Search results for: survival function

Authors: Ping Xu, Gregory T. Golm, Guanghan (Frank) Liu

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In the presence of competing events, traditional survival analysis may not be appropriate and can result in biased estimates, as it assumes independence between competing events and the event of interest. Instead, competing risk analysis should be considered to correctly estimate the survival probability of the event of interest and the hazard ratio between treatment groups. The COVID-19 pandemic has provided a potential source of competing risks in clinical trials, as participants in trials may experienceCOVID-related competing events before the occurrence of the event of interest, for instance, death due to COVID-19, which can affect the incidence rate of the event of interest. We have performed simulation studies to compare multiple competing risk analysis models, including the cumulative incidence function, the sub-distribution hazard function, and the cause-specific hazard function, to the traditional survival analysis model under various scenarios. We also provide a general recommendation on conducting competing risk analysis in randomized clinical trials during the era of the COVID-19 pandemic based on the extensive simulation results.

Keywords: competing risk, survival analysis, simulations, randomized clinical trial, COVID-19 pandemic

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Authors: Khandoker Akib Mohammad

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While analyzing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest, and they are said to be cured. When this feature of survival models is taken into account, the models are commonly referred to as cure models. In the presence of covariates, the conditional survival function of the population can be modelled by using the cure model, which depends on the probability of being uncured (incidence) and the conditional survival function of the uncured subjects (latency), and a combination of logistic regression and Cox proportional hazards (PH) regression is used to model the incidence and latency respectively. In this paper, we have shown the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator with an implicit function in the profile likelihood. We have also shown the efficient score function based on projection theory and the profile likelihood score function are equal. Our contribution in this paper is that we have expressed the efficient information matrix as the variance of the profile likelihood score function. A simulation study suggests that the estimated standard errors from bootstrap samples (SMCURE package) and the profile likelihood score function (our approach) are providing similar and comparable results. The numerical result of our proposed method is also shown by using the melanoma data from SMCURE R-package, and we compare the results with the output obtained from the SMCURE package.

Keywords: Cox PH model, cure model, efficient score function, EM algorithm, implicit function, profile likelihood

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Authors: Pius Marthin, Nihal Ata Tutkun

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Survival analysis has become one of the paramount procedures in the modeling of time-to-event data. When we encounter complex survival problems, the traditional approach remains limited in accounting for the complex correlational structure between the covariates and the outcome due to the strong assumptions that limit the inference and prediction ability of the resulting models. Several studies exist on the deep learning approach to survival modeling; moreover, the application for the case of complex survival problems still needs to be improved. In addition, the existing models need to address the data structure's complexity fully and are subject to noise and redundant information. In this study, we design a deep learning technique (CmpXRnnSurv_AE) that obliterates the limitations imposed by traditional approaches and addresses the above issues to jointly predict the risk-specific probabilities and survival function for recurrent events with competing risks. We introduce the component termed Risks Information Weights (RIW) as an attention mechanism to compute the weighted cumulative incidence function (WCIF) and an external auto-encoder (ExternalAE) as a feature selector to extract complex characteristics among the set of covariates responsible for the cause-specific events. We train our model using synthetic and real data sets and employ the appropriate metrics for complex survival models for evaluation. As benchmarks, we selected both traditional and machine learning models and our model demonstrates better performance across all datasets.

Keywords: cumulative incidence function (CIF), risk information weight (RIW), autoencoders (AE), survival analysis, recurrent events with competing risks, recurrent neural networks (RNN), long short-term memory (LSTM), self-attention, multilayers perceptrons (MLPs)

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Authors: Al Omari Mohammed Ahmed

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This paper focuses on Maximum Likelihood Estimator with Covariate. Covariates are incorporated into the Weibull model. Under this regression model with regards to maximum likelihood estimator, the parameters of the covariate, shape parameter, survival function and hazard rate of the Weibull regression distribution with right censored data are estimated. The mean square error (MSE) and absolute bias are used to compare the performance of Weibull regression distribution. For the simulation comparison, the study used various sample sizes and several specific values of the Weibull shape parameter.

Keywords: weibull regression distribution, maximum likelihood estimator, survival function, hazard rate, right censoring

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Authors: S. Thaiudom, W. Toommuangpak

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Yoghurt ice cream (YIC) containing prebiotics and probiotics seems to be much more recognized among consumers who concern for their health. Not only can it be a benefit on consumers’ health but also its taste and freshness provide people easily accept. However, the survival of such probiotic especially Bifidobacterium longum, found in human gastrointestinal tract and to be benefit to human gut, was still needed to study in the severe condition as whipping and freezing in ice cream process. Low and full-fat yoghurt ice cream containing 2 and 10% (w/w) fat content (LYIC and FYIC), respectively was produced by mixing 20% yoghurt containing B. longum into milk ice cream mix. Fructo-oligosaccharides (FOS) or galacto-oligosaccharides (GOS) at 0, 1, and 2% (w/w) were separately used as prebiotic in order to improve the survival of B. longum. Survival of this bacteria as a function of ice cream storage time and ice cream properties were investigated. The results showed that prebiotic; especially FOS could improve viable count of B. longum. The more concentration of prebiotic used, the more is the survival of B. Longum. These prebiotics could prolong the survival of B. longum up to 60 days, and the amount of survival number was still in the recommended level (106 cfu per gram). Fat content and prebiotic did not significantly affect the total acidity and the overrun of all samples, but an increase of fat content significantly increased the fat particle size which might be because of partial coalescence found in FYIC rather than in LYIC. However, addition of GOS or FOS could reduce the fat particle size, especially in FYIC. GOS seemed to reduce the hardness of YIC rather than FOS. High fat content (10% fat) significantly influenced on lowering the melting rate of YIC better than 2% fat content due to the 3-dimension networks of fat partial coalescence theoretically occurring more in FYIC than in LYIC. However, FOS seemed to retard the melting rate of ice cream better than GOS. In conclusion, GOS and FOS in YIC with different fat content can enhance the survival of B. longum and affect physical and chemical properties of such yoghurt ice cream.

