Characterizations of bivariate models using dynamic Kullback–Leibler discrimination measures

In this paper, the residual Kullback–Leibler discrimination information measure is extended to conditionally specified models. The extension is used to characterize some bivariate distributions. These distributions are also characterized in terms of proportional hazard rate models and weighted distributions. Moreover, we also obtain some bounds for this dynamic discrimination function by using the likelihood ratio order and some preceding results.

Characterizations of Bivariate Models Using Some Dynamic Conditional Information Divergence Measures

In this article, we study some relevant information divergence measures viz. Renyi divergence and Kerridge’s inaccuracy measures. These measures are extended to conditionally specifiedmodels and they are used to characterize some bivariate distributions using the concepts of weighted and proportional hazard rate models. Moreover, some bounds are obtained for these measures using the likelihood ratio order

Do Changes in Regulation Affect Employment Duration in Temporary Work Agencies? CES Germany & Europe Working Papers, No. 07.1, 2007

Over the past three decades Germany has repeatedly deregulated the law on temporary agency work by stepwise increasing the maximum period for hiring-out employees and allowing temporary work agencies to conclude fixed-term contracts. These reforms should have had an effect on employment duration within temporary work agencies. Based on an informative administrative data set we use a mixed proportional hazard rate model to examine whether employment duration has changed in response to these reforms. We find that the repeated prolongation of the maximum period for hiring-out employees significantly increased average employment duration while the authorization of fixed-term contracts reduced employment tenure.

Modelling and Analysis of Bivariate Lifetime Data using Reversed Hazard Rates

Department of Statistics, Cochin University of Science and Technology

Reliability prediction using the non-parametric explicit hazard model : a case study

Survival probability prediction using covariate-based hazard approach is a known statistical methodology in engineering asset health management. We have previously reported the semi-parametric Explicit Hazard Model (EHM) which incorporates three types of information: population characteristics; condition indicators; and operating environment indicators for hazard prediction. This model assumes the baseline hazard has the form of the Weibull distribution. To avoid this assumption, this paper presents the non-parametric EHM which is a distribution-free covariate-based hazard model. In this paper, an application of the non-parametric EHM is demonstrated via a case study. In this case study, survival probabilities of a set of resistance elements using the non-parametric EHM are compared with the Weibull proportional hazard model and traditional Weibull model. The results show that the non-parametric EHM can effectively predict asset life using the condition indicator, operating environment indicator, and failure history.

Asset health prediction using the explicit hazard model

The ability to estimate the asset reliability and the probability of failure is critical to reducing maintenance costs, operation downtime, and safety hazards. Predicting the survival time and the probability of failure in future time is an indispensable requirement in prognostics and asset health management. In traditional reliability models, the lifetime of an asset is estimated using failure event data, alone; however, statistically sufficient failure event data are often difficult to attain in real-life situations due to poor data management, effective preventive maintenance, and the small population of identical assets in use. Condition indicators and operating environment indicators are two types of covariate data that are normally obtained in addition to failure event and suspended data. These data contain significant information about the state and health of an asset. Condition indicators reflect the level of degradation of assets while operating environment indicators accelerate or decelerate the lifetime of assets. When these data are available, an alternative approach to the traditional reliability analysis is the modelling of condition indicators and operating environment indicators and their failure-generating mechanisms using a covariate-based hazard model. The literature review indicates that a number of covariate-based hazard models have been developed. All of these existing covariate-based hazard models were developed based on the principle theory of the Proportional Hazard Model (PHM). However, most of these models have not attracted much attention in the field of machinery prognostics. Moreover, due to the prominence of PHM, attempts at developing alternative models, to some extent, have been stifled, although a number of alternative models to PHM have been suggested. The existing covariate-based hazard models neglect to fully utilise three types of asset health information (including failure event data (i.e. observed and/or suspended), condition data, and operating environment data) into a model to have more effective hazard and reliability predictions. In addition, current research shows that condition indicators and operating environment indicators have different characteristics and they are non-homogeneous covariate data. Condition indicators act as response variables (or dependent variables) whereas operating environment indicators act as explanatory variables (or independent variables). However, these non-homogenous covariate data were modelled in the same way for hazard prediction in the existing covariate-based hazard models. The related and yet more imperative question is how both of these indicators should be effectively modelled and integrated into the covariate-based hazard model. This work presents a new approach for addressing the aforementioned challenges. The new covariate-based hazard model, which termed as Explicit Hazard Model (EHM), explicitly and effectively incorporates all three available asset health information into the modelling of hazard and reliability predictions and also drives the relationship between actual asset health and condition measurements as well as operating environment measurements. The theoretical development of the model and its parameter estimation method are demonstrated in this work. EHM assumes that the baseline hazard is a function of the both time and condition indicators. Condition indicators provide information about the health condition of an asset; therefore they update and reform the baseline hazard of EHM according to the health state of asset at given time t. Some examples of condition indicators are the vibration of rotating machinery, the level of metal particles in engine oil analysis, and wear in a component, to name but a few. Operating environment indicators in this model are failure accelerators and/or decelerators that are included in the covariate function of EHM and may increase or decrease the value of the hazard from the baseline hazard. These indicators caused by the environment in which an asset operates, and that have not been explicitly identified by the condition indicators (e.g. Loads, environmental stresses, and other dynamically changing environment factors). While the effects of operating environment indicators could be nought in EHM; condition indicators could emerge because these indicators are observed and measured as long as an asset is operational and survived. EHM has several advantages over the existing covariate-based hazard models. One is this model utilises three different sources of asset health data (i.e. population characteristics, condition indicators, and operating environment indicators) to effectively predict hazard and reliability. Another is that EHM explicitly investigates the relationship between condition and operating environment indicators associated with the hazard of an asset. Furthermore, the proportionality assumption, which most of the covariate-based hazard models suffer from it, does not exist in EHM. According to the sample size of failure/suspension times, EHM is extended into two forms: semi-parametric and non-parametric. The semi-parametric EHM assumes a specified lifetime distribution (i.e. Weibull distribution) in the form of the baseline hazard. However, for more industry applications, due to sparse failure event data of assets, the analysis of such data often involves complex distributional shapes about which little is known. Therefore, to avoid the restrictive assumption of the semi-parametric EHM about assuming a specified lifetime distribution for failure event histories, the non-parametric EHM, which is a distribution free model, has been developed. The development of EHM into two forms is another merit of the model. A case study was conducted using laboratory experiment data to validate the practicality of the both semi-parametric and non-parametric EHMs. The performance of the newly-developed models is appraised using the comparison amongst the estimated results of these models and the other existing covariate-based hazard models. The comparison results demonstrated that both the semi-parametric and non-parametric EHMs outperform the existing covariate-based hazard models. Future research directions regarding to the new parameter estimation method in the case of time-dependent effects of covariates and missing data, application of EHM in both repairable and non-repairable systems using field data, and a decision support model in which linked to the estimated reliability results, are also identified.

