Weibull Proportional Hazards Model Research Articles

On the Relationship Among Linear Type Traits and Functional Longevity in the Italian Mediterranean Buffalo Using a Weibull Proportional Hazards Model

Weibull proportional hazards model was used to identify the non-genetic effects that affect length of productive life (LPL) of the Italian Mediterranean Buffalo (IMB). Data were provided by the Italian National Association of Buffalo Breeders (ANASB) and included records of reproductive, productive, and linear type traits from 59,943 buffalo with first calving from 2002 to 2019. Data were divided into 4 geographical regions to determine if the relationship between the investigated effects and LPL varied by region. LPL was defined as the number of days from the first calving to culling for those buffaloes that were culled (uncensored) or to the date of the last test-day for those that are still alive (censored). The Weibull model included time-dependent effects of herd-year-season of calving, parity and stage of lactation, production as within-herd deviations, as well as time-independent effects of age at first calving, year of birth, type of reproduction (natural mating vs artificial insemination), classifier and ten linear type traits. The average duration of productive life was 1,604 days. Both year of birth and production level had a significant effect on culling risk. Moreover, culling risk decreased linearly across parities. The reference point for age at first calving relative to other classes was set at 35 months. A significant relationship between linear type traits and relative culling risk was also observed, being highest for buffaloes with the lowest linear scores. The results show that the Weibull model provides consistent and robust risk estimates. Therefore, this model would be recommended for future implementation of the first genetic evaluation of LPL in the Italian Mediterranean Buffalo.

Impact of reproductive traits on productive life in Iranian Holstein dairy cows.

Enhancing reproductive performance is a key strategy to mitigate involuntary culling rates, thereby extending productive life (PL) and ultimately improving profitability in dairy cattle herds. A piecewise Weibull proportional hazards model was used to investigate the effect of several important reproductive traits on PL in Holstein dairy cows. Data comprised 200,747 lactation records from 82,505 cows sired by 1952 bulls across 36 dairy herds. PL was defined as the number of days from the first calving to the last milk record or censoring. The statistical model accounted for the time-dependent fixed effects of changes in herd size, year-season, milk production, fat and protein contents, and the time-independent fixed effect of age at first calving. Herd-year and sire effects were also included as random effects. Reproductive traits include calving traits such as calving ease (CE), calf size (CZ), and calf survival (CS), as well as female fertility traits such as number of inseminations per conception (NI), days from calving to first service (CFS), days from first service to conception (FSC), and days open (DO). All reproductive traits had a significant effect on PL (p < 0.001). Each reproductive trait was analysed separately. The relative risk (RR) of being culled increased as the severity of calving difficulties increased in both primiparous and multiparous cows. Cows that calved small or large calves showed a higher risk of being culled compared with those that calved medium size calves. The increased RR of culling was observed only for primiparous cows that gave birth to dead calves. In addition, cows that required more NI, a longer CFS, FSC, and DO had shorter longevity. These insights can deepen our comprehension of the factors affecting PL and provide information for refining management and breeding strategies, which could lead to increased profitability and sustainability in Iranian dairy farming.

Data-Driven Reliability Prediction for District Heating Networks

As district heating networks age, current asset management practices, such as those relying on static life expectancies and age- and rule-based approaches, need to be replaced by data-driven asset management. As an alternative to physics-of-failure models that are typically preferred in the literature, this paper explores the application of more accessible traditional and novel machine learning-enabled reliability models for analyzing the reliability of district heating pipes and demonstrates how common data deficiencies can be accommodated by modifying the models’ likelihood expressions. The tested models comprised the Herz, Weibull, and the Neural Weibull Proportional Hazard models. An assessment of these models on data from an actual district heating network in Funen, Denmark showed that the relative youth of the network complicated the validation of the models’ distributional assumptions. However, a comparative evaluation of the models showed that there is a significant benefit in employing data-driven reliability modeling as they enable pipes to be differentiated based on the their working conditions and intrinsic features. Therefore, it is concluded that data-driven reliability models outperform current asset management practices such as age-based vulnerability ranking.

