Weibull Proportional Hazards Model Research Articles

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.

Phenotypic relationship between linear descriptive type traits and functional longevity of Holstein cows in different housing systems using a Weibull proportional hazards model

Phenotypic relationship between linear descriptive type traits and functional longevity of Holstein cows in different housing systems using a Weibull proportional hazards model

Practical health indicator construction methodology for bearing ensemble remaining useful life prediction with ISOMAP-DE and ELM-WPHM

To improve the accuracy of our previous bearing ensemble remaining useful life (RUL) prediction model using the genetic algorithm (GA), support vector regression, and the Weibull proportional hazard model (WPHM) (see Qiu et al (2020 Measurement 150 107097)), we proposed a more practical health indicator (HI) construction methodology for bearing ensemble RUL prediction. A weighted coefficient determination method for four prognostic metrics-monotonicity, robustness, trendability, and consistency-was proposed to select sensitive health features accurately using the analytic hierarchy process. The selected sensitive health features were fused through isometric feature mapping (ISOMAP), and differential evolution (DE) was employed to replace GA for computing the optimal weight coefficients of each input fused feature. One-dimensional HI was constructed by multiplying each input fused feature with the corresponding optimal weight coefficient, and RUL prediction was implemented through an extreme learning machine (ELM) and WPHM. The accuracy and effectiveness of the proposed method were validated by a bearing experiment. The results show that HI construction with ISOMAP-DE has achieved the best performance, and the proposed ELM-WPHM model is compared with BP-WPHM, SVM-WPHM, LSTM-WPHM, and DLSTM-WPHM in terms of RMSE criteria. The minimum error and training time appear in ELM-WPHM, indicating the superiority of the proposed bearing ensemble RUL prediction model.

Fleckscore system of exterior evaluation as a more accurate indirect predictor of longevity in Slovak Simmental dairy cows

The goal of the work was to discover the influence of conformation traits evaluated by the Fleckscore system on the length of productive life of Slovak Simmental dairy cows. Evaluation of body conformation traits according to the Fleckscore system was performed on 3 452 cows. The relationship of individual traits to longevity was analysed using the Weibull proportional hazard model. The results confirmed that smaller and longer cows, which were well muscular and with a deeper body, had a lower risk of early culling than cows in the reference group. Hock angularity, pastern and hoof height scored with low or high marks were associated with an early culling of cows. In terms of the length of productive life, a slightly more elastic pattern is required. Cows with a deeper udder and a stronger and tighter fore udder attachment, which were also average in notching and height central ligament and centrally placed teats, reached a longer productive life.

Modeling Pipe Break Data Using Survival Analysis with Machine Learning Imputation Methods

The development of asset life estimation tools based on historical data is essential to the effective management of pipeline assets. One tool that may assist with asset management is survival analysis. However, left-truncated break records pose a challenge in the practice of survival analysis to obtain sound inferences and predictions. In this study, we propose a data-driven approach that integrates machine learning imputation methods with survival analysis. To demonstrate the proposed methodology, we perform a case study using ductile iron (DI) water distribution pipes from an anonymized utility in the midwestern United States. Two artificial neural network (ANN) models are developed as imputation methods to calibrate the survival curves and mean time to first failure (MTTF) estimates from the Weibull proportional hazards model (WPHM). Results show that the MTTF estimation bias is reduced from 14.3% to 2.1% by using imputation as a preceding procedure. Empirical findings show that despite the limited accuracy of imputation models, the use of imputation methods can still improve the survival analysis results and mitigate the impact of left-truncated break records.