Keywords: Bifidobacterium longum, prebiotic, survival, yoghurt ice cream

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Authors: Noora Al-Shanfari, M. Mazharul Islam

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The cumulative incidence function (CIF) is a fundamental approach for analyzing survival data in the presence of competing risks, which estimates the marginal probability for each competing event. Parametric modeling of CIF has the advantage of fitting various shapes of CIF and estimates the impact of covariates with maximum efficiency. To calculate the total CIF's covariate influence using a parametric model., it is essential to parametrize the baseline of the CIF. As the CIF is an improper function by nature, it is necessary to utilize an improper distribution when applying parametric models. The Gompertz distribution, which is an improper distribution, is limited in its applicability as it only accounts for monotone hazard shapes. The generalized Gompertz distribution, however, can adapt to a wider range of hazard shapes, including unimodal, bathtub, and monotonic increasing or decreasing hazard shapes. In this paper, the generalized Gompertz distribution is used to parametrize the baseline of the CIF, and the parameters of the proposed model are estimated using the maximum likelihood approach. The proposed model is compared with the existing Gompertz model using the Akaike information criterion. Appropriate statistical test procedures and model-fitting criteria will be used to test the adequacy of the model. Both models are applied to the ‘colon’ dataset, which is available in the “biostat3” package in R.

Keywords: competing risks, cumulative incidence function, improper distribution, parametric modeling, survival analysis

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Authors: Richard L. Summers

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The advanced computational analysis of biological systems is becoming increasingly dependent upon an understanding of the information-theoretic structure of the materials, energy and interactive processes that comprise those systems. The stability and survival of these living systems are fundamentally contingent upon their ability to acquire and process the meaning of information concerning the physical state of its biological continuum (biocontinuum). The drive for adaptive system reconciliation of a divergence from steady-state within this biocontinuum can be described by an information metric-based formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of Kullback-Leibler information minimization driven by survival replicator dynamics. If the mathematical expression of this process is the Lagrangian integrand for any change within the biocontinuum then it can also be considered as an action functional for the living system. In the direct method of Lyapunov, such a summarizing mathematical formulation of global system behavior based on the driving forces of energy currents and constraints within the system can serve as a platform for the analysis of stability. As the system evolves in time in response to biocontinuum perturbations, the summarizing function then conveys information about its overall stability. This stability information portends survival and therefore has absolute existential meaning for the living system. The first derivative of the Lyapunov energy information function will have a negative trajectory toward a system's steady state if the driving force is dissipating. By contrast, system instability leading to system dissolution will have a positive trajectory. The direction and magnitude of the vector for the trajectory then serves as a quantifiable signature of the meaning associated with the living system’s stability information, homeostasis and survival potential.

Keywords: meaning, information, Lyapunov, living systems

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Authors: Muhammad Noor Ul Ane, Dong-Soon Kim, Myron P. Zalucki

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Models can be useful to help understand population dynamics of insects under diverse environmental conditions and in developing strategies to manage pest species better. Adult longevity and fecundity of Helicoverpa armigera (Hübner) were evaluated against a wide range of constant temperatures (15, 20, 25, 30, 35 and 37.5ᵒC). The modified Sharpe and DeMichele model described adult aging rate and was used to estimate adult physiological age. Maximum fecundity of H. armigera was 973 egg/female at 25ᵒC decreasing to 72 eggs/female at 37.5ᵒC. The relationship between adult fecundity and temperature was well described by an extreme value function. Age-specific cumulative oviposition rate and age-specific survival rate were well described by a two-parameter Weibull function and sigmoid function, respectively. An oviposition model was developed using three temperature-dependent components: total fecundity, age-specific oviposition rate, and age-specific survival rate. The oviposition model was validated against independent field data and described the field occurrence pattern of egg population of H. armigera very well. Our model should be a useful component for population modeling of H. armigera and can be independently used for the timing of sprays in management programs of this key pest species.

Keywords: cotton bollworm, life table, temperature-dependent adult development, temperature-dependent fecundity

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Authors: Sazzad Hossain Talukder

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Survival in the competitive international market with unforeseen environmental contingencies has always been a concern of the firms that led to adopting different strategies to deal with different situations. Language strategy is considered to enhance the international performance of a firm by organizing language diversity and fostering communications within and outside the firm. Yet there is a lack of theoretical attention or model development on the role of language strategy on firm international survival. From resource dependence perspective, the adoption of language strategy and its relationship with firm survival are determined by the firm´s capability to prevent dependency concentration and/or increase relative power on the external environment. However, the impact of language strategy on firm survival is complex and multifaceted as the strategy influence firm performance indirectly through communication, coordination, learning and value creation. The evidence of various types of language strategies and different forms of firm survival also bring in complexities to understand the effects of a language strategy on the international survival of a firm. Based on language literatures and resource dependence logic, certain propositions are developed to conceptualize the relationship between language strategy and firm international survival in this conceptual paper. For the purpose of this paper, a conceptual model is proposed to examine how different kinds of language strategy foster reduction of resource dependency that lead to firm international survival in respond to local responsiveness and global integration. In this proposed model, it is theorized that language strategy has a positive relationship with the international survival of the firm, as the strategy is likely to reduce external resource dependency and increase the ability to continue independent operations both in short and long term.