Propensity weighting plus adjustment in proportional hazards model is not doubly robust.

Recently, it has become common for applied works to combine commonly used survival analysis modeling methods, such as the multivariable Cox model and propensity score weighting, with the intention of forming a doubly robust estimator of an exposure effect hazard ratio that is unbiased in large samples when either the Cox model or the propensity score model is correctly specified. This combination does not, in general, produce a doubly robust estimator, even after regression standardization, when there is truly a causal effect. We demonstrate via simulation this lack of double robustness for the semiparametric Cox model, the Weibull proportional hazards model, and a simple proportional hazards flexible parametric model, with both the latter models fit via maximum likelihood. We provide a novel proof that the combination of propensity score weighting and a proportional hazards survival model, fit either via full or partial likelihood, is consistent under the null of no causal effect of the exposure on the outcome under particular censoring mechanisms if either the propensity score or the outcome model is correctly specified and contains all confounders. Given our results suggesting that double robustness only exists under the null, we outline 2 simple alternative estimators that are doubly robust for the survival difference at a given time point (in the above sense), provided the censoring mechanism can be correctly modeled, and one doubly robust method of estimation for the full survival curve. We provide R code to use these estimators for estimation and inference in the supporting information.

Quantifying the short- and long-term effects of promotional incentives in a loyalty program: Evidence from birthday rewards in a large retail company

Nowadays, many retail companies implement their original loyalty programs to stimulate the willingness of their customers to make a purchase. In these programs, promotional incentives are often incorporated to further enhance customer loyalty; however, few previous studies have assessed the effectiveness of such incentives. Therefore, our study examined both short- and long-term effects of promotional incentives in a loyalty program on customer purchase behavior by analyzing a loyalty program using birthday rewards implemented by a major retail company in Japan. For the analysis, we used the Weibull proportional hazards model, generalized linear model, and Pareto/NBD & gamma-gamma framework after implementing propensity score matching. The estimation results indicated that promotional incentives in a loyalty program temporarily weaken the points pressure effect on the purchase frequency. In addition, promotional incentives in a loyalty program had no positive effect of increasing the customer lifetime value. Furthermore, our study revealed that the lifetime values of loyalty program members who do not exhibit their active purchasing behavior for a certain period of time after impulsive actions induced by promotional incentives are particularly low. These findings will help companies to decide how promotional incentives should be incorporated into their loyalty programs.

Evaluation of Inbreeding in the Slovak Simmental Breed and Its Effect on Length of Productive Life.

This study aimed to estimate the average inbreeding coefficient in Slovak Simmental dairy cattle and evaluate the effect of inbreeding on the length of productive life. All pedigrees included 463,282 animals dating back to 1914. The inbreeding coefficients for each animal in the pedigree were computed using the software CFC 1.0. Length of productive life (LPL) was defined as the time (days) from the first calving to culling, death, or censoring. The influence of inbreeding on the length of productive life was calculated and tested using the Weibull proportional hazards model. The average inbreeding coefficient, the average number of discrete generation equivalents, and the average longest ancestral path for inbred animals were 0.01, 6.59, and 13.08, respectively. While the largest decrease in the mean coefficient of inbreeding was observed from the year of birth 1995 (F = 1.50%) to 2001 (F = 0.59%), an increasing trend of inbreeding in the population was found from 2003 onwards. A weak but significant effect of inbreeding on the length of productive life of Simmental cows was confirmed using survival analysis.

