Discrete-time Proportional Hazards Models Research Articles

Firm dynamics of hi-tech start-ups: Does innovation matter?

Innovation plays a vital role in corporate issues since it brings potentially appreciable profits and shores up their statuses in certain fields, although it may also harness firms, especially smaller ones, with high survival risks. This concern brings forth our research topic: will participating in innovation activities diminish small firms' risk of exit from the market? Our paper concentrates on hi-tech start-ups and complements existing firm dynamic studies by adopting a comprehensive annual survey dataset from a considerable science park located in Beijing. Using an efficient discrete-time proportional hazards model, and thanks to extensive data available, we can take a deeper investigation into this topic. Our research complies with most of the previous studies that show that the benefit from innovativeness outweighs the cost and we solidify our conclusions by considering a few distinctive features existing in China's economy.

A general semiparametric Bayesian discrete-time recurrent events model

Event time variables are often recorded in a discrete fashion, especially in the case of patient-reported outcomes. This work is motivated by a study of illicit drug users, in which time to drug use cessation has been recorded as a number of whole months. Existing approaches for handling such discrete data include treating the survival times as continuous (with adjustments for inevitable tied outcomes), or using discrete models that omit important features like random effects. We provide a general Bayesian discrete-time proportional hazards model, incorporating a number of features popular in continuous-time models such as competing risks and frailties. Our model also provides flexible baseline hazards for time effects, as well as generalized additive models style semiparametric incorporation of other time-varying covariates. Our specific modeling choices enable efficient Markov chain Monte Carlo inference algorithms, which we provide to the user in the form of a freely available R package called $\texttt{brea}$. We demonstrate that our model performs better on our motivating substance abuse application than existing approaches. We also present a reproducible application of the $\texttt{brea}$ software to a freely available data set from a clinical trial of anesthesia administration methods.

Contraceptive use at first intercourse is associated with subsequent sexual behaviors

ObjectiveWomen's contraceptive use at first sexual intercourse (FSI) may be associated with subsequent sexual behaviors. We examined associations between contraceptive methods used at FSI and subsequent number of lifetime partners, induced abortions and sexually transmitted infections (STIs). Study designDuring 2011–2012, we collected questionnaire data from a random sample of women aged 18–45 years from Denmark, Norway and Sweden. We used logistic regression and discrete-time proportional hazards models to estimate odds ratios (ORs) and hazard ratios (HRs) with 95% confidence intervals (CIs), comparing different contraceptive methods used at FSI in the whole study sample and in women with FSI in 2001 or later [when emergency contraceptive pills (ECPs) were available without prescription]. ResultsOf 45,361 women in the study sample, those who did not use contraception at FSI (n=8155; 18.0%) were more likely than condom users to have ≥11 lifetime partners (OR=1.34; 95% CI 1.27–1.42), induced abortions (HR=1.62; 95% CI 1.53–1.71) and STIs (HR=1.15; 95% CI 1.10–1.20). ECP users (n=440, 1.0%) were more likely than condom users to have ≥11 lifetime partners (OR=1.76; 95% CI 1.40–2.22), induced abortions (HR=1.44; 95% CI 1.11–1.86) and STIs (HR=1.84; 95% CI 1.56–2.16). A similar pattern was seen in safe periods/withdrawal users. The associations did not change among women with FSI in 2001 or later (n=14,445). ConclusionsCompared with condom use, contraceptive nonuse, safe periods/withdrawal use and ECP use at FSI were associated with subsequent number of sexual partners, induced abortions and STIs. ImplicationsContraceptive method used at first intercourse was associated with subsequent sexual behaviors in women. This study highlights the importance of early sexual behaviors and may help understand patterns of women's sexual behaviors.