Keywords: language strategy, language diversity, firm international survival, resource dependence logic

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Authors: Madaki Umar Yusuf, Mohd Rizam B. Abubakar

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The survival censored data with incomplete covariate data is a common occurrence in many studies in which the outcome is survival time. With model when the missing covariates are categorical, a useful technique for obtaining parameter estimates is the EM by the method of weights. The survival outcome for the class of generalized linear model is applied and this method requires the estimation of the parameters of the distribution of the covariates. In this paper, we propose some clinical trials with ve covariates, four of which have some missing values which clearly show that they were fully censored data.

Keywords: EM algorithm, incomplete categorical covariates, ignorable missing data, missing at random (MAR), Weibull Distribution

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Authors: Mais Khader, Xingjie Wei

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This research sheds light on female entrepreneurs by providing new insights on the survival predictions of companies led by females in the UK. This study aims to build a predictive machine learning model of the survival of female-led & co-led small & medium enterprises (SMEs) in the UK over the period 2000-2020. The predictive model built utilised a combination of financial and non-financial features related to both companies and their directors to predict SMEs' survival. These features were studied in terms of their contribution to the resultant predictive model. Five machine learning models are used in the modelling: Decision tree, AdaBoost, Naïve Bayes, Logistic regression and SVM. The AdaBoost model had the highest performance of the five models, with an accuracy of 73% and an AUC of 80%. The results show high feature importance in predicting companies' survival for company size, management experience, financial performance, industry, region, and females' percentage in management.

Keywords: company survival, entrepreneurship, females, machine learning, SMEs

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Authors: Elnaz Saeedi, Jamileh Abolaghasemi, Mohsen Nasiri Tousi, Saeedeh Khosravi

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Goals and Objectives: A typical analysis of survival data involves the modeling of time-to-event data, such as the time till death. A frailty model is a random effect model for time-to-event data, where the random effect has a multiplicative influence on the baseline hazard function. This article aims to investigate the use of gamma frailty model with concomitant variable in order to individualize the prognostic factors that influence the liver cirrhosis patients’ survival times. Methods: During the one-year study period (May 2008-May 2009), data have been used from the recorded information of patients with liver cirrhosis who were scheduled for liver transplantation and were followed up for at least seven years in Imam Khomeini Hospital in Iran. In order to determine the effective factors for cirrhotic patients’ survival in the presence of latent variables, the gamma frailty distribution has been applied. In this article, it was considering the parametric model, such as Exponential and Weibull distributions for survival time. Data analysis is performed using R software, and the error level of 0.05 was considered for all tests. Results: 305 patients with liver cirrhosis including 180 (59%) men and 125 (41%) women were studied. The age average of patients was 39.8 years. At the end of the study, 82 (26%) patients died, among them 48 (58%) were men and 34 (42%) women. The main cause of liver cirrhosis was found hepatitis 'B' with 23%, followed by cryptogenic with 22.6% were identified as the second factor. Generally, 7-year’s survival was 28.44 months, for dead patients and for censoring was 19.33 and 31.79 months, respectively. Using multi-parametric survival models of progressive and regressive, Exponential and Weibull models with regard to the gamma frailty distribution were fitted to the cirrhosis data. In both models, factors including, age, bilirubin serum, albumin serum, and encephalopathy had a significant effect on survival time of cirrhotic patients. Conclusion: To investigate the effective factors for the time of patients’ death with liver cirrhosis in the presence of latent variables, gamma frailty model with parametric distributions seems desirable.

Keywords: frailty model, latent variables, liver cirrhosis, parametric distribution

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Authors: T. Motsima, K. Zuma, E Rapoo

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Childhood mortality is a key sign of the coverage of child survival interventions, social and economic progressions. Although the level of under-five mortality has been declining, it is still unacceptably high. The primary aim of this paper is to establish and analyse the levels and trends of under-five mortality for the periods 1998, 2003 and 2012 in South Africa. Methods: The data used for analysis came from the 1998 SADHS, the 2003 SADHS and the 2012 SABSSM which collected information on the survival status of children. The Kaplan-Meier estimate of the survival function method was used to determine the probabilities of failure (death) from birth up to 59 months. Results and Conclusion: The overall U5MR declined by 28.2% from 53.1 in 1998 to 38.1 in 2012. The U5MR of male children declined from 59.2 in 1998 to 46.2 in 2003 and dropped further to 41.4 in 2012. The U5MR of children of mothers aged 40 years and older increased from 64.0 in 1998 to 89.0 in 2003 and rose further to 129.9 in 2012. The U5MR of children of mothers with education level of 12 years or more increased from 32.2 in 1998 to 35.2 in 2003 and declined substantially to 17.5 in 2012.

Keywords: demographic and health survey, Kaplan-Meier, levels and trends, under-five mortality

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Authors: Sarpong Boateng, Rohit Balasundaram, Akua Afrah Amoah

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Introduction: Racial and Gender disparities have been found to be independently associated with Salivary Gland Cancers (SGCs) survival; however, to our best knowledge, there are no previous studies on the interplay of these social determinants on the prognosis of SGCs. The objective of this study was to examine the joint effect of race and gender on the survival of SGCs. Methods: We analyzed survival outcomes of 13,547 histologically confirmed cases of SGCs using the Surveillance Epidemiology and End Results (SEER) database (2004 to 2015). Multivariable Cox regression analysis and Kaplan-Meier curves were used to estimate hazard ratios (HR) after controlling for age, tumor characteristics, treatment type and year of diagnosis. Results: 73.5% of the participants were whites, 8.5% were blacks, 10.1% were Hispanics and 58.5% were males. Overall, males had poorer survival than females (HR = 1.16, p=0.003). In the adjusted multivariable model, there were no significant differences in survival by race. However, the interaction of gender and race was statistically significant (p=0.01) in Hispanic males. Thus, compared to White females (reference), Hispanic females had significantly better survival (HR=0.53), whiles Hispanic males had worse survival outcomes (HR=1.82) for SGCs. Conclusions: Our results show significant interactions between race and gender, with racial disparities varying across the different genders for SGCs survival. This study indicates that racial and gender differences are crucial factors to be considered in the prognostic counseling and management of patients with SGCs. Biologic factors, tumor genetic characteristics, chemotherapy, lifestyle, environmental exposures, and socioeconomic and dietary factors are potential yet proven reasons that could account for racial and gender differences in the survival of SGCs.