Survival Analysis of Students’ Dropout in a Nigerian University System

Formal education remains the vehicle for socio-economic development and social mobilization in any society. Academic institutions are increasingly interested in monitoring the performance of their students. This interest has given rise to the need for research, collation, analysis, and interpretation of data to formulate evidence-based academic policies that aim to improve student performance and reduce dropout rates. Data obtained from the university comprises of Gender, Age at Entry, Marital Status, Sponsorship, Mode of Entry, Program of Study and Cumulative Grade Point Average (CGPA). This study investigated how these factors influence students’ dropout at Modibbo Adama University, Yola Adamawa State Nigeria. Survival analysis was carried out using Log-logistic, Lognormal, Weibull and Cox Proportional Hazard models. The lognormal survival model was judged as the best model due to its lowest AIC value of 1199.773. The Gender, CGPA and students’ program of study have significant effect on student dropout. Also, it was observed that 41.42% of male students dropped out when compared to 38.94% female students dropped out before their graduation year. Of all the programs of study considered, Physics has the highest number of dropped out before graduation. It accounted for 68.75%. In terms of academic performance, majority (85.05%) students who had CGPA of third class at the beginning of their studies dropped out before expected years of graduation. The study recommends that government and university management provide financial support to assist the male students who are on self-sponsorship, as financial pressure may contribute to their dropout rates

Rams-based comprehensive evaluation method for EMU components

EMU (Electric Multiple Units) components were evaluated in multiple dimensions, i.e. reliability, availability, maintainability, and safety. A parameter estimation method, which is based on the data on the mileage between failures and quantities monitored in the actual operation, was put forward for the Weibull proportional hazard model to determine their operational reliability. A multi-index component maintainability evaluation model, which is based on empirical distribution functions, and a maintainability cluster evaluation model, which is based on whitened weight functions, were built, and the entropy weight method was introduced to determine the estimates of the indexes. A component safety evaluation method, which has the safety risk factor as its evaluation basis, was built using both the fuzzy theory and the analytic hierarchy process. A RAMS comprehensive evaluation model based on the linear weighted synthesis method was proposed. All of the models and methods are aimed at meeting the needs of this multidimensional component evaluation. This evaluation method was verified using actual gearbox operation parameters. The reliability and availability evaluation curves based on the Weibull proportional hazard model, whose parameters were determined according to the failure data, show that the EMU component reliability and availability decrease as the EMU mileage increases, thus verifying that this evaluation method is reasonable. The calculated EMU gearbox degree of safety is 0.8659, at an excellent level. The evaluated EMU gearbox maintainability is at the moderate level of III. The proposed evaluation method can reflect the relations of the component reliability and availability to the quantities monitored in operation more accurately and more comprehensively and the actual component maintainability and safety levels in a more objective way. It can provide a theoretical basis for managers and design departments to improve and evaluate the performance of the components, determine their maintenance intervals, and develop scientific preventive maintenance strategies in order to reduce their overhaul cost and increase their maintenance efficiency.

Risk factors and genetic parameters of longevity in Spanish dairy goat breeds using a Weibull proportional hazards model

The aim of this study was to assess the most important risk factors that influence productive life (PL) and to estimate genetic parameters for PL using a Weibull proportional hazards model in two Spanish dairy goat breeds belonging to different production systems. The dataset consisted of 70,695 and 49,176 lactation records of Florida and Payoya females, respectively, collected over the last two decades. A total of 6,227 (24.21%) Florida and 3,452 (20.42%) Payoya females had censored information. The pedigree included a total of 56,901 animals for Florida and 59,957 for Payoya. The effects included in the model for both breeds were the age at first kidding and the herd-year-season of birth of the doe as time-independent effects; and the age at kidding, the herd-year-season of kidding, the within-herd class of milk production deviation and the combination between the lactation number and the duration of lactation as time-dependent effects. Estimation of genetic parameters was made using a Weibull proportional hazards model using Survival Kit V6.0 software. The results from the Weibull animal models gave estimates of additive genetic variances of 0.99 ± 0.0003 and 0.156 ± 0.021, which corresponds to a heritability of 0.43 ± 0.025 and 0.11 ± 0.021 for Florida and Payoya, respectively. The magnitude of heritability obtained for PL suggests that a substantial response to selection may be expected for longevity, especially in the Florida breed. These results may contribute to the development of a routine genetic evaluation to improve PL in Spanish dairy goat breeds.

