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 Table of Contents  
ORIGINAL ARTICLE
Year : 2019  |  Volume : 6  |  Issue : 2  |  Page : 82-88

Survival parametric models to estimate the factors of under-five child mortality


1 Department of Kayachikitsa, Institute of Medical Sciences, Banaras Hindu University, Varanasi, India
2 Department of Statistics, MMV, Banaras Hindu University, Varanasi, India
3 Biostatistics LC Pharmaceutical Services, Bangalore, India
4 Department of Community Medicine, Institute of Medical Sciences, Banaras Hindu University, Varanasi, India

Date of Submission20-Mar-2019
Date of Acceptance14-May-2019
Date of Web Publication23-Jul-2019

Correspondence Address:
Dr. Rakesh Kumar Saroj
Centre for Infectious Disease Research in Zambia, Analysis Unit, Lusaka, Zambia

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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/jhrr.jhrr_22_19

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  Abstract 

Aims: Child survival status is one of the major health-related concerns in all over the developing countries. There are various socioeconomic, demographic, environmental, and proximate and biological factors which are responsible for under-five child mortality. Our aim was to find the significant factors among various responsible factors under study using parametric and semi-parametric models. Materials and Methods: In this article, National Family Health Survey (NFHS)-IV data is used state of Uttar Pradesh in India after authentication and permission. Cox regression analysis (semi-parametric model) was performed to obtain the significant role of variables. Parametric models (Weibull, exponential, log-logistic, and log-normal) were performed to estimate the survival. Results: By using the Cox regression model, it was found that socioeconomic, demographic (education level, women's age, and religion), and proximate and biological factors (women's age in years, total number of children ever born, birth in the last 5 years, number of living children, currently breastfeeding, smokers, desire for more children, size of child, delivery by cesarean section, antenatal care visits, and birth order) play a significant role in the context of under-five child mortality. Based on the Akaike Information Criterion's (32985.3) minimum value, the Weibull model was found to be best fitted among all the other parametric models. Conclusions: There is used different parametric models. It is found that Weibull model is best fitted among all models. The study concludes that child mortality influences by the different factors. The study suggests that public health researcher, clinicians, health policy makers and other demographer need to implement more health programs related to child health especially for the under-five year children.

Keywords: Cox regression model, Survival analysis, Weibull distribution, Weibull regression model


How to cite this article:
Saroj RK, Murthy K H, Kumar M, Singh R, Kumar A. Survival parametric models to estimate the factors of under-five child mortality. J Health Res Rev 2019;6:82-8

How to cite this URL:
Saroj RK, Murthy K H, Kumar M, Singh R, Kumar A. Survival parametric models to estimate the factors of under-five child mortality. J Health Res Rev [serial online] 2019 [cited 2019 Oct 15];6:82-8. Available from: http://www.jhrr.org/text.asp?2019/6/2/82/263241


  Introduction Top


Reducing child mortality is now a global concern. Globally, under-five child mortality rate has decreased by 58%, from an estimated rate of 93 deaths per 1000 livebirths in 1990 to 39 deaths per 1000 livebirths in 2017.[1] A lot of work has been done in the literature of under-five child mortality in different regions of the world.

In the Indian context, studies on child mortality have mainly addressed the role of maternal, socioeconomic, and health-related determinants. As far as Uttar Pradesh, India, is concerned, poor health delivery system and poor maternal and health-care services are responsible for low infant and child mortality.[2] This is a matter of grave concern for human as well as social development of the state. The determinants of maternal health service data of Uttar Pradesh were analyzed by logistic regression methods.[3],[4]

The research wok has been done on the survival analysis of under-five mortality data by Cox proportional hazard model and frailty models.[5] The author has applied classical and Bayesian approaches to Cox proportional hazard model on under-five child mortality data.[6] Another citation is related to the survival analysis of under-five mortality of children and its associated risk factors.[7]

All the above citations are related to survival models which are used on different types of large sample data of underdeveloping countries. This is the difficult task to compare the parametric survival models together in real life data due to complex mathematical assumption and software suitability.[8]

Cox proportional hazard model is very important in survival analysis; the advantage of this model is that it includes nonparametric and parametric models both.[7] These studies were restricted to the analysis of mortality risks in children through survival analysis. After review, it was found that only few studies have been done on under-five child mortality survival status, but none of them has found combined fitting of parametric survival models in the under-five child mortality data. Through this study, we intend to emphasize those determinants which are nearer in time to the outcome and can be modified by program than those which are remote or far apart in time to the outcome of concern.

This study aimed to identify the risk factors which affect child survival by using Cox proportional hazard model and parametric models, and hence, to find out the best fitted parametric model in under-five child mortality. The Weibull regression model is also performed.


  Materials and Methods Top


In this study, we aimed to find the critical factors that affect under-five child mortality by using survival analysis.