Female adiposity and time-to-pregnancy: a multiethnic prospective cohort

Are higher overall and central adiposity associated with reduced fecundability, measured by time-to-pregnancy (TTP), in Asian women? Higher overall adiposity, but not central adiposity, was associated with longer TTP in Asian women. High body mass index (BMI) has been associated with a longer TTP, although the associations of body composition and distribution with TTP are less clear. There are no previous studies of TTP in Asian women, who have a relatively higher percentage of body fat and abdominal fat at relatively lower BMI. Prospective preconception cohort using data from 477 Asian (Chinese, Malay and Indian) women who were planning to conceive and enrolled in the Singapore PREconception Study of long-Term maternal and child Outcomes (S-PRESTO) study, 2015-2017. Women's mean age was 30.7 years. Overall adiposity was assessed by BMI, sum of 4-site skinfold thicknesses (SFT) and total body fat percentage (TBF%, measured using air displacement plethysmography); central adiposity was assessed by waist circumference (WC), waist-to-hip ratio (WHR), waist-to-height ratio (WHtR) and A body Shape Index (ABSI). Pregnancy occurring within one year from recruitment was ascertained by ultrasonography. Those who did not conceive within one year of recruitment, were lost to follow-up, or initiated fertility treatment were censored. TTP was measured in cycles. Discrete-time proportional hazards models were used to estimate the fecundability ratio (FR) and 95% confidence interval (CI) for each anthropometric measure in association with fecundability, adjusting for confounders. Compared to women with a normal BMI of 18.5-22.9 kg/m2, women with higher BMI of 23-27.4 and ≥27.5 kg/m2 showed lower FR of 0.66 (95% CI 0.45, 0.97) and 0.53 (0.31, 0.89), respectively. Compared to women in the lowest quartile of SFT (25-52.9 mm), those in the highest quartile of ≥90.1 mm showed lower FR of 0.58 (95% CI 0.36, 0.95). Compared to women in the lowest quartile of TBF% (13.6-27.2%), those in the upper two quartiles of 33.0-39.7% and ≥39.8% showed lower FR of 0.56 (95% CI 0.32, 0.98) and 0.43 (0.24, 0.80), respectively. Association of high BMI with reduced fecundability was particularly evident among nulliparous women. Measures of central adiposity (WC, WHR, WHtR, ABSI) were not associated with fecundability. Small sample size could restrict power of analysis.The analysis was confined to planned pregnancies, which could limit generalizability of findings to non-planned pregnancies, estimated at around 44% in Singapore. Information on the date of last menstrual period for each month was not available, hence the accuracy of self-reported menstrual cycle length could not be validated, potentially introducing error into TTP estimation. Measures of exposures and covariates such as cycle length were not performed repeatedly over time; cycle length might have changed during the period before getting pregnant. Other than using BMI as the surrogate measure of body fat, we provide additional evidence showing that higher amounts of subcutaneous fat that based on the measure of SFT at the sites of biceps, triceps, suprailiac and subscapular, and TBF% are associated with longer TTP. Achieving optimal weight and reducing total percentage body fat may be a potential intervention target to improve female fertility. The null results observed between central adiposity and TTP requires confirmation in further studies. This research is supported by Singapore National Research Foundation under its Translational and Clinical Research Flagship Programme and administered by the Singapore Ministry of Health's National Medical Research Council, (NMRC/TCR/004-NUS/2008; NMRC/TCR/012-NUHS/2014). Additional funding is provided by the Singapore Institute for Clinical Sciences, Agency for Science Technology and Research (A*STAR), Singapore. Y.S.C., K.M.G., F.Y. and Y.S.L. have received reimbursement to speak at conferences sponsored by companies selling nutritional products. Y.S.C., K.M.G. and S.Y.C. are part of an academic consortium that has received research funding from Abbott, Nutrition, Nestle and Danone. Other authors declared no conflicts of interest. N/A.

Time course of panic disorder and posttraumatic stress disorder onsets.

Posttraumatic stress disorder (PTSD) often co-occurs with panic disorder (PD), with some etiological models positing a causal role of panic reactivity in PTSD onset; however, data addressing the temporal ordering of these conditions are lacking. The aim of this study was to examine the bi-directional associations between PD and PTSD in a nationally representative, epidemiologic sample of trauma-exposed adults. Participants were community-dwelling adults (62.6% women; Mage = 48.9, SD 16.3) with lifetime DSM-IV PTSD criterion A trauma exposure drawn from the 2001/2 National Epidemiologic Survey on Alcohol and Related Conditions (NESARC) and re-interviewed in 2004/5 (N = 12,467). Cox discrete-time proportional hazards models with time-varying covariates were used to investigate the bi-directional associations between lifetime PD and PTSD, accounting for demographic characteristics, trauma load, and lifetime history of major depression, generalized anxiety disorder, and social anxiety disorder. PD was significantly associated with subsequent onset of PTSD (HR 1.210, 95%CI = 1.207-1.214, p < .001), and PTSD was significantly associated with onset of PD (HR 1.601, 95% CI 1.597-1.604, p < .001). The association between PTSD and subsequent PD was stronger in magnitude than that between PD and subsequent PTSD (Z = - 275.21, p < .01). Men evidenced stronger associations between PD and PTSD compared to women. Results were consistent with a bidirectional pathway of risk, whereby PD significantly increased risk for the development of PTSD, and PTSD significantly increased risk for PD. Given the association between PTSD and subsequent PD, particularly among men, clinicians may consider supplementing PTSD treatment with panic-specific interventions, such as interoceptive exposure, to prevent or treat this disabling comorbidity.