Expectation-Maximization Algorithm for the Weibull Proportional Hazard Model under Current Status Data

Due to the flexibility of the Weibull distribution and the proportional hazard (PH) model, Weibull PH is widely used in survival analysis under right censored data and interval censored data but it is seldom investigated under current status data, partially because there is less information in current status data than in right censored data and interval censored data. This paper considers the Weibull PH model under the current status data and introduces the Poisson latent variables to augment the data, then uses the expectation-maximization (EM) algorithm to obtain the maximum likelihood estimators of the model parameters. The EM algorithm is compared with the Newton–Raphson (NR) algorithm from several perspectives in the simulation studies, and the results show that the proposed method has several highlights, such as computational simplicity, improved convergence stability, and overall estimator results that are either comparable or slightly better in terms of bias. Furthermore, the performance of the Weibull PH model and the semi-parametric PH model is compared under two simulation scenarios, and two standard model selection criteria are used for model selection. The results indicate that the Weibull PH model has significant advantages when failure time follows a Weibull distribution. Lastly, the Weibull PH model along with EM algorithm is applied to lung tumor data and intraocular lens (IOL) calcification data with the aim of assessing the impact of covariates, including environmental factors and gender, on event timing and risk.

KPCA-WPHM-SCNs-based remaining useful life prediction method for motor rolling bearings

Motor rolling bearings are the important supporting components of motors. It can ensure the stable operation of motor equipment in the power grid, and bearing life prediction of it is a key issue. To solve the problem of low accuracy of remaining useful life (RUL) prediction for motor rolling bearings, a neural network model based on Weibull proportional hazards model (WPHM) and stochastic configuration networks (SCNs) is proposed. To better extract and analyze features of the bearing vibration signal in both time and frequency domains, kernel principal component analysis (KPCA) is used to reduce the dimensionality of the data. Then, a WPHM model using the top three contributing feature parameters is built, which sets the start time based on the failure rate curve and reliability function. Finally, the validity of the model is verified with the rolling bearing full life cycle dataset from the IEEE PHM 2012 Data Challenge, and a comparison with other machine learning models shows that the accuracy of the proposed model in RUL prediction is higher.

Risk factors and genetic parameter estimates for preweaning survival of Fogera calves

This study utilised mortality records of 1 043 Fogera calves maintained at Andassa Livestock Research Center from 1984 to 2021 to investigate the factors that influence survival and estimate genetic parameters for the preweaning survival of Fogera calves. Survival was defined as the probability of surviving in a given length of time. Survival analysis was done using the Weibull proportional hazard model with Survival Kit version 6.1 software. Genetic variance and heritability estimates were estimated using the sire model. The proportion of right-censored calves up to 1, 4, and 8 months of age was 90.8, 87.8, and 83.5%, respectively. Around 55.8% of all deaths (16.5%) occurred up to one month of age. In addition to birth year, sex, season, and weight at birth were the most important risk factors for calf mortality. The heritability estimates for the survival of calves at 1, 4, and 8 months of age were 0.26 ± 0.14, 0.22 ± 0.13, and 0.38 ± 0.18, respectively. Moderate heritability was estimated at the age of eight months, implying that the inclusion of survival traits in the selection criteria and inclusion in the breeding goal will enhance the preweaning survival rate of calves. Similarly, higher differences in estimated breeding values of sires for survival suggest that the selection of sires with higher estimated breeding values could improve the survival potential of calves. The decreased genetic trend of 3.34% year−1 for the survival potential of Fogera calves during the study periods suggested that survival traits should be included in the breeding goal to reduce the mortality rate.

A two-stage approach for Bayesian joint models: reducing complexity while maintaining accuracy

Several joint models for longitudinal and survival data have been proposed in recent years. In particular, many authors have preferred to employ the Bayesian approach to model more complex structures, make dynamic predictions, or use model averaging. However, Markov chain Monte Carlo methods are computationally very demanding and may suffer convergence problems, especially for complex models with random effects, which is the case for most joint models. These issues can be overcome by estimating the parameters of each submodel separately, leading to a natural reduction in the complexity of the joint modelling, but often producing biased estimates. Hence, we propose a novel two-stage approach that uses the estimations from the longitudinal submodel to specify an informative prior distribution for the random effects when estimating them within the survival submodel. In addition, as a bias correction mechanism, we incorporate the longitudinal likelihood function in the second stage, where its fixed effects are set according to the estimation using only the longitudinal submodel. Based on simulation studies and real applications, we empirically compare our proposal with joint specification and standard two-stage approaches considering different types of longitudinal responses (continuous, count and binary) that share information with a Weibull proportional hazard model. The results show that our estimator is more accurate than its two-stage competitor and as good as jointly estimating all parameters. Moreover, the novel two-stage approach significantly reduces the computational time compared to the joint specification.

