Standard Proportional Hazards Research Articles

Displacement and debt – the role of debt in returning to work after displacement

PurposeThis paper aims to analyze the question of how household indebtedness impacts households’ incentives to search for and accept work after displacement.Design/methodology/approachTo analyze the relationship between household indebtedness and unemployment duration, this paper applies standard proportional hazard models. For data, this paper relies on the longitudinal US National Survey of Income and Program Participation (SIPP), covering the period between 2008 and 2012.FindingsThe findings show that a 10% increase in household debt increases the likelihood (hazard) of leaving unemployment by 0.2%–0.4% points. Independent of measuring a household's indebtedness and in light of a series of robustness tests, the results indicate that the pressure of servicing an existing debt burden forces individuals to return to work.Social implicationsFrom a policy perspective, the research findings support the notion that household indebtedness plays an important mediating role for labor market outcomes through influencing households’ incentives to return to work after displacement. This finding has important implications for the design of effective policy responses to mass layoffs during the current pandemic.Originality/valueA key innovation of the research is that we can show that household indebtedness impacts the labor supply side. From a macroeconomic perspective, this insight is important in better understanding the role of increased indebtedness (and financialization) in amplifying aggregate macroeconomic dynamics.

Estimating heterogeneous treatment effects for latent subgroups in observational studies.

Individuals may vary in their responses to treatment, and identification of subgroups differentially affected by a treatment is an important issue in medical research. The risk of misleading subgroup analyses has become well known, and some exploratory analyses can be helpful in clarifying how covariates potentially interact with the treatment. Motivated by a real data study of pediatric kidney transplant, we consider a semiparametric Bayesian latent model and examine its utility for an exploratory subgroup effect analysis using secondary data. The proposed method is concerned with a clinical setting where the number of subgroups is much smaller than that of potential predictors and subgroups are only latently associated with observed covariates. The semiparametric model is flexible in capturing the latent structure driven by data rather than dictated by parametric modeling assumptions. Since it is difficult to correctly specify the conditional relationship between the response and a large number of confounders in modeling, we use propensity score matching to improve the model robustness by balancing the covariates distribution. Simulation studies show that the proposed analysis can find the latent subgrouping structure and, with propensity score matching adjustment, yield robust estimates even when the outcome model is misspecified. In the real data analysis, the proposed analysis reports significant subgroup effects on steroid avoidance in kidney transplant patients, whereas standard proportional hazards regression analysis does not.

Performance of Principal Stratification Method Adjusting for Treatment Noncompliance in Two Arms of a Randomized Trial

The method of principal stratification is a unifying framework for modelling cause and effect which is applicable to adjusting for treatment noncompliance in multiple arms of a trial. Baseline covariates which predict compliance with treatment are useful in addressing parameter identification problem associated with principal stratification. Roy, Hogan and Marcus (RHM) (2008) proposed a principal stratification framework in which they used baseline covariates to adjust for imperfect compliance in both arms of a two-active treatments trial. Key to the application of this method is a defining but untestable distributional assumption whose robustness is unknown. The present work uses statistically designed simulation studies in the framework of a clinical trial comparing two active treatments as applied to survival data under both homogeneous and heterogeneous treatment effect assumptions to evaluate the performance of the RHM method in terms of bias and $95\%$ credible intervals. We first apply the standard proportional hazard model to obtain the ITT estimate and evaluate resulting bias if viewed as estimating a causal hazard ratio. We then compare the method's performance in terms of stratum-specific causal relative risk for different specifications of a user-defined spectrum parameter. The results showed no effect of the spectrum parameter on the ITT estimates. The RHM method performed poorly by producing significantly biased efficacy estimates in all strata with wider corresponding $95\%$ credible intervals under heterogeneous treatment effect assumption. The resulting efficacy estimates varied a lot depending on the value of the unknown (user-defined) spectrum parameter.

NPHMC: An R-package for estimating sample size of proportional hazards mixture cure model

Due to advances in medical research, more and more diseases can be cured nowadays, which largely increases the need for an easy-to-use software in calculating sample size of clinical trials with cure fractions. Current available sample size software, such as PROC POWER in SAS, Survival Analysis module in PASS, powerSurvEpi package in R are all based on the standard proportional hazards (PH) model which is not appropriate to design a clinical trial with cure fractions. Instead of the standard PH model, the PH mixture cure model is an important tool in handling the survival data with possible cure fractions. However, there are no tools available that can help design a trial with cure fractions. Therefore, we develop an R package NPHMC to determine the sample size needed for such study design.