Keywords: salivary, cancer, survival, disparity, race, gender, SEER

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Authors: A. Hayrapetyan, A. Simon, P. Marques, G. Renart

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Business survival is a question of greatest interest for any economy. Firm characteristics that can explain or predict performance and, ultimately, business survival become of the greatest significance, as the sustainable longevity of any business can mean health for the future of the country. Family Firms (FFs) are one of the most ubiquitous forms of business worldwide, as more than half of European firms (60%) are considered as family firms. Therefore, the inherent characteristics of FFs are one of the possible explanatory variables for firm survival because FFs have strategic goals that differentiate them from other types of businesses. Although there is literature on the performance of FFs across generations, there are fewer studies on the factors that impact the survival of family and non-family FFs, as there is a lack of data on failed firms. To address this gap, this paper explores the differential survival of family firms versus non-family firms with a representative sample of companies of the region of Catalonia (Northeast of Spain) that were adhoc classified as family or nonfamily firms, as well as classified as failed or surviving, since no census data for family firms or for failed firms is available in Spain. By using the COX regression model on a representative sample of 629 family and non-family firms, this study investigates to what extent financial ratios, such as Liquidity, Solvency Rate can impact business survival, taking into consideration the socioemotional side of family firms, as well as revealing the differences between family and non-family firms. The findings show that the liquidity rate is significant for non-family firm survival, whereas not for family firms. On the other hand, FFs can benefit while having a higher solvency rate. Ultimately, this paper discovers that FFs increase their chances of survival when they are small, as the growth in size starts negatively impacting the socioemotional objectives of the firm. This study proves the existence of significant differences between family and non-family firms’ survival during economic crises, suggesting that the prioritization of emotional wealth creates distinct conditions for both types of firms.

Keywords: COX regression, economy crises, family firm, non-family firm, survival

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Authors: Yemane Hailu Fissuh, Zhongzhan Zhang

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In biomedical researches and randomized clinical trials, the most commonly interested outcomes are time-to-event so-called survival data. The importance of robust models in this context is to compare the effect of randomly controlled experimental groups that have a sense of causality. Causal estimation is the scientific concept of comparing the pragmatic effect of treatments conditional to the given covariates rather than assessing the simple association of response and predictors. Hence, the causal effect based semiparametric transformation model was proposed to estimate the effect of treatment with the presence of possibly time-varying covariates. Due to its high flexibility and robustness, the semiparametric transformation model which shall be applied in this paper has been given much more attention for estimation of a causal effect in modeling left-truncated and right censored survival data. Despite its wide applications and popularity in estimating unknown parameters, the maximum likelihood estimation technique is quite complex and burdensome in estimating unknown parameters and unspecified transformation function in the presence of possibly time-varying covariates. Thus, to ease the complexity we proposed the modified estimating equations. After intuitive estimation procedures, the consistency and asymptotic properties of the estimators were derived and the characteristics of the estimators in the finite sample performance of the proposed model were illustrated via simulation studies and Stanford heart transplant real data example. To sum up the study, the bias of covariates was adjusted via estimating the density function for truncation variable which was also incorporated in the model as a covariate in order to relax the independence assumption of failure time and truncation time. Moreover, the expectation-maximization (EM) algorithm was described for the estimation of iterative unknown parameters and unspecified transformation function. In addition, the causal effect was derived by the ratio of the cumulative hazard function of active and passive experiments after adjusting for bias raised in the model due to the truncation variable.

Keywords: causal estimation, EM algorithm, semiparametric transformation models, time-to-event outcomes, time-varying covariate