Analysis of Calving Ease and Stillbirth and Their Impact on the Length of Functional Productive Life in Slovak Holstein Cattle.

The aim of the study was to determine the frequency of births according to the categories of calving difficulty and stillbirths and to evaluate the effect of these factors on the longevity of cows. Longevity is one of the traits that affect the overall profit in the dairy industry. A Weibull proportional hazard model was used to evaluate the influence of functional traits such as calving ease and stillbirth. Longevity was expressed as the length of a functional, productive life from the first calving to death or censoring, which was corrected for milk yield. The database included 918,568 calvings, where calving without assistance represented 83.34%, calving with the assistance of one person or the use of a slight mechanical pull represented 14.47%, difficult calving with the assistance of several people, the use of mechanical traction or the intervention of a veterinarian represented 2.16%, and cesarean section represented 0.03%. The mortality of calves, stillborn or dead within 48 h of birth, represented 1.07% and 6.59%, respectively. The frequency of alive female calves was higher (46.84%) than male calves (45.50%). Cows with higher lactations had almost half as many stillborn calves as heifers. The most stillborn calves were found in difficult births (59.48%). In easy calving, this proportion was 2.48%. Using survival analysis, we estimated the significant influence of the factors such as parity, milk production, herd size, age at first calving, herd × year × season, sex of calf, calving ease, and stillbirth on the length of the functional, productive life of cows. The risk of early culling of the cows with moderately difficult calving was 1.259 times higher than in the cows with easy calving. Difficult calving and cesarean section shorten the productive life, and the risk of culling reached 1.711 and 1.894, respectively. Cows that gave birth to a dead calf achieved a 2.939 times higher risk of culling compared to cows that gave birth to a live calf. In this study, a higher risk of early culling was found in cows that gave birth to a male calf. Evaluation of the calving ease and stillbirth can be used as indirect indicators at an earlier age of the animal in the selection process for long-lived animals with good productive and reproductive performance.

Prediction of Tool Remaining Useful Life Based on NHPP-WPHM

A tool remaining useful life prediction method based on a non-homogeneous Poisson process and Weibull proportional hazard model (WPHM) is proposed, taking into account the grinding repair of machine tools during operation. The intrinsic failure rate model is built according to the tool failure data. The WPHM is established by collecting vibration information during operation and introducing covariates to describe the failure rate of the tool operation. In combination with the tool grinding repair, the NHPP-WPHM under different repair times is established to describe the tool comprehensive failure rate. The failure threshold of the tool life is determined by the maximum availability, and the remaining tool life is predicted. Take the cylindrical turning tool of the CNC lathe as an example, the root mean square error, mean absolute error, mean absolute percentage error, and determination coefficient (R2) are used as indicators. The proposed method is compared with the actual remaining useful life and the remaining useful life prediction model based on the WPHM to verify the effectiveness of the model.

Genetic Parameters for Functional Longevity, Type Traits, and Production in the Serbian Holstein.