Remaining useful life prediction of rotating equipment using covariate-based hazard models : industry applications

The ability to estimate the expected Remaining Useful Life (RUL) is critical to reduce maintenance costs, operational downtime and safety hazards. In most industries, reliability analysis is based on the Reliability Centred Maintenance (RCM) and lifetime distribution models. In these models, the lifetime of an asset is estimated using failure time data; however, statistically sufficient failure time data are often difficult to attain in practice due to the fixed time-based replacement and the small population of identical assets. When condition indicator data are available in addition to failure time data, one of the alternate approaches to the traditional reliability models is the Condition-Based Maintenance (CBM). The covariate-based hazard modelling is one of CBM approaches. There are a number of covariate-based hazard models; however, little study has been conducted to evaluate the performance of these models in asset life prediction using various condition indicators and data availability. This paper reviews two covariate-based hazard models, Proportional Hazard Model (PHM) and Proportional Covariate Model (PCM). To assess these models’ performance, the expected RUL is compared to the actual RUL. Outcomes demonstrate that both models achieve convincingly good results in RUL prediction; however, PCM has smaller absolute prediction error. In addition, PHM shows over-smoothing tendency compared to PCM in sudden changes of condition data. Moreover, the case studies show PCM is not being biased in the case of small sample size.

Microeconometric Studies on Unemployment and Business Cycles

Väitöskirja koostuu neljästä esseestä, joissa tutkitaan empiirisen työntaloustieteen kysymyksiä. Ensimmäinen essee tarkastelee työttömyysturvan tason vaikutusta työllistymiseen Suomessa. Vuonna 2003 ansiosidonnaista työttömyysturvaa korotettiin työntekijöille, joilla on pitkä työhistoria. Korotus oli keskimäärin 15 % ja se koski ensimmäistä 150 työttömyyspäivää. Tutkimuksessa arvioidaan korotuksen vaikutus vertailemalla työllistymisen todennäköisyyksiä korotuksen saaneen ryhmän ja vertailuryhmän välillä ennen uudistusta ja sen jälkeen. Tuloksien perusteella työttömyysturvan korotus laski työllistymisen todennäköisyyttä merkittävästi, keskimäärin noin 16 %. Korotuksen vaikutus on suurin työttömyyden alussa ja se katoaa kun oikeus korotettuun ansiosidonnaiseen päättyy. Toinen essee tutkii työttömyyden pitkän aikavälin kustannuksia Suomessa keskittyen vuosien 1991 – 1993 syvään lamaan. Laman aikana toimipaikkojen sulkeminen lisääntyi paljon ja työttömyysaste nousi yli 13 prosenttiyksikköä. Tutkimuksessa verrataan laman aikana toimipaikan sulkemisen vuoksi työttömäksi jääneitä parhaassa työiässä olevia miehiä työllisinä pysyneisiin. Työttömyyden vaikutusta tarkastellaan kuuden vuoden seurantajaksolla. Vuonna 1999 työttömyyttä laman aikana kokeneen ryhmän vuosiansiot olivat keskimäärin 25 % alemmat kuin vertailuryhmässä. Tulojen menetys johtui sekä alhaisemmasta työllisyydestä että palkkatasosta. Kolmannessa esseessä tarkastellaan Suomen 1990-luvun alun laman aiheuttamaa työttömyysongelmaa tutkimalla työttömyyden kestoon vaikuttavia tekijöitä yksilötasolla. Kiinnostuksen kohteena on työttömyyden rakenteen ja työn kysynnän muutoksien vaikutus keskimääräiseen kestoon. Usein oletetaan, että laman seurauksena työttömäksi jää keskimääräistä