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Authors: Rahul Kumar

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Background: Under-FiveMortality Rate(U5MR)ofanationiswidelyacceptedandlong-standing indicators of well-beingofherchildren.They measuredtheprobability of dying before theageoffive(expressedper1000livebirths).TheU5MRisanappropriate indicator of the cumulative exposure totheriskofdeathduringthefirstfiveyearsoflife, and accepted globalindicator ofthehealthandsocioeconomicstatusofagiven population.Itisalsousefulforassessing theimpactofvariousintervention programmes aimed at improving child survival.Under-fivemortalitytrendsconstitutealeadingindicatorofthelevel ofchildhealthandoveralldevelopmentincountries. Objectives: The first aim of our research is to study the level, trends, and Pattern of Under-five mortality using different sources of data. The second objective is to examine the survival pattern of Under-five mortality by different background characteristics. Data Source and Methodology: SRS and NFHS data have been used forobservingthelevelandtrendofUnder-Five mortality rate. Kaplan Meier Estimate has been used to understand the survival Pattern of Under-five mortality. Result: WefindthatallmostallthestatesmadesomeprogressbyreducingU5MRin recent decades.During1992-93highestU5MR(per thousand live birth) was observed in Assam(142)followed by up(141),Odisha(131),MP(130),andBihar(127.5).While the least U5MR(perthousandlive birth)wasobservedinRajasthan(102). The highestU5MR(per thousandlive birth)isobservedinUP(78.1), followed by MP(64.9)and Chhattisgarh(63.7)which are far away from the national level(50). Among them, Uttarakhand(46.7)hadleastU5MR(perthousandlivebirth), followed by Odisha(48.6). TheU5MR(perthousandlivebirth)ofcombinedhighfocusstateis63.7whichisfar away fromthenationallevel(50). Weidentified thatthesurvivalprobability ofunder-fivechildrenfromadolescentmotherislessin comparisontootherchildrenbornby differentagegroupofmothers. thatduringneonatalperiodusually male mortality exceedsthefemale mortality butthisdifferentialreversedinthepostneonatalperiod. Astheirageincreasesand approachingtofiveyears,weidentifiedthatthesurvivalprobability ofbothsexdecreasesbut female’s survival probabilitydecrement is more than male as their ageincreases. The poorer children’s survival probability is minimum. Children using improved toilet facility has more survival probability throughout thefiveyearsthan who uses unimproved. The survival probability of children under five who got Full ANCis more than the survival probability of children under five who doesn’t get any ANC. Conclusions: Improvement of maternal education is an urgent need to improve their health seeking behavior and thus the health of their children. Awareness on reproductive health and environmental sanitation should be strengthened.

Keywords: under-five mortality, survival pattern, ANC, trend

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Authors: Marta Fernández Olmos, Ana Gargallo Castel, Alice Salami

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The literature has shown the importance of studying the issue of business survival in highly competitive environments. In particular, the wine sector has certain characteristics that make it interesting to study factors that increase the possibility of wineries' survival, such as individual productivity, winery size, age, innovation efforts or the maturity of the industry itself, among others. Due to the importance of these factors, this research aims to analyze whether the possibility of wineries' survival increases if they are family businesses or if there is gender diversity in senior management. To this end, a nationwide survey was carried out. The sample was made up of wineries from all the Spanish appellations of origin, using this sample to analyze the survival of the diverse types of wineries according to the factors to be studied. The main results indicate that family wineries survive longer, suggesting that this may be due to the fact that the main objective of family wineries is the continuity of the business in the long term. Regarding gender diversity, wineries that have a female presence in top roles in management, adding gender diversity, survive more than those with a predominantly male presence. Based on these results, it is advisable to consider the importance of family businesses, especially in this type of sector. In addition, support should be provided for the inclusion of a female labor force to improve the possibility of survival.

Keywords: gender, family business, wine industry, survival

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Authors: Yemane Hailu Fissuh, Zhongzhan Zhang

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a systematic observation from a defined time of origin up to certain failure or censor is known as survival data. Survival analysis is a major area of interest in biostatistics and biomedical researches. At the heart of understanding, the most scientific and medical research inquiries lie for a causality analysis. Thus, the main concern of this study is to investigate the causal effect of treatment on survival time conditional to the possibly time-varying covariates. The theory of causality often differs from the simple association between the response variable and predictors. A causal estimation is a scientific concept to compare a pragmatic effect between two or more experimental arms. To evaluate an average treatment effect on survival outcome, the estimating equation was adjusted for time-varying covariates under the semi-parametric transformation models. The proposed model intuitively obtained the consistent estimators for unknown parameters and unspecified monotone transformation functions. In this article, the proposed method estimated an unbiased average causal effect of treatment on survival time of interest. The modified estimating equations of semiparametric transformation models have the advantage to include the time-varying effect in the model. Finally, the finite sample performance characteristics of the estimators proved through the simulation and Stanford heart transplant real data. To this end, the average effect of a treatment on survival time estimated after adjusting for biases raised due to the high correlation of the left-truncation and possibly time-varying covariates. The bias in covariates was restored, by estimating density function for left-truncation. Besides, to relax the independence assumption between failure time and truncation time, the model incorporated the left-truncation variable as a covariate. Moreover, the expectation-maximization (EM) algorithm iteratively obtained unknown parameters and unspecified monotone transformation functions. To summarize idea, the ratio of cumulative hazards functions between the treated and untreated experimental group has a sense of the average causal effect for the entire population.

Keywords: a modified estimation equation, causal effect, semiparametric transformation models, survival analysis, time-varying covariate

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Authors: Dalia Rimawi, Walid Salameh, Amal Al-Omari, Hadeel AbdelKhaleq

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Predication of Survival time of patients with cancer, is a core factor that influences oncologist decisions in different aspects; such as offered treatment plans, patients’ quality of life and medications development. For a long time proportional hazards Cox regression (ph. Cox) was and still the most well-known statistical method to predict survival outcome. But due to the revolution of data sciences; new predication models were employed and proved to be more flexible and provided higher accuracy in that type of studies. Artificial neural network is one of those models that is suitable to handle time to event predication. In this study we aim to compare ph Cox regression with artificial neural network method according to data handling and Accuracy of each model.

Keywords: Cox regression, neural networks, survival, cancer.