In this study, the authors focused on the evaluation of the genetic parameters of longevity, milk yield traits, and type traits in dairy cattle populations in the Republic of Serbia. The total dataset used consisted of production records and pedigree data for 32,512 Holstein cows that calved from 1981 to 2015. The animal model was applied to determine the variance and covariance components and genetic parameters of the analyzed traits by applying the restricted maximum likelihood (REML) approach and using the programs VCE6 and PEST. The heritability of longevity traits was estimated using the Survival Kit V6.0 software package. Variance and covariance were estimated for five production traits: milk yield (MY), fat yield (FY), protein yield (PY), milk fat content (MC), and protein content (PC), and three longevity traits: length of productive life (LPL), lifetime milk yield (LMY), and the number of lactations achieved (NL) as well as for 18 standard type traits. Heritabilities for the milk, fat, and protein yield traits were 0.20 (MY), 0.15 (FY), and 0.19 (PY), respectively. The estimated coefficients of heritability for the longevity traits were higher when using the Weibull proportional hazards model compared to the traditional linear methods and ranged from 0.08 for NL to 0.10 for LPL. Heritability values for the type traits varied from a low of 0.10 (RLSsv-rear legs set-side view) to medium values of 0.32 (ST-stature). Genetic correlations were found between MY and the following longevity traits: LPL, LMY, and NL with values of -0.18, -0.11, and -0.09, respectively. Genetic correlations were found between MY and a number of linear type traits and varied from 0.02 (between MY and RUH-rear udder height) to 0.28 (between MY and FUA-fore udder attachment). Genetic correlations between the 18 investigated type traits ranged from -0.33 between TL (top line) and RTP (rear teats position) to 0.71 between AN (angularity) and RUH (rear udder height). Genetic correlations between most linear type traits and longevity traits (LPL, LMY, and NL) were generally negative and very low. The highest positive genetic correlation was found between UD and LPL (rxy = 0.38).

Stroke-related length of hospitalization trends and in-hospital mortality in Peru.

Peru faces challenges to provide adequate care to stroke patients. Length of hospitalization and in-hospital mortality are two well-known indicators of stroke care. We aimed to describe the length of stay (LOS) of stroke in Peru, and to assess in-hospital mortality risk due to stroke, and subtypes. This retrospective cohort study used hospitalization registries coding with ICD-10 from 2002 to 2017 (N = 98,605) provided by the Ministry of Health; in-hospital mortality was available for 2016-2017 (N = 6,566). Stroke cases aged ≥35 years were divided into subarachnoid hemorrhage (I60), intracerebral hemorrhage (I61), cerebral infarction (I63), and stroke not specified as hemorrhage or infarction (I64). Data included stroke LOS and in-hospital mortality; socio-demographic and clinical variables. We fitted a region- and hospital level-stratified Weibull proportional hazard model to assess the in-hospital mortality. The median LOS was 7 days (IQR: 4-13). Hemorrhagic strokes had median LOS longer than ischemic strokes and stroke not specified as hemorrhage or infarction (P = <0.001). The case fatality rate (CFR) of patients with stroke was 11.5% (95% CI [10-12%]). Subarachnoid hemorrhage (HR = 2.45; 95% CI [1.91-3.14]), intracerebral hemorrhage (HR = 1.95; 95% CI [1.55-2.46]), and stroke not specified as hemorrhage or infarction (HR = 1.45; 95% CI [1.16-1.81]) were associated with higher in-hospital mortality risk in comparison to ischemic strokes. Between 2002 and 2017, LOS due to stroke has not changed in Peru in stroke patients discharged alive. Hemorrhagic cases had the longest LOS and highest in-hospital mortality risk during 2016 and 2017. The findings of our study seem to be consistent with a previous study carried out in Peru and similar to that of HIC and LMIC, also there is an increased median LOS in stroke cases managed in specialized centers. Likewise, LOS seems to depend on the type of stroke, where ischemic stroke cases have the lowest LOS. Peru needs to improve access to stroke care.

The impact of long-term exposure to PM10, SO2, O3, NO2, and COon incident dysglycemia: a population-based cohort study.