Operating Environment effect on Remaining Useful Life Case study: Sungun Copper Mine

The Remaining Useful Life (RUL) valuation of mining machinery is a principal to ensure the production/output and customer satisfaction in the mining zone. In many cases, it may be of attention to know the expected value of the remaining life of the item before it fails from an arbitrary time that known RUL. The system's failure is also evaluated with the reliability index, which describes up-times. An individual unit's reliability during field use is essential in many mining equipment applications. This index, especially in industrial systems, and being affected by the internal condition also affects operating environmental conditions. For example, the loader performance in cold weather will be different from that of warm, which will affect the machine's reliability and thus the RUL. In reliability engineering, operating environmental conditions are considered Risk factors or Covariates. Therefore, in this paper, an approach is proposed first to analyze the system's reliability considering covariates' effect and then estimate the RUL for different scenarios. The proportional hazard model was used in reliability analysis to be realistic and take the operational influencing factors in calculation. Methods are presented for calculating the reliability function and computing the RUL as a function of the current conditions to guarantee the desired output. The remaining useful life estimation of a Komatsu PC-1250 from the Sungun copper mine was evaluated as a case study of this approach. Systems operating environmental factors such as shift, dump-truck kind, rock kind, … (known as covariates) are assumed to influence covariate in this context. As a result, the Weibull proportional hazard model was fitted to describe the failure behavior, and the RUL of four selected scenarios was evaluated. Presented results can be used, e.g., for developing operational performance, planning of maintenance activities, spare parts provision, and the profitability of the owner of an asset.

Effect of Calving Difficulties and Calf Mortality on Functional Longevity in Polish Holstein-Friesian Cows.

Simple SummaryLongevity, or the length of a cow’s productive life, is important in terms of profitability, animal welfare and environmental sustainability. In genetic evaluations, interest focuses on functional longevity, defined as a cow’s ability to avoid forced culling, an ability that increases the possibility of voluntary disposal based on economic criteria. Longevity is affected by several non-productive functional traits, among them those related to calving performance: calving ease (dystocia) and perinatal calf mortality (stillbirth). Parturition is a critical event in a cow’s life that has a number of different short- and long-term consequences. In the Polish Holstein-Friesian population, the incidence of dystocia and stillbirth is within the lower range of frequencies found in other dairy cattle populations. Our research showed that both traits affect functional longevity. Difficult calvings occur more frequently in heifers and increase the risk of involuntary culling more than in later parturitions. Additionally, a higher risk of culling is related to birth of a male calf. Moreover, the negative impact of calf mortality on longevity is also more pronounced in primiparous cows and in the case of delivery of male calves. Reducing the incidence of calving problems and perinatal mortality may improve the longevity of dairy cows.Longevity is one of the functional traits that considerably affect dairy herd profitability. A Weibull proportional hazards model was used to evaluate the impact of difficult calvings and calf stillbirths on cow functional longevity, defined as length of productive life corrected for milk production. The data for analysis comprised calving ease and calf mortality scores of 2,163,426 calvings, 34.4% of which came from primiparous cows. The percentage of male calves was 53.4%. Calving ease was scored as “without assistance” (34.44%), “with assistance” (62.03%), “difficult—hard pull” (3.39%), and “very difficult, including caesarean section” (0.14%). Calf mortality scores were “live born” (94.21%) and “stillborn or died within 24 h” (5.79%). The Weibull proportional hazards model included classes of calving ease or calf mortality scores × parity (1, ≥2) × sex of calf as time-dependent fixed effect. The model also included time-dependent fixed effects of year × season, parity × stage of lactation, annual change in herd size, fat yield and protein yield, time-independent fixed effect of age at first calving, and time dependent random herd × year × season. In first-parity cows, very difficult birth of a bull or heifer increased the relative risk of culling, respectively, 2.18 or 1.26 times as compared with calving without assistance. In later parities, the relative risk of culling related to very difficult calving was 2.0 times (for male calves) and 1.33 times (for female calves) higher than the relative risk of culling associated with calving without assistance. Calf mortality showed a negative impact on longevity in both heifers and cows. First-parity stillbirth increased the relative risk of culling depending on sex of calf by 18% in females and by 15% in males; in later parities the increase of the relative risk of culling was lower (by 7% for females, 9% for males). Difficult calvings and their consequences, especially in primiparous cows, may negatively influence dairy herd profitability by reducing the length of cows’ productive life.