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Authors: Wisam Ismail, Sarah Hosgood, Michael Nicholson

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The research hypothesis is that early post-transplant allograft fibrosis will be linked to donor factors and that acute rejection and/or delayed graft function in the recipient will be independent risk factors for the development of fibrosis. This research hypothesis is to explore whether acute rejection/delay graft function has an effect on the renal transplant fibrosis within the first year post live donor kidney transplant between 1998 and 2009. Methods: The study has been designed to identify five time points of the renal transplant biopsies [0 (pre-transplant), 1 month, 3 months, 6 months and 12 months] for 300 live donor renal transplant patients over 12 years period between March 1997 – August 2009. Paraffin fixed slides were collected from Leicester General Hospital and Leicester Royal Infirmary. These were routinely sectioned at a thickness of 4 Micro millimetres for standardization. Conclusions: Fibrosis at 1 month after the transplant was found significantly associated with baseline fibrosis (p<0.001) and HTN in the transplant recipient (p<0.001). Dialysis after the transplant showed a weak association with fibrosis at 1 month (p=0.07). The negative coefficient for HTN (-0.05) suggests a reduction in fibrosis in the absence of HTN. Fibrosis at 1 month was significantly associated with fibrosis at baseline (p 0.01 and 95%CI 0.11 to 0.67). Fibrosis at 3, 6 or 12 months was not found to be associated with fibrosis at baseline (p=0.70. 0.65 and 0.50 respectively). The amount of fibrosis at 1 month is significantly associated with graft survival (p=0.01 and 95%CI 0.02 to 0.14). Rejection and severity of rejection were not found to be associated with fibrosis at 1 month. The amount of fibrosis at 1 month was significantly associated with graft survival (p=0.02) after adjusting for baseline fibrosis (p=0.01). Both baseline fibrosis and graft survival were significant predictive factors. The amount of fibrosis at 1 month was not found to be significantly associated with rejection (p=0.64) after adjusting for baseline fibrosis (p=0.01). The amount of fibrosis at 1 month was not found to be significantly associated with rejection severity (p=0.29) after adjusting for baseline fibrosis (p=0.04). Fibrosis at baseline and HTN in the recipient were found to be predictive factors of fibrosis at 1 month. (p 0.02, p <0.001 respectively). Age of the donor, their relation to the patient, the pre-op Creatinine, artery, kidney weight and warm time were not found to be significantly associated with fibrosis at 1 month. In this complex model baseline fibrosis, HTN in the recipient and cold time were found to be predictive factors of fibrosis at 1 month (p=0.01,<0.001 and 0.03 respectively). Donor age was found to be a predictive factor of fibrosis at 6 months. The above analysis was repeated for 3, 6 and 12 months. No associations were detected between fibrosis and any of the explanatory variables with the exception of the donor age which was found to be a predictive factor of fibrosis at 6 months.

Keywords: fibrosis, transplant, renal, rejection

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Authors: Lola T. Alimkhodjaeva, Lola T. Zakirova, Soniya S. Ziyavidenova

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Background: Breast cancer occupies the first place among the cancer in women in the world. It is urgent today to study the role of molecular markers which are capable of predicting the dynamics and outcome of the disease. The aim of this study is to define the prognostic value of the content of estrogen receptor (ER), progesterone receptor (PgR), and amplification of HER-2 / neu oncoprotein by studying 3 and 5-year overall and relapse-free survival in 470 patients with primary operable and 280 patients with locally–advanced breast cancer. Materials and methods: Study results of 3 and 5-year overall and relapse-free survival, depending on the content of RE, PgR in primary operable patients showed that ER positive (+) and PgR (+) survival was 100 (96.2%) and 97.3 (94.6%), for ER negative (-) and PgR (-) - 69.2 (60.3%) and 65.4 (57.7%), for ER positive (+) and negative PgR (-) 87.4 (80.1%) and 81.5 (79.3%), for ER negative (-) and positive PgR (+) - 97.4 (93.4%) and 90.4 (88.5%), respectively. Survival results depended also on the level of HER-2 / neu expression. In patients with HER-2 / neu negative the survival rates were as follows: 98.6 (94.7%) and 96.2 (92.3%). In group of patients with the level of HER-2 / neu (2+) expression these figures were: 45.3 (44.3%) and 45.1 (40.2%), and in group of patients with the level of HER-2 / neu (3+) expression - 41.2 (33.1%) and 34.3 (29.4%). The combination of ER negative (-), PgR (-), HER-2 / neu (-) they were 27.2 (25.4%) and 19.5 (15.3%), respectively. In patients with locally-advanced breast cancer the results of 3 and 5-year OS and RFS for ER (+) and PgR (+) were 76.3 (69.3%) and 62.2 (61.4%), for ER (-) and RP (-) 29.1 (23.7%) and 18.3 (12.6%), for ER (+) and PgR (-) 61.2 (47.2%) and 39.4 (25.6%), for ER (-) and PgR (+) 54.3 (43.1%) and 41.3 (18.3%), respectively. The level of HER-2 / neu expression also affected the survival results. Therefore, in HER-2/ neu negative patients the survival rate was 74.1 (67.6%) and 65.1 (57.3%), with the level of expression (2+) 20.4 (14.2%) and 8.6 (6.4%), with the level of expression (3+) 6.2 (3.1%) and 1.2 (1.5%), respectively. The combination for ER, PgR, HER-2 / neu negative was 22.1 (14.3%) and 8.4 (1.2%). Conclusion: Thus, the presence of steroid hormone receptors in breast tumor tissues at primary operable and locally- advanced process as the lack of HER-2/neu oncoprotein correlates with the highest rates of 3- and 5-year overall and relapse-free survival. The absence of steroid hormone receptors as well as of HER-2/neu overexpression in malignant breast tissues significantly degrades the 3- and 5-year overall and relapse-free survival. Tumors with ER, PgR and HER-2/neu negative have the most unfavorable prognostics.