huonommin työllistyviä henkilöitä, jolloin se itsessään pidentäisi keskimääräistä työttömyyden kestoa. Tuloksien perusteella makrotason kysyntävaikutus oli keskeinen työttömyyden keston kannalta ja rakenteen muutoksilla oli vain pieni kestoa lisäävä vaikutus laman aikana. Viimeisessä esseessä tutkitaan suhdannevaihtelun vaikutusta työpaikkaonnettomuuksien esiintymiseen. Tutkimuksessa käytetään ruotsalaista yksilötason sairaalahoitoaineistoa, joka on yhdistetty populaatiotietokantaan. Aineiston avulla voidaan tutkia vaihtoehtoisia selityksiä onnettomuuksien lisääntymiselle noususuhdanteessa, minkä on esitetty johtuvan esim. stressin tai kiireen vaikutuksesta. Tuloksien perusteella työpaikkaonnettomuudet ovat syklisiä, mutta vain tiettyjen ryhmien kohdalla. Työvoiman rakenteen vaihtelu saattaa selittää osan naisten onnettomuuksien syklisyydestä. Miesten kohdalla vain vähemmän vakavat onnettomuudet ovat syklisiä, mikä saattaa johtua strategisesta käyttäytymisestä.

Survival analysis of adult tuberculosis disease

Background: We conducted a survival analysis of all the confirmed cases of Adult Tuberculosis (TB) patients treated in Cork-City, Ireland. The aim of this study was to estimate Survival time (ST), including median time of survival and to assess the association and impact of covariates (TB risk factors) to event status and ST. The outcome of the survival analysis is reported in this paper. Methods: We used a retrospective cohort study research design to review data of 647 bacteriologically confirmed TB patients from the medical record of two teaching hospitals. Mean age 49 years (Range 18–112). We collected information on potential risk factors of all confirmed cases of TB treated between 2008–2012. For the survival analysis, the outcome of interest was ‘treatment failure’ or ‘death’ (whichever came first). A univariate descriptive statistics analysis was conducted using a non- parametric procedure, Kaplan -Meier (KM) method to estimate overall survival (OS), while the Cox proportional hazard model was used for the multivariate analysis to determine possible association of predictor variables and to obtain adjusted hazard ratio. P value was set at <0.05, log likelihood ratio test at >0.10. Data were analysed using SPSS version 15.0. Results: There was no significant difference in the survival curves of male and female patients. (Log rank statistic = 0.194, df = 1, p = 0.66) and among different age group (Log rank statistic = 1.337, df = 3, p = 0.72). The mean overall survival (OS) was 209 days (95%CI: 92–346) while the median was 51 days (95% CI: 35.7–66). The mean ST for women was 385 days (95%CI: 76.6–694) and for men was 69 days (95%CI: 48.8–88.5). Multivariate Cox regression showed that patient who had history of drug misuse had 2.2 times hazard than those who do not have drug misuse. Smokers and alcohol drinkers had hazard of 1.8 while patients born in country of high endemicity (BICHE) had hazard of 6.3 and HIV co-infection hazard was 1.2. Conclusion: There was no significant difference in survival curves of male and female and among age group. Women had a higher ST compared to men. But men had a higher hazard rate compared to women. Anti-TNF, immunosuppressive medication and diabetes were found to be associated with longer ST, while alcohol, smoking, RICHE, BICHE was associated with shorter ST.

Mid-term results and factors affecting outcome of a metal-backed unicompartmental knee design: a case series.

