events, multiple outcomes and frailty

A thesis submitted in partial fulfillment of the requirements for the degree of Doctor in Information Management, specialization in Statistics and EconometricsThis thesis worked on the application of advanced survival models in consumer credit risk assessment, particularly to address issues of recurrent delinquency (or default) and recovery (cure) events as well as multiple risk events and frailty. Each chapter (2 to 5) addressed a separate problem and several key conclusions were reached. Chapter 2 addressed the neglected area of modelling recovery from delinquency to normal performance on retail consumer loans taking into account the recurrent nature of delinquency and also including time-dependent macroeconomic variables. Using data from a lending company in Zimbabwe, we provided a comprehensive analysis of the recovery patterns using the extended Cox model. The findings vividly showed that behavioural variables were the most important in understanding recovery patterns of obligors. This confirms and underscores the importance of using behavioural models to understand the recovery patterns of obligors in order to prevent credit loss. The findings also strongly revealed that the falling real gross domestic product, representing a deteriorating economic situation significantly explained the diminishing rate of recovery from delinquency to normal performance among consumers. The study pointed to the urgent need for policy measures aimed at promoting economic growth for the stabilisation of consumer welfare and the financial system at large.Chapter 3 extends the work in chapter 2 and notes that, even though multiple failure-time data are ubiquitous in finance and economics especially in the credit risk domain, it is unfortunate that naive statistical techniques which ignore the subsequent events are commonly used to analyse such data. Applying standard statistical methods without addressing the recurrence of the events produces biased and inefficient estimates, thus offering erroneous predictions. We explore various ways of modelling and forecasting recurrent delinquency and recovery events on consumer loans. Using consumer loans data from a severely distressed economic environment, we illustrate and empirically compare extended Cox models for ordered recurrent recovery events. We highlight that accounting for multiple events proffers detailed information, thus providing a nuanced understanding of the recovery prognosis of delinquents. For ordered indistinguishable recurrent recovery events, we recommend using the Andersen and Gill (1982) model since it fits these assumptions and performs well on predicting recovery.Chapter 4 extends chapters 2 and 3 and highlight that rigorous credit risk analysis is not only of significance to lenders and banks but is also of paramount importance for sound regulatory and economic policy making. Increasing loan impairment or delinquency, defaults and mortgage foreclosures signals a sick economy and generates considerable financial stability concerns. For lenders and banks, the accurate estimation of credit risk parameters remains essential for pricing, profit testing, capital provisioning as well as for managing delinquents. Traditional credit scoring models such as the logit regression only provide estimates of the lifetime probability of default for a loan but cannot identify the existence of cures and or other movements. These methods lack the ability to characterise the progression of borrowers over time and cannot utilise all the available data to understand the recurrence of risk events and possible occurrence of multiple loan outcomes. In this paper, we propose a system-wide multi-state framework to jointly model state occupations and the transitions between normal performance (current), delinquency, prepayment, repurchase, short sale and foreclosure on mortgage loans. The probability of loans transitioning to and from the various states is estimated in a discrete-time multi-state Markov model with seven allowable states and sixteen possible transitions. Additionally, we investigate the relationship between the probability of loans transitioning to and from various loan outcomes and loan-level covariates. We empirically test the performance of the model using the US single-family mortgage loans originated during the first quarter of 2009 and were followed on their monthly repayment performance until the third quarter of 2016. Our results show that the main factors affecting the transition into various loan outcomes are affordability as measured by debt-to-income ratio, equity as marked by loan-to-value ratio, interest rates and the property type. In chapter 5, we note that there has been increasing availability of consumer credit in Zimbabwe, yet the credit information sharing systems are not as advanced. Using frailty survival models on credit bureau data from Zimbabwe, the study investigates the possible underestimation of credit losses under the assumption of independence of default event times. The study found that adding a frailty term significantly improved the models, thus indicating the presence of unobserved heterogeneity. The major policy recommendation is for the regulator to institute appropriate policy frameworks to allow robust and complete credit information sharing and reporting as doing so will significantly improve the functioning of the credit market

Weibull Racing Survival Analysis for Competing Events and a Study of Loan Payoff and Default

We propose Bayesian nonparametric Weibull delegate racing (WDR) to explicitly model surviving under competing events and to interpret how the covariates accelerate or decelerate the event times. WDR explains non-monotonic covariate effects by racing a potentially infinite number of sub-events, relaxing the ubiquitous proportional-hazards assumption which may be too restrictive. WDR can handle different types of censoring and missing event times or types. For inference, we develop a Gibbs-sampler-based MCMC algorithm along with a maximum a posteriori estimation for big data applications. We use synthetic data analysis to demonstrate the flexibility and parsimonious nonlinearity of WDR. We also use a data set of time to loan payoff and default from Prosper.com to showcase the interpretability.Comment: 40 pages, 7 figures, 14 table

Long-term outcome of patients with newly diagnosed chronic myeloid leukemia: a randomized comparison of stem cell transplantation with drug treatment.