Relation of Coronary Artery Calcium and Extra-Coronary Aortic Calcium to Incident Hypertension (from the Multi-Ethnic Study of Atherosclerosis)

Arterial calcification reflects an atherosclerotic process associated with vascular stiffness. Whether baseline coronary artery calcium (CAC) and extra-coronary calcium (ECC), measured using noncontrast computed tomography imaging, are associated with incident hypertension is poorly understood. We studied participants from the Multi-Ethnic Study of Atherosclerosis without measured or self-reported hypertension at baseline. Incident hypertension was defined by blood pressure criteria (BP, ≥140/90 mmHg), BP medication use, or both, and was assessed at in-person visits. We analyzed incident hypertension using multivariable-adjusted discrete-time proportional hazards models. Net reclassification improvement (NRI) assessed whether CAC reclassified hypertension risk when added to the Framingham hypertension risk score. Among 3,304 subjects analyzed, mean age was 59 ± 10 years; 48% were male and 42% were white. There were 1,283 incident hypertension cases over a median (interquartile range) follow-up time of 10.6 (4.5, 11.5) years. Each 1-unit increase in ln(CAC+1) was independently associated with a 12% higher risk of hypertension (95% confidence interval [CI] 9% to 16%). Relative to CAC = 0, patients with CAC >400 had a hazard ratio for incident hypertension of 2.2 (95% CI 1.8 to 2.9). There was no interaction by age, gender, or baseline BP (p = 0.43, 0.19, 0.09, respectively). Continuous NRI analyses demonstrated that CAC can reclassify risk of incident hypertension; NRI = 0.19 (95% CI 0.10 to 0.26). Furthermore, all measurements of ECC were significantly associated with incident hypertension, even after adjustment for CAC (hazard ratios ranging from 1.36 to 1.38). In conclusion, patients with CAC and ECC are at markedly higher risk of incident hypertension and may benefit from more intensified prevention efforts.

Faster Estimation of Discrete Time Duration Models with Unobserved Heterogeneity Using Hshaz2

This article presents hshaz2, a new Stata command that uses d2 ml method to estimate discrete time duration models with unobserved heterogeneity. The main advantage of using hshaz2 is the gain in computation speed, that takes special relevance as the sample size increases. Estimation results show that, on a sample size of 568,042 observations, hshaz2 spends 0.42 and 1.13 minutes to achieve the convergence of a discrete time proportional hazard model with two and three points of support, respectively. Furthermore, hshaz2 allows for the estimation of multispell duration models, where individuals may be observed at risk of exiting more than once. Using a sample with 1,547,507 observations, hshaz2 spends 1.17 and 2.17 minutes to achieve convergence of a multispell discrete time proportional hazard model with two and three points of support, respectively.

The Relationship of Financial Pressures and Community Characteristics to Closure of Private Safety Net Clinics.

In order to better understand what threatens vulnerable populations' access to primary care, it is important to understand the factors associated with closing safety net clinics. This article examines how a clinic's financial position, productivity, and community characteristics are associated with its risk of closure. We examine patterns of closures among private-run primary care clinics (PCCs) in California between 2006 and 2012. We use a discrete-time proportional hazard model to assess relative hazard ratios of covariates, and a random-effect hazard model to adjust for unobserved heterogeneity among PCCs. We find that lower net income from patient care, smaller amount of government grants, and lower productivity were associated with significantly higher risk of PCC closure. We also find that federally qualified health centers and nonfederally qualified health centers generally faced the same risk factors of closure. These results underscore the critical role of financial incentives in the long-term viability of safety net clinics.

Helminth infection is associated with hen mortality in Danish organic egg production

The aim of this study was to investigate whether two highly prevalent helminth infections (Ascaridia galli and Heterakis species) are associated with an increased mortality rate for hens at the...

Military service and smoking in a cohort of northern Vietnamese older adults.