Uncovering Symptom Progression History from Disease Registry Data with Application to Young Cystic Fibrosis Patients

The growing availability of various disease registry data has brought precious opportunities to epidemiologists to understand the natural history of the registered diseases. It also presents challenges to the traditional data analysis techniques because of complicated censoring/truncation schemes and temporal dynamics of covariate influences. In a case study of the Cystic Fibrosis Foundation Patient Registry data, we propose analyses of progressive symptoms using temporal process regressions, as an alternative to the commonly employed proportional hazards models. Two endpoints are considered, the prevalence of ever positive and currently positive for Pseudomonas aeruginosa (PA) infection in the lungs, which capture different aspect of the disease process. The analysis of ever PA positive via a time-varying coefficient model demonstrates the lack of fit, as well as the potential loss of information, in the standard proportional hazards analysis. The analysis of currently PA positive yields results that are clinically meaningful and have not previously been reported in the cystic fibrosis literature. Our analyses demonstrate that prenatal/neonatal screening results in lower prevalence of PA infection compared to traditional diagnosis via signs and symptoms, but this benefit attenuates with age. Calendar years of diagnosis also affect the risk of PA infection; patients diagnosed in more recent cohort show higher prevalence of ever PA positive but lower prevalence of currently PA positive.

Analysis of time-to-event and duration outcomes in neonatal clinical trials with twin births

When conducting neonatal trials in pre-term and/or low-birth-weight infants, twins may represent 10–20% of the study sample. Frailty models and proportional hazards regression with a robust sandwich variance estimate are common approaches for handling correlated time-to-event data or duration outcomes that are subject to censoring. However, the operating characteristics of these methods for mixes of correlated and independent time-to-event data are not well established. Simulation studies were conducted to compare frailty models and proportional hazards regression models with a robust sandwich variance estimate to standard proportional hazards regression models to estimate the treatment effect in two-armed clinical trials. While overall frailty models showed the best performance, caution must be exercised as the interpretation of the parameters differs from the marginal models. Data from the National Institute of Child Health & Human Development sponsored PROPHET trial are used for illustration.

Incorporating validation subsets into discrete proportional hazards models for mismeasured outcomes

Standard proportional hazards methods are inappropriate for mismeasured outcomes. Previous work has shown that outcome mismeasurement can bias estimation of hazard ratios for covariates. We previously developed an adjusted proportional hazards method that can produce accurate hazard ratio estimates when outcome measurement is either non-sensitive or non-specific. That method requires that mismeasurement rates (the sensitivity and specificity of the diagnostic test) are known. Here, we develop an approach to handle unknown mismeasurement rates. We consider the case where the true failure status is known for a subset of subjects (the validation set) until the time of observed failure or censoring. Five methods of handling these mismeasured outcomes are described and compared. The first method uses only subjects on whom complete data are available (validation subset), whereas the second method uses only mismeasured outcomes (naive method). Three other methods include available data from both validated and non-validated subjects. Through simulation, we show that inclusion of the non-validated subjects can improve efficiency relative to use of the complete case data only and that inclusion of some true outcomes (the validation subset) can reduce bias relative to use of mismeasured outcomes only. We also compare the performance of the validation methods proposed using an example data set.

Estimation of genetic and environmental factors for melanoma onset using population‐based family data

Estimation of genetic and environmental contributions to cancers falls in the framework of generalized linear mixed modelling with several random effect components. Computational challenges remain, however, in dealing with binary or survival phenotypes. In this paper, we consider the analysis of melanoma onset in a population of 2.6 million nuclear families in Sweden, for which none of the current survival-based methodologies is feasible. We treat the disease outcome as a binary phenotype, so that the standard proportional hazard model leads to a generalized linear model with the complementary-log link function. For rare diseases this link is very close to the probit link, and thus allows the use of marginal likelihood for the estimation of the variance components. We correct for the survival length bias by censoring the parent generation within each family at the time they attain the same cumulative hazard as the child generation, thus improving the validity of the estimates. Our finding that childhood shared environment in addition to genetic factors had a considerable effect on the development of melanoma is consistent with epidemiological studies.

Discrete proportional hazards models for mismeasured outcomes.

Outcome mismeasurement can lead to biased estimation in several contexts. Magder and Hughes (1997, American Journal of Epidemiology 146, 195-203) showed that failure to adjust for imperfect outcome measures in logistic regression analysis can conservatively bias estimation of covariate effects, even when the mismeasurement rate is the same across levels of the covariate. Other authors have addressed the need to account for mismeasurement in survival analysis in selected cases (Snapinn, 1998, Biometrics 54, 209-218; Gelfand and Wang, 2000, Statistics in Medicine 19, 1865-1879; Balasubramanian and Lagakos, 2001, Biometrics 57, 1048-1058, 2003, Biometrika 90, 171-182). We provide a general, more widely applicable, adjusted proportional hazards (APH) method for estimation of cumulative survival and hazard ratios in discrete time when the outcome is measured with error. We show that mismeasured failure status in a standard proportional hazards (PH) model can conservatively bias estimation of hazard ratios and that inference, in most practical situations, is more severely affected by poor specificity than by poor sensitivity. However, in simulations over a wide range of conditions, the APH method with correctly specified mismeasurement rates performs very well.