To examine the associations between long-term exposure to five major air pollutants including SO2, PM10, O3, NO2, and CO, and incident dysglycemia, impaired fasting glucose (IFG), and diabetes, separately. A total of 4254 (1720 men) normoglycemic individuals aged 20-69years at baseline were followed from 2001 to 2018 every 3years. To measure the long-term hazards of air pollutants for incident dysglycemia, the Weibull proportional hazards models for every 10-unit increment adjusted for diabetes risk factors were fitted. The air pollutants were put in the models in the form of averages of 1-, 2-, and 3-year periods. During a median follow-up of 12.2years, we observed 1780 dysglycemia events. In contrast to NO2, the increase in SO2, O3, and PM10 levels were significantly associated with a higher risk of dysglycemia and IFG in all time spans excluding PM10 at 2years. The largest hazard ratios for incident dysglycemia and IFG were attributable to PM10 in 3years (2.20 (95% CI 1.67, 2.89) and 2.08 (1.55, 2.80), respectively). Moreover, exposure to all the pollutants except NO2 in 1year (0.89 (0.80, 0.98)) had no significant associations with incident diabetes. There was a signal that younger (< 45years) and never-smoker individuals were more predispose to dysglycemic effects of air pollution (all P for interactions > 0.03). Our findings suggested that long-term exposure to air pollution increased incident dysglycemia risk, the effect which was mainly attributable to IFG status.

An approach to functional longevity in Latxa dairy sheep

Productivity and profitability of sheep farming are strongly influenced by the productive performance of ewe during it lifetime. For that, it is relevant to quantify the genetic and non-genetic factors affecting functional longevity in order to consider its inclusion as a trait in a breeding scheme. In this investigation, a Weibull proportional hazard model was applied to study the length of productive live as functional longevity indicator in Latxa dairy sheep breeds. The time from the first calving to the date of culling was individually calculated using records from 28,466 Latxa Cara Rubia (LCR), 26,045 Latxa Cara Negra from Euskadi (LCNEAE) and 10,385 Latxa Cara Negra from Navarre (LCNNAF) from commercial flocks, born between 2000 and 2018. The culling risk associated to the age at first lambing, number of lambs born per lambing and total milk yield produced per lactation was estimated using a likelihood ratio test, and the genetic component of longevity was estimated using a sire-maternal grandsire model. The results concerning the relative culling risk showed that ewes having their first lambing at 2 years of age had around 1.30 times more risk of disposal compared with those of 1 year, regardless of the Latxa population. Similarly, it was found that LCR and LCNEAE having 2 o 3 lambs born per lambing had 1.20 and 1.34 higher risk to be culled in comparison to having 1 lamb, whereas the risk was 1.04 in LCNNAF. In contrast, the probability to be culled was drastically reduced by around 1.50 in all the Latxa populations as the milk yield moved from low to intermediate levels and by around 3.0 times when it moved from low to high. Regarding the genetic parameters of longevity, heritability values ranged from 0.042 to 0.061, which indicates that it is under low additive genetic control. Furthermore, a decreasing genetic was observed, although the decrease rate was smaller during recent years possibly due to the parallel improvement on udder traits. In the light of the results of this first longevity study in Latxa, it is possible to infer that ewes’ on-herd durability is negatively affected by a reproductive delay and a high prolificacy, whereas the higher the milk production, the lower the risk. Moreover, given the genetic findings, it can also be deduced that although selection on longevity is viable, the genetic progress may be a long process.

Risk factors and clustering of mortality among older adults in the India Human Development Survey

With wide socioeconomic mortality differential among older adults in India, a constant question of death clustering across high-risk families and communities arises. The present study uses a follow-up survey from India to investigate the socioeconomic, demographic and health predictors of old-age mortality clustering. Data of 16,964 older adults nested within 12,981 households from 2352 communities were used from India Human Development Survey (IHDS) round-I (2005) who were further tracked down in round-II (2012). Bivariate association between the determinants of old-age mortality was investigated using the log-rank test. The multivariate analysis involved estimating the random-intercept Weibull proportional hazard model with three levels—individual (level 1), family (level 2) and community (level 3). We analyzed the sensitivity of multivariate results to unobservable variable and selection biases using the e-value method. The empirical analysis confirms that the risk of mortality is significantly heterogeneous between the families. The health status of older adults and the family’s socioeconomic status in the early years emerged as prominent predictors of a longer lifespan. With a strong association between household income and mortality hazard risk, the present study urges early life interventions as those started in late-life might have negligible impact on keeping the older adults alive and healthy.