Wide-ranging scholarship demonstrates war's impacts on US veterans' health. We ask whether, among Vietnamese men of a certain age, wartime experiences contributed to initiating smoking, and thus shaped one behavioral pathway linking war exposure and older adult health. We analyze the Vietnam Health and Aging Pilot Study (VHAPS), a survey of adults ages 55 and older (N=405) conducted in one commune of northern Vietnam. We implement Cox discrete-time proportional hazards models to discern the effects of military service upon the initiation of smoking. Military service results in a heightened risk of initiating smoking within this cohort (HR 2.13, [CI 1.36, 3.35]). Smoking initiation is also significantly gendered and age graded. Socioeconomic position and social capital variables in the models are statistically insignificant. This study finds that, among older northern Vietnamese men whose early adulthood coincided with mass mobilization in the Vietnam War, involvement in formal military service significantly increased the risk of initiating smoking. Military-induced smoking emerges where tobacco products were not provided by the military institution, but where social availability of tobacco was widespread.

Frequent injection cocaine use increases the risk of renal impairment among hepatitis C and HIV coinfected patients.

To examine the association between injection cocaine use, hepatitis C virus (HCV) infection, and chronic renal impairment (CRI). Prospective observational cohort study of HIV-HCV coinfected patients. Data from 1129 participants in the Canadian Co-Infection Cohort with baseline and follow-up serum creatinine measurements between 2003 and 2014 were analyzed. Prevalent and incident cohorts were created to examine the association between self-reported past, current, and cumulative cocaine use and chronic HCV with CRI. CRI was defined as an estimated glomerular filtration rate below 70 ml/min per 1.73 m. Multivariate logistic regression was used to calculate odds ratios, and discrete-time proportional-hazards models were used to calculate hazard ratios for cocaine use, in the two respective cohorts, adjusted for HCV RNA and important demographic, HIV disease stage, and comorbidity confounders. Eighty-seven participants (8%) had prevalent CRI. Past injection cocaine use was associated with a two-fold greater risk of prevalent CRI [odds ratio 2.03, 95% confidence interval (CI) 0.96, 4.32]. During follow-up, 126 of 1061 participants (12%) developed incident CRI (31 per 1000 person-years). Compared to nonusers, heavy (≥ 3 days/week) and frequent injection cocaine users (≥75% of follow-up time) experienced more rapid progression to CRI (hazard ratio 2.65, 95% CI 1.35, 5.21; and hazard ratio 1.82, 95% CI 1.07, 3.07, respectively). There was no association between chronic HCV and CRI in either cohort. After accounting for HCV RNA, frequent and cumulative injection cocaine abuse was associated with CRI progression and should be taken into consideration when evaluating impaired renal function in HIV-HCV coinfection.

Preoperative motor strength and time to surgery are the most important predictors of improvement in foot drop due to degenerative lumbar disease

ObjectivePalsy of dorsiflexion, or foot drop, may be due to degenerative lumbar disease and amenable to posterior spinal decompression. The objective of this study is to measure prognostic factors of and time to foot drop improvement after posterior lumbar decompression. MethodsWe retrospectively reviewed 71 patients undergoing first-time, posterior lumbar decompression for foot drop due to degenerative spinal disease. Patient sex, age, comorbidities (Charlson Comorbidity Index), preoperative anterior tibialis strength (manual muscle testing, MMT), and duration of foot drop were ascertained from clinical notes. Prognostic factors affecting foot drop improvement were calculated with a discrete time proportional hazards model, in which follow-up times and outcome measures were binned into six time intervals: 1week, 6weeks, 3months, 6months, 1year, and ≥1year. ResultsOf the 71 patients, the mean age was 54.6±16.0years, and 66.2% (n=47) were males. The mean Charlson Comorbidity Index was 2.42. During a mean follow-up of 30.4months, dorsiflexion function improved postoperatively in 73.2% (n=52) of patients. The median time to surgery from onset of foot drop was within 6weeks, and the median preoperative MMT strength of patients with foot drop improvement was 3. Following a discrete-time proportional hazards model, duration of anterior tibialis palsy (HR=0.67, P=0.004) and preoperative muscle strength (HR=1.10, P=0.010) were significant predictors of foot drop improvement. Following an adjusted Kaplan–Meier analysis, the median time to foot drop improvement was within 6weeks of surgical intervention. ConclusionsPreoperative muscle strength and palsy duration were statistically significant predictors of foot drop improvement. Furthermore, the median time to improvement was 6weeks.