Keywords: breast cancer, estrogen receptor, oncoprotein, progesterone receptor

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Authors: Latifa Hamoudi-Belarbi, L'Hadi Nouri, Khaled Belkacemi

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The effect of three methods of drying (traditional drying, freeze-drying and spray-drying) on the survival of concentrated cultures of Geotrichum fragrans and Wickerhamomyces anomalus was studied. The survival of yeast cultures was initially compared immediately after freeze-drying using HES 12%(w/v)+Sucrose 7% (w/v) as protectant, traditional drying in dry rice cakes and finally spray-drying with whey proteins. The survival of G. fragrans and W. anomalus was studied during 4 months of storage at 4°C and 25°C, in the darkness, under vacuum and at 0% relative humidity. The results demonstrated that high survival was obtained using traditional method of preservation in rice cakes (60% for G. fragrans and 65% for W. anomalus) and freeze-drying in (68% for G. fragrans and 74% for W. anomalus). However, poor survival was obtained by spray-drying method in whey protein with 20% for G. fragrans and 29% for W. anomalus. During storage at 25°C, yeast cultures of G. fragrans and W. anomalus preserved by traditional and freeze-drying methods showed no significant loss of viable cells up to 3 months of storage. Spray-dried yeast cultures had the greatest loss of viable count during the 4 months of storage at 25°C. During storage at 4°C, preservation of yeasts cultures using traditional method of preservation provided better survival than freeze-drying. This study demonstrated the effectiveness of the traditional method to preserve yeasts cultures compared to the high cost methods like freeze-drying and spray-drying.

Keywords: freeze-drying, traditional drying, spray drying, yeasts

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Authors: Zeytu G. Asfaw, Serkalem K. Abrha, Demisew G. Degefu

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Background: HIV/AIDS remains a major public health problem in Ethiopia and heavily affecting people of productive and reproductive age. We aimed to compare the performance of Parametric Survival Analysis and Bayesian Survival Analysis using simulations and in a real dataset application focused on determining predictors of HIV patient survival. Methods: A Parametric Survival Models - Exponential, Weibull, Log-normal, Log-logistic, Gompertz and Generalized gamma distributions were considered. Simulation study was carried out with two different algorithms that were informative and noninformative priors. A retrospective cohort study was implemented for HIV infected patients under Highly Active Antiretroviral Therapy in Alamata General Hospital, North Ethiopia. Results: A total of 320 HIV patients were included in the study where 52.19% females and 47.81% males. According to Kaplan-Meier survival estimates for the two sex groups, females has shown better survival time in comparison with their male counterparts. The median survival time of HIV patients was 79 months. During the follow-up period 89 (27.81%) deaths and 231 (72.19%) censored individuals registered. The average baseline cluster of differentiation 4 (CD4) cells count for HIV/AIDS patients were 126.01 but after a three-year antiretroviral therapy follow-up the average cluster of differentiation 4 (CD4) cells counts were 305.74, which was quite encouraging. Age, functional status, tuberculosis screen, past opportunistic infection, baseline cluster of differentiation 4 (CD4) cells, World Health Organization clinical stage, sex, marital status, employment status, occupation type, baseline weight were found statistically significant factors for longer survival of HIV patients. The standard error of all covariate in Bayesian log-normal survival model is less than the classical one. Hence, Bayesian survival analysis showed better performance than classical parametric survival analysis, when subjective data analysis was performed by considering expert opinions and historical knowledge about the parameters. Conclusions: Thus, HIV/AIDS patient mortality rate could be reduced through timely antiretroviral therapy with special care on the potential factors. Moreover, Bayesian log-normal survival model was preferable than the classical log-normal survival model for determining predictors of HIV patients survival.

Keywords: antiretroviral therapy (ART), Bayesian analysis, HIV, log-normal, parametric survival models

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Authors: Duhania O. Mahara, Santi W. Purnami, Aulia N. Fitria, Merissa N. Z. Wirontono, Revina Musfiroh, Shofi Andari, Sagiran Sagiran, Estiana Khoirunnisa, Wahyudi Widada

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For assessing interventions in numerous disease areas, the use of multiple time-to-event outcomes is common. An individual might experience two different events called bivariate time-to-event data, the events may be correlated because it come from the same subject and also influenced by individual characteristics. The bivariate time-to-event case can be applied by copula-based bivariate Cox survival model, using the Clayton and Frank copulas to analyze the dependence structure of each event and also the covariates effect. By applying this method to modeling the recurrent event infection of hemodialysis insertion on chronic kidney disease (CKD) patients, from the AIC and BIC values we find that the Clayton copula model was the best model with Kendall’s Tau is (τ=0,02).

Keywords: bivariate cox, bivariate event, copula function, survival copula

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Authors: Nur Rokhman

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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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Authors: Abdisalam Hassan Muse, Samuel Mwalili, Oscar Ngesa

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A generalized log-logistic distribution with variable shapes of the hazard rate was introduced and studied, extending the log-logistic distribution by adding an extra parameter to the classical distribution, leading to greater flexibility in analysing and modeling various data types. The proposed distribution has a large number of well-known lifetime special sub-models such as; Weibull, log-logistic, exponential, and Burr XII distributions. Its basic mathematical and statistical properties were derived. The method of maximum likelihood was adopted for estimating the unknown parameters of the proposed distribution, and a Monte Carlo simulation study is carried out to assess the behavior of the estimators. The importance of this distribution is that its tendency to model both monotone (increasing and decreasing) and non-monotone (unimodal and bathtub shape) or reversed “bathtub” shape hazard rate functions which are quite common in survival and reliability data analysis. Furthermore, the flexibility and usefulness of the proposed distribution are illustrated in a real-life data set and compared to its sub-models; Weibull, log-logistic, and BurrXII distributions and other parametric survival distributions with 3-parmaeters; like the exponentiated Weibull distribution, the 3-parameter lognormal distribution, the 3- parameter gamma distribution, the 3-parameter Weibull distribution, and the 3-parameter log-logistic (also known as shifted log-logistic) distribution. The proposed distribution provided a better fit than all of the competitive distributions based on the goodness-of-fit tests, the log-likelihood, and information criterion values. Finally, Bayesian analysis and performance of Gibbs sampling for the data set are also carried out.