BACKGROUND: Controversies exist regarding the indications for unicompartmental knee arthroplasty. The objective of this study is to report the mid-term results and examine predictors of failure in a metal-backed unicompartmental knee arthroplasty design. METHODS: At a mean follow-up of 60 months, 80 medial unicompartmental knee arthroplasties (68 patients) were evaluated. Implant survivorship was analyzed using Kaplan-Meier method. The Knee Society objective and functional scores and radiographic characteristics were compared before surgery and at final follow-up. A Cox proportional hazard model was used to examine the association of patient's age, gender, obesity (body mass index > 30 kg/m2), diagnosis, Knee Society scores and patella arthrosis with failure. RESULTS: There were 9 failures during the follow up. The mean Knee Society objective and functional scores were respectively 49 and 48 points preoperatively and 95 and 92 points postoperatively. The survival rate was 92% at 5 years and 84% at 10 years. The mean age was younger in the failure group than the non-failure group (p < 0.01). However, none of the factors assessed was independently associated with failure based on the results from the Cox proportional hazard model. CONCLUSION: Gender, pre-operative diagnosis, preoperative objective and functional scores and patellar osteophytes were not independent predictors of failure of unicompartmental knee implants, although high body mass index trended toward significance. The findings suggest that the standard criteria for UKA may be expanded without compromising the outcomes, although caution may be warranted in patients with very high body mass index pending additional data to confirm our results. LEVEL OF EVIDENCE: IV.

Association between smoking and recurrence of venous thromboembolism and bleeding in elderly patients with past acute venous thromboembolism.

BACKGROUND: While the association between smoking and arterial cardiovascular events has been well established, the association between smoking and venous thromboembolism (VTE) remains controversial. OBJECTIVES: To assess the association between smoking and the risk of recurrent VTE and bleeding in patients who have experienced acute VTE. PATIENTS/METHODS: This study is part of a prospective Swiss multicenter cohort that included patients aged ≥65years with acute VTE. Three groups were defined according to smoking status: never, former and current smokers. The primary outcome was the time to a first symptomatic, objectively confirmed VTE recurrence. Secondary outcomes were the time to a first major and clinically relevant non-major bleeding. Associations between smoking status and outcomes were analysed using proportional hazard models for the subdistribution of a competing risk of death. RESULTS: Among 988 analysed patients, 509 (52%) had never smoked, 403 (41%) were former smokers, and 76 (8%) current smokers. After a median follow-up of 29.6months, we observed a VTE recurrence rate of 4.9 (95% confidence interval [CI] 3.7-6.4) per 100 patient-years for never smokers, 6.6 (95% CI 5.1-8.6) for former smokers, and 5.2 (95% CI 2.6-10.5) for current smokers. Compared to never smokers, we found no association between current smoking and VTE recurrence (adjusted sub-hazard ratio [SHR] 1.05, 95% CI 0.49-2.28), major bleeding (adjusted SHR 0.59, 95% CI 0.25-1.39), and clinically relevant non-major bleeding (adjusted SHR 1.21, 95% CI 0.73-2.02). CONCLUSIONS: In this multicentre prospective cohort study, we found no association between smoking status and VTE recurrence or bleeding in elderly patients with VTE.

Characterizations of distributions using log odds rate

In this paper, we examine the relationships between log odds rate and various reliability measures such as hazard rate and reversed hazard rate in the context of repairable systems. We also prove characterization theorems for some families of distributions viz. Burr, Pearson and log exponential models. We discuss the properties and applications of log odds rate in weighted models. Further we extend the concept to the bivariate set up and study its properties.

SAS macros for point and interval estimation of area under the receiver operating characteristic curve for non-proportional and proportional hazards Weibull models

Aims and objectives  For prediction of risk of cardiovascular end points using survival models the proportional hazards assumption is often not met. Thus, non-proportional hazards models are more appropriate for developing risk prediction equations in such situations. However, computer program for evaluating the prediction performance of such models has been rarely addressed. We therefore developed SAS macro programs for evaluating the discriminative ability of a non-proportional hazards Weibull model developed by Anderson (1991) and that of a proportional hazards Weibull model using the area under receiver operating characteristic (ROC) curve.

Method  Two SAS macro programs for non-proportional hazards Weibull model using Proc NLIN and Proc NLP respectively and model validation using area under ROC curve (with its confidence limits) were written with SAS IML language. A similar SAS macro for proportional hazards Weibull model was also written.

Results  The computer program was applied to data on coronary heart disease incidence for a Framingham population cohort. The five risk factors considered were current smoking, age, blood pressure, cholesterol and obesity. The predictive ability of the non-proportional hazard Weibull model was slightly higher than that of its proportional hazard counterpart. An advantage of SAS Proc NLP in terms of the example provided here is that it provides significance level for the parameter estimates whereas Proc NLIN does not.

Conclusion  The program is very useful for evaluating the predictive performance of non-proportional and proportional hazards Weibull models.