Manual muscle test at C5 palsy onset predicts the likelihood of and time to C5 palsy resolution

The primary objective of this study was to identify time to and prognostic factors of C5 palsy resolution. All patients over a 7year period who experienced C5 palsy following a posterior decompression and instrumented fusion surgery were retrospectively reviewed. C5 palsy resolution was defined as a recovery of deltoid muscle function equal to or greater than the preoperative condition as defined by the manual muscle test (MMT). Of the 511 patients who met the selection criteria, 8.6% (n=44) experienced C5 palsy. MMT information was available for 43 patients; 81.4% (n=35) had full resolution from their condition. Of the 35 patients who resolved, the median MMT score at onset was 3−. Following a discrete-time proportional hazards model, the hazards of C5 palsy resolution increased by 19% for every one-grade increase in MMT score at symptom onset (hazard ratio [HR]=1.19, p=0.005). Moreover, males displayed a 71% lower hazard of resolution than females (HR=0.29, p=0.003). Following an adjusted Kaplan–Meier analysis, the median time to C5 palsy resolution was between 6months and 1year. In a multiple linear regression, a lower MMT score at the onset of C5 palsy predicted a longer time to C5 palsy resolution (coefficient=−0.19, p=0.003). Time to C5 palsy onset was not statistically associated with hazards of palsy resolution (p=0.381) or time to resolution (p=0.121). A higher MMT score at the onset of C5 palsy statistically significantly predicted a higher chance of resolution and a shorter recovery time. Female sex was also associated with a higher hazard of resolution.

Retinal microvascular calibre and risk of diabetes mellitus: a systematic review and participant-level meta-analysis.

The calibre of the retinal vessels has been linked to diabetes mellitus but studies have not shown consistent results. We conducted a participant-level meta-analysis to evaluate the association between retinal arteriolar and venular calibre and diabetes. We performed a systematic review on MEDLINE and EMBASE for articles published up to December 2014. We identified five population-based prospective cohort studies that provided individual-level data on 18,771 diabetes-free participants. We used discrete time proportional hazards models to estimate pooled HRs of diabetes associated with 1 SD (20 μm) change in retinal vascular calibre. We identified 2,581 incident cases of diabetes over a median follow-up period of 10 years (interquartile interval of 3.4-15.8 years). After adjustment for demographic, lifestyle and clinical factors, retinal venular calibre was significantly associated with incident diabetes (pooled HR 1.09 [95% CI 1.02, 1.15] per SD increase in venular calibre). This association persisted in analyses excluding individuals with <5 years of follow-up (1.07 [1.0, 1.12]) or those with impaired fasting glucose at baseline (1.10 [1.03, 1.17]); in subgroup analyses, the association was stronger in men than in women but was consistent across subgroups of race/ethnicity, smoking status, hypertension and BMI categories. Retinal arteriolar calibre was not associated with diabetes (0.95 [0.86, 1.06] per SD decrease in arteriolar calibre). Wider retinal venules but not narrower retinal arterioles were associated with a modestly increased risk for diabetes. Knowledge of pathological mechanisms underlying wider retinal venule may provide further insights concerning microvascular alterations in diabetes.

Hepatic Fibrosis Progression in HIV-Hepatitis C Virus Co-Infection--The Effect of Sex on Risk of Significant Fibrosis Measured by Aspartate-to-Platelet Ratio Index.

BackgroundIn Hepatitis C virus (HCV) mono-infection, male sex is associated with faster liver fibrosis progression but the effects of sex have not been well studied in HIV-HCV co-infected patients. We examined the influence of sex on progression to significant liver fibrosis in HIV-HCV co-infected adults receiving antiretroviral therapy (ART) using the aspartate aminotransferase-to-platelet ratio index (APRI) as a surrogate biomarker of liver fibrosis.MethodsWe evaluated 308 HIV infected, HCV RNA positive participants of a Canadian multicentre prospective cohort receiving antiretrovirals and without significant liver fibrosis or end-stage liver disease at baseline. We used multivariate discrete-time proportional hazards models to assess the effect of sex on time to significant fibrosis (APRI≥1.5) adjusting for baseline age, alcohol use, cigarette smoking, HCV duration, and APRI and time-updated CD4 count and HIV RNA.ResultsOverall, 55 (18%) participants developed an APRI ≥ 1.5 over 544 person-years of at-risk follow-up time; 18 (21%) women (incidence rate (IR)=14.0/100 PY; 7.5-20.4) and 37 (17%) men (IR=8.9/100 PY; 6.0-11.8). Women had more favourable profiles with respect to traditional risk factors for liver disease progression (younger, shorter duration of HCV infection and less alcohol use). Despite this, female sex was associated with a greater than two-fold increased risk of fibrosis progression (adjusted hazard rate (HR) =2.23; 1.22-4.08).ConclusionsHIV-HCV co-infected women receiving antiretroviral therapy were at significantly greater risk of progressing to liver fibrosis as measured by APRI compared with men. Enhanced efforts to engage and treat co-infected women for HCV are needed.