Tyrosine kinase inhibitors represent today's treatment of choice in chronic myeloid leukemia (CML). Allogeneic hematopoietic stem cell transplantation (HSCT) is regarded as salvage therapy. This prospective randomized CML-study IIIA recruited 669 patients with newly diagnosed CML between July 1997 and January 2004 from 143 centers. Of these, 427 patients were considered eligible for HSCT and were randomized by availability of a matched family donor between primary HSCT (group A; N=166 patients) and best available drug treatment (group B; N=261). Primary end point was long-term survival. Survival probabilities were not different between groups A and B (10-year survival: 0.76 (95% confidence interval (CI): 0.69-0.82) vs 0.69 (95% CI: 0.61-0.76)), but influenced by disease and transplant risk. Patients with a low transplant risk showed superior survival compared with patients with high- (P<0.001) and non-high-risk disease (P=0.047) in group B; after entering blast crisis, survival was not different with or without HSCT. Significantly more patients in group A were in molecular remission (56% vs 39%; P=0.005) and free of drug treatment (56% vs 6%; P<0.001). Differences in symptoms and Karnofsky score were not significant. In the era of tyrosine kinase inhibitors, HSCT remains a valid option when both disease and transplant risk are considered

Five-year follow-up mortality prognostic index for colorectal patients

Correction to: Five-year follow-up mortality prognostic index for colorectal patients. Int J Colorectal Dis. 2023 Jun 24;38(1):177. doi: 10.1007/s00384-023-04472-z. PMID: 37354325.Purpose: To identify 5-year survival prognostic variables in patients with colorectal cancer (CRC) and to propose a survival prognostic score that also takes into account changes over time in the patient's health-related quality of life (HRQoL) status. Methods: Prospective observational cohort study of CRC patients. We collected data from their diagnosis, intervention, and at 1, 2, 3, and 5 years following the index intervention, also collecting HRQoL data using the EuroQol-5D-5L (EQ-5D-5L), European Organization for Research and Treatment of Cancer's Quality of Life Questionnaire-Core 30 (EORTC-QLQ-C30), and Hospital Anxiety and Depression Scale (HADS) questionnaires. Multivariate Cox proportional models were used. Results: We found predictors of mortality over the 5-year follow-up to be being older; being male; having a higher TNM stage; having a higher lymph node ratio; having a result of CRC surgery classified as R1 or R2; invasion of neighboring organs; having a higher score on the Charlson comorbidity index; having an ASA IV; and having worse scores, worse quality of life, on the EORTC and EQ-5D questionnaires, as compared to those with higher scores in each of those questionnaires respectively. Conclusions: These results allow preventive and controlling measures to be established on long-term follow-up of these patients, based on a few easily measurable variables. Implications for cancer survivors: Patients with colorectal cancer should be monitored more closely depending on the severity of their disease and comorbidities as well as the perceived health-related quality of life, and preventive measures should be established to prevent adverse outcomes and therefore to ensure that better treatment is received. Trial registration: ClinicalTrials.gov identifier: NCT02488161.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was supported in part by grants from the Instituto de Salud Carlos III and the European Regional Development Fund (PS09/00314, PS09/00910, PS09/00746, PS09/00805, PI09/90460, PI09/90490, PI09/90453, PI09/90441, PI09/90397); the Spanish Ministry of the Economy (PID2020-115738 GB-I00); the Departments of Health (2010111098) and Education, Language Policy and Culture (IT1456-22; IT1598-22; IT-1187–19) of the Basque Government; the Research Committee of Galdakao Hospital; the REDISSEC (Red de Investigación en Servicios de Salud en Enfermedades Crónicas) thematic network of the Instituto de Salud Carlos III; and the Department of Education of the Basque Government through the Consolidated Research Group MATHMODE (IT1456-22) and the Basque Government through BMTF “Mathematical Modeling Applied to Health” Project.S