Keywords: hazard rate function, log-logistic distribution, maximum likelihood estimation, generalized log-logistic distribution, survival data, Monte Carlo simulation

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Authors: Hanei Son

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Since the beginning of the 2010s, ‘start-up boom’ has continued with the creation of many new enterprises in Korea. Such tendency was led by various changes in society such as emergence and diffusion of smartphones. Especially, the Korean government has been interested in start-ups and entrepreneurship as an alternative engine for Korea's economic growth. With strong support from the government, as a result, many new enterprises have been established for recent years and the Korean government seems to have achieved its goal: expanding the basis of start-ups. However, it is unclear which factors affect the survival and growth of these new enterprises after their creation. Therefore, this study aims to identify which start-ups from early 2010s survived and which factors influenced their survival and growth. The study will strongly focus on which industries the new enterprises were in, as environmental elements are expected to be critical factors for business of start-ups in Korean context. For this purpose, 105 companies which were introduced as high potential start-ups from 2010 to 2012 were considered in the analysis. According to their current status, dead or alive, the start-ups were categorized by their industries and service area. Through this analysis, it was observed that many start-ups that are still in business are in internet or mobile platform businesses and four major sectors. In each group, a representative case has been studied to reveal its survival and growth factors. The results point to the importance of industrial characteristics for the survival and success of Korean startups and offer political implications in which sector and business more potentials for start-ups in Korea lie in.

Keywords: government support for start-ups, industrial characteristics, Korean start-ups, survival of start-ups

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Authors: Geir Kirkebøen

Abstract:

Most patients with serious diagnoses want to know their prognosis, in particular their expected survival time. As part of the informed consent process, physicians are legally obligated to communicate such information to patients. However, there is no established (evidence based) ‘best practice’ for how to do this. The two questions explored in this study are: How do physicians communicate expected survival time to patients, and how should it be done? We explored the first, descriptive question in a study with Norwegian oncologists as participants. The study had a scenario and a survey part. In the scenario part, the doctors should imagine that a patient, recently diagnosed with a serious cancer diagnosis, has asked them: ‘How long can I expect to live with such a diagnosis? I want an honest answer from you!’ The doctors should assume that the diagnosis is certain, and that from an extensive recent study they had optimal statistical knowledge, described in detail as a right-skewed survival curve, about how long such patients with this kind of diagnosis could be expected to live. The main finding was that very few of the oncologists would explain to the patient the variation in survival time as described by the survival curve. The majority would not give the patient an answer at all. Of those who gave an answer, the typical answer was that survival time varies a lot, that it is hard to say in a specific case, that we will come back to it later etc. The survey part of the study clearly indicates that the main reason why the oncologists would not deliver the mortality prognosis was discomfort with its uncertainty. The scenario part of the study confirmed this finding. The majority of the oncologists explicitly used the uncertainty, the variation in survival time, as a reason to not give the patient an answer. Many studies show that patients want realistic information about their mortality prognosis, and that they should be given hope. The question then is how to communicate the uncertainty of the prognosis in a realistic and optimistic – hopeful – way. Based on psychological research, our hypothesis is that the best way to do this is by explicitly describing the variation in survival time, the (usually) right skewed survival curve of the prognosis, and emphasize to the patient the (small) possibility of being a ‘lucky outlier’. We tested this hypothesis in two scenario studies with lay people as participants. The data clearly show that people prefer to receive expected survival time as a median value together with explicit information about the survival curve’s right skewedness (e.g., concrete examples of ‘positive outliers’), and that communicating expected survival time this way not only provides people with hope, but also gives them a more realistic understanding compared with the typical way expected survival time is communicated. Our data indicate that it is not the existence of the uncertainty regarding the mortality prognosis that is the problem for patients, but how this uncertainty is, or is not, communicated and explained.

Keywords: cancer patients, decision psychology, doctor-patient communication, mortality prognosis

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Authors: Mario Isaza-Ruget, Claudia C. Colmenares-Mejia, Nancy Yomayusa, Camilo A. González, Andres Cely, Jossie Murcia

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Quantification of risks associated with complications development from chronic kidney disease (CKD) through accurate survival models can help with patient management. A retrospective cohort that included patients diagnosed with CKD from a primary care program and followed up between 2013 and 2018 was carried out. Time-dependent and static covariates associated with demographic, clinical, and laboratory factors were included. Deep Learning (DL) survival analyzes were developed for three CKD outcomes: CKD stage progression, >25% decrease in Estimated Glomerular Filtration Rate (eGFR), and Renal Replacement Therapy (RRT). Models were evaluated and compared with Random Survival Forest (RSF) based on concordance index (C-index) metric. 2.143 patients were included. Two models were developed for each outcome, Deep Neural Network (DNN) model reported C-index=0.9867 for CKD stage progression; C-index=0.9905 for reduction in eGFR; C-index=0.9867 for RRT. Regarding the RSF model, C-index=0.6650 was reached for CKD stage progression; decreased eGFR C-index=0.6759; RRT C-index=0.8926. DNN models applied in survival analysis context with considerations of longitudinal covariates at the start of follow-up can predict renal stage progression, a significant decrease in eGFR and RRT. The success of these survival models lies in the appropriate definition of survival times and the analysis of covariates, especially those that vary over time.

Keywords: artificial intelligence, chronic kidney disease, deep neural networks, survival analysis

Procedia PDF Downloads 134