Psychiatric readmissions in a community-based sample of patients with mental disorders.

This study examined whether receipt of outpatient psychiatric services after hospital discharge was associated with reduced risk of readmission. Treatment records from patients admitted to San Diego County psychiatric hospitals over a one-year period were obtained from the San Diego County Behavioral Health Services electronic health record system. A discrete-time proportional hazards model was used to examine the association of receipt of outpatient psychiatric services with readmission within 30 days of discharge from the index hospitalization. Of the 4,663 patients, 16% were readmitted within 30 days. In an adjusted model, receipt of outpatient therapy after discharge was associated with a greater likelihood of being readmitted (hazard ratio=1.36, 95% confidence interval=1.14-1.67), whereas receipt of case management or medication management was not associated with readmission. The differential risk of readmission by service type suggests a need for studies that explore reasons for an increased risk of readmission with certain types of services.

The Determinants of Subprime Mortgage Performance Following a Loan Modification

We examine the evolution of mortgage modification terms obtained by distressed subprime borrowers during the recent housing crisis and the effect of the various types of modifications on the subsequent loan performance. Using the CoreLogic Loan Performance dataset that contains detailed loan level information on mortgages, modification terms, second liens, and home values, we estimate a discrete time proportional hazard model with competing risks to examine the determinants of post-modification mortgage outcomes. We find that principal reductions are particularly effective at improving loan outcomes, as high loan-to-value ratios are the single greatest contributor to re-default and foreclosure. However, any modification that reduces total payment and interest (P&I) reduces the likelihood of subsequent re-default and foreclosure. Modifications that increase the loan principal—primarily through capitalized interest and fees—are more likely to fail, even while controlling for changes in P&I.

The Determinants of Subprime Mortgage Performance Following a Loan Modification

We examine the evolution of mortgage modification terms obtained by distressed subprime borrowers during the recent housing crisis, and the effect of the various types of modifications on the subsequent loan performance. Using the CoreLogic LoanPerformance dataset that contains detailed loan level information on mortgages, modification terms, second liens, and home values, we estimate a discrete time proportional hazard model with competing risks to examine the determinants of post-modification mortgage outcomes. We find that principal reductions are particularly effective at improving loan outcomes, as high loan-to-value ratios are the single greatest contributor to re-default and foreclosure. However, any modification that reduces total payment and interest (P&I) reduces the likelihood of subsequent re-default and foreclosure. Modifications that involve increasing the loan principal -- primarily through capitalized interest and fees -- are more likely to fail, even controlling for changes in P&I.

The determinants of subprime mortgage performance following a loan modification

We examine the evolution of mortgage modification terms obtained by distressed subprime borrowers during the recent housing crisis, and the effect of the various types of modifications on the subsequent loan performance. Using the CoreLogic LoanPerformance dataset that contains detailed loan level information on mortgages, modification terms, second liens, and home values, we estimate a discrete time proportional hazard model with competing risks to examine the determinants of post-modification mortgage outcomes. We find that principal reductions are particularly effective at improving loan outcomes, as high loan-to-value ratios are the single greatest contributor to re-default and foreclosure. However, any modification that reduces total payment and interest (P&amp;amp;I) reduces the likelihood of subsequent re-default and foreclosure. Modifications that involve increasing the loan principal—primarily through capitalized interest and fees—are more likely to fail, even controlling for changes in P&amp;amp;I.

The Determinants of Subprime Mortgage Performance Following a Loan Modification

We examine the evolution of mortgage modification terms obtained by distressed subprime borrowers during the recent housing crisis, and the effect of the various types of modifications on the subsequent loan performance. Using the CoreLogic LoanPerformance dataset that contains detailed loan level information on mortgages, modification terms, second liens, and home values, we estimate a discrete time proportional hazard model with competing risks to examine the determinants of post-modification mortgage outcomes. We find that principal reductions are particularly effective at improving loan outcomes, as high loan-to-value ratios are the single greatest contributor to re-default and foreclosure. However, any modification that reduces total payment and interest (P&I) reduces the likelihood of subsequent re-default and foreclosure. Modifications that involve increasing the loan principal--primarily through capitalized interest and fees--are more likely to fail, even controlling for change in P&I.