Martingale difference residuals as a diagnostic tool for the Cox model

The proportional hazards model makes two major assumptions: the hazard ratio is constant over time, and the relationship between the hazard and continuous covariates is log‐linear. Methods exist for checking and relaxing each of these assumptions, but in both cases the methods rely on the other assumption being true. Problems can occur if neither of the assumptions is appropriate, or even if only one of the assumptions is appropriate but it is not known which. We propose a new kind of residual for checking the two assumptions simultaneously. The smoothed residuals provide a flexible estimate of the hazard ratio, which may deviate from the standard proportional hazards model by having a time‐dependent hazard ratio, transformed covariates or both. The methods are illustrated using data from the Medical Research Council's myeloma trials.

Joint models for efficient estimation in proportional hazards regression models.

In survival studies, information lost through censoring can be partially recaptured through repeated measures data which are predictive of survival. In addition, such data may be useful in removing bias in survival estimates, due to censoring which depends upon the repeated measures. Here we investigate joint models for survival T and repeated measurements Y, given a vector of covariates Z. Mixture models indexed as f (T/Z) f (Y/T,Z) are well suited for assessing covariate effects on survival time. Our objective is efficiency gains, using non-parametric models for Y in order to avoid introducing bias by misspecification of the distribution for Y. We model (T/Z) as a piecewise exponential distribution with proportional hazards covariate effect. The component (Y/T,Z) has a multinomial model. The joint likelihood for survival and longitudinal data is maximized, using the EM algorithm. The estimate of covariate effect is compared to the estimate based on the standard proportional hazards model and an alternative joint model based estimate. We demonstrate modest gains in efficiency when using the joint piecewise exponential joint model. In a simulation, the estimated efficiency gain over the standard proportional hazards model is 6.4 per cent. In clinical trial data, the estimated efficiency gain over the standard proportional hazards model is 10.2 per cent.

Semiparametric Autoregressive Conditional Proportional Hazard Models

A new semiparametric proportional hazard rate model is proposed which extends standard models to include a dynamic specification. Two main problems are resolved in the course of this paper. First, the partial likelihood approach to estimate the components of a standard proportional hazard model is not available in a dynamic model involving lags of the log integrated baseline hazard. We use therefore a discretisation approach to obtain a semiparametric estimate of the baseline hazard. Therefore, second, the log integrated baseline hazard is not observed directly, but only through a threshold function. We employ a special type of observation driven dynamic which allows for a computationally simple maximum likelihood estimation. This specification approximates a standard ARMA model in the log integrated baseline hazard and is identical if the baseline hazard is known. It is shown that this estimator is quite exible and easily extended to include unobserved heterogeneity, censoring and state dependent hazard rates. A Monte Carlo study on the approximation quality of the model and an empirical study on BUND future trading at the former DTB complement the paper.

Analysis of competing risks survival data when some failure types are missing

We propose a method to analyse competing risks survival data when failure types are missing for some individuals. Our approach is based on a standard proportional hazards structure for each of the failure types, and involves the solution to estimating equations. We present consistent and asymptotically normal estimators of the regression coefficients and related score tests. An appealing feature is that individuals with known failure types make the same contributions as they would to a standard proportional hazards analysis. Contributions of individuals with unknown failure types are weighted according to the probability that they failed from the cause of interest. Efficiency and robustness are discussed. Results are illustrated with data from a breast cancer trial.

Extent of blood transfusion and cancer‐related mortality after cystectomy and urinary diversion for bladder cancer

To assess the possible adverse effect of peri-operative blood transfusion on cancer-related survival after radical cystectomy for bladder cancer. The hospital records of 130 patients treated with cystectomy and urinary diversion for bladder cancer between 1967 and 1986 were retrospectively reviewed. Standard proportional hazards estimation revealed tumour stage and radiation response after pre-operative irradiation to be significantly associated with cancer-related mortality, whereas age, tumour grade or the extent of peri-operative blood transfusion were not. In models which allowed time varying effects a significantly changed effect of blood transfusion (> or = 7 versus < or = 6 units) was observed, from an initially insignificantly increased relative hazard (RH) (RH = 1.44 at 6 months) to an insignificantly decreased effect after longer follow-up (RH = 0.53 after 2 years). Although no overall association between blood transfusion and cancer-related mortality was found, a tendency towards an increased risk early in the follow-up period was observed if more than 6 units were transfused. However, these results need confirmation in further studies before a restrictive attitude towards peri-operative blood transfusion is recommended.

An Application of Dynamic Survival Models in Unemployment Studies

New dynamic Bayesian models for survival data analysis are applied in a study of contributory factors to unemployment. The models treat survival data as time series data, reflecting the need to model time varying relationships with explanatory variables that cannot be accommodated within standard proportional hazard models. In the present study, prior expectations that the effects of various socio-economic variables on unemployment spells are time dependent are verified. Assessment of these effects are given and uses of the model in predicting unemployment illustrated.