Five-year follow-up mortality prognostic index for colorectal patients

Purpose: To identify 5-year survival prognostic variables in patients with colorectal cancer (CRC) and to propose a survival prognostic score that also takes into account changes over time in the patient's health-related quality of life (HRQoL) status. Methods: Prospective observational cohort study of CRC patients. We collected data from their diagnosis, intervention, and at 1, 2, 3, and 5 years following the index intervention, also collecting HRQoL data using the EuroQol-5D-5L (EQ-5D-5L), European Organization for Research and Treatment of Cancer's Quality of Life Questionnaire-Core 30 (EORTC-QLQ-C30), and Hospital Anxiety and Depression Scale (HADS) questionnaires. Multivariate Cox proportional models were used. Results: We found predictors of mortality over the 5-year follow-up to be being older; being male; having a higher TNM stage; having a higher lymph node ratio; having a result of CRC surgery classified as R1 or R2; invasion of neighboring organs; having a higher score on the Charlson comorbidity index; having an ASA IV; and having worse scores, worse quality of life, on the EORTC and EQ-5D questionnaires, as compared to those with higher scores in each of those questionnaires respectively. Conclusions: These results allow preventive and controlling measures to be established on long-term follow-up of these patients, based on a few easily measurable variables. Implications for cancer survivors: Patients with colorectal cancer should be monitored more closely depending on the severity of their disease and comorbidities as well as the perceived health-related quality of life, and preventive measures should be established to prevent adverse outcomes and therefore to ensure that better treatment is received. Trial registration: ClinicalTrials.gov identifier: NCT02488161Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work was supported in part by grants from the Instituto de Salud Carlos III and the European Regional Development Fund (PS09/00314, PS09/00910, PS09/00746, PS09/00805, PI09/90460, PI09/90490, PI09/90453, PI09/90441, PI09/90397); the Spanish Ministry of the Economy (PID2020-115738 GB-I00); the Departments of Health (2010111098) and Education, Language Policy and Culture (IT1456-22; IT1598-22; IT-1187–19) of the Basque Government; the Research Committee of Galdakao Hospital; the REDISSEC (Red de Investigación en Servicios de Salud en Enfermedades Crónicas) thematic network of the Instituto de Salud Carlos III; and the Department of Education of the Basque Government through the Consolidated Research Group MATHMODE (IT1456-22) and the Basque Government through BMTF “Mathematical Modeling Applied to Health” Project

Derivation and validation of a prognostic model for predicting in-hospital mortality in patients admitted with COVID-19 in Wuhan, China:the PLANS (platelet lymphocyte age neutrophil sex) model

Background Previous published prognostic models for COVID-19 patients have been suggested to be prone to bias due to unrepresentativeness of patient population, lack of external validation, inappropriate statistical analyses, or poor reporting. A high-quality and easy-to-use prognostic model to predict in-hospital mortality for COVID-19 patients could support physicians to make better clinical decisions. Methods Fine-Gray models were used to derive a prognostic model to predict in-hospital mortality (treating discharged alive from hospital as the competing event) in COVID-19 patients using two retrospective cohorts (n = 1008) in Wuhan, China from January 1 to February 10, 2020. The proposed model was internally evaluated by bootstrap approach and externally evaluated in an external cohort (n = 1031). Results The derivation cohort was a case-mix of mild-to-severe hospitalized COVID-19 patients (43.6% females, median age 55). The final model (PLANS), including five predictor variables of platelet count, lymphocyte count, age, neutrophil count, and sex, had an excellent predictive performance (optimism-adjusted C-index: 0.85, 95% CI: 0.83 to 0.87; averaged calibration slope: 0.95, 95% CI: 0.82 to 1.08). Internal validation showed little overfitting. External validation using an independent cohort (47.8% female, median age 63) demonstrated excellent predictive performance (C-index: 0.87, 95% CI: 0.85 to 0.89; calibration slope: 1.02, 95% CI: 0.92 to 1.12). The averaged predicted cumulative incidence curves were close to the observed cumulative incidence curves in patients with different risk profiles. Conclusions The PLANS model based on five routinely collected predictors would assist clinicians in better triaging patients and allocating healthcare resources to reduce COVID-19 fatality