A data set of under-five child mortality of Uttar Pradesh was extracted from secondary data (National Family Health Survey [NFHS]-IV) published in 2016.[2] From the data sets, we extracted the socioeconomic and demographic factors which include educational level; sex of household head; women's age in years; current marital status; husband's/partner's education level; husband's/partner's occupation; number of respondents currently working; and respondent's occupation, district, religion, and caste. Proximate and biological factors included total number of children ever born, births in the last 5 years, number of living children, currently breastfeeding, anemia level, smoking cigarettes, chewing tobacco, desire for more children, sex of child, size of child at birth, birth weight (kg), delivery by cesarean section, antenatal care (ANC) visits, birth order, media exposure, and birth interval. Environmental factors included place of residence, wealth index, source of drinking water, slum designation by observation, and type of toilet facility.

The outcome variable of under-five child mortality was defined as mortality from the age of 1 month to the age of 59 months. Therefore, the dependent variable in this study was “the risk of death occurring in an age interval in the 1–59 month period.” The outcome variable was thus survival time in months of children under the age of five.[8]

The explanatory variables were total number of children ever born, births in the last 5 years, number of living children, currently breastfeeding, anemia level, smoking cigarettes, chewing tobacco, desire for more children, sex of the child, size of the child at birth, birth weight (kg), delivery by cesarean section, ANC visits, birth order, media exposure, and birth interval.

Proportional hazard models are a class of survival models. Survival models are related to the time that passes, before some event occurs, to one or more covariates that may be associated with that quantity of time. This model comprises two sections: the fundamental work, frequently significant as h0(t), portraying how the risk of the occasion per time unit changes after some time at baseline levels of covariates; and the impact parameters depicting how the risk shifts in light of explanatory covariates (X) which is a vector of explanatory covariates and β which is a vector of unknown regression parameters. The hazard function in Cox's regression model is given in Eq 1. The Cox PH model (for p independent variables, X1,X2...Xp.) is described by the following equation:



Where h(t) is the hazard function, h0(t) is called the baseline hazard function (the expected hazard without any effect of the considered factors), e is a base of the natural logarithm, β 1, β 2…. β 3 are the regression coefficients. The expression h(t)/h0(t) is called the hazard ratio (HR).[9]

Different parametric models such as Weibull, exponential, log-normal, and log-logistic are used. Exponential distribution is one-parameter lifetime dissemination and a special case of Weibull distribution. In this distribution, hazard function is always constant.[10]

Weibull distribution is one of the adaptable parametric models to study the lifetime data utilized frequently in health field, and hazard function of this distribution could be expanding, decreasing, or constant.[11] Log-logistic is another elective model in place of Weibull distribution. The hazard rate in this distribution is hump shaped (it first increases and then decreases). Log-normal is another distribution which is extensively used in medical sciences.[12],[13] The Weibull, exponential, log-normal, and log-logistic parametric models are fitted on under-five child mortality data.

Model formulation

Consider that the model for parametric fitting is described as γ(x) = γ1(women's age in years) + γ2(education) + γ3(religion) + γ4(total children ever born) + γ5(birth in the last 5 years) + γ6(number of living children) + γ7(currently breastfeeding) + γ8(smoking) + γ9(desire for more children) + γ10(size of child) + γ11(delivery by cesarean section) + γ12(ANC visits) + γ13(birth order). By this model, we have fitted Weibull, exponential, log-normal, and log-logistic models.

Akaike information criterion (AIC) is used to measure the goodness of fit of the estimated statistical models.[14] The AIC value of the model is given as follows:

AIC = −2 × log(L) + 2k

Where k is the number of estimated parameters in the model, L is the maximum value of the likelihood function, and AIC compares the performance of parametric models. The minimum value of AIC gives the best fit model; the distribution of time to event, T, as a function of single covariate is written as follows:[15]

In(T) = β0+ β1x + σε

Where β1 is the coefficient for the corresponding covariate, ε follows extreme minimum value distribution G(0, σ), and σ is the shape parameter. This is also called the accelerated failure-time model because the effect of the covariate is multiplicative on the time scale, and it is said to “accelerate” the survival time. The hazard function of Weibull regression model in proportional hazards form is given by the following equation:







Where and and the baseline hazard function is h0(t) = λγ tλ−1. Parameter θ1 has a HR interpretation for subject-matter audience. The accelerated failure-time form of the hazard function can be written as follows:



Weibull regression model can be written in both accelerated and proportional forms. Weibull model has two parameters, where γ is the shape parameter and λ is the scale parameter.

  • At γ<1, the failure rate decreases over time
  • At γ =1, failure rate remains constant over time
  • At γ >1, failure rate increases over time.


After fitting the parametric models, it was found that the Weibull model is the best for under-five child mortality data, and hence, the Weibull regression model has been used in these data.


  Results Top


Cox proportional hazard model is used to find the significant role of different variables of under-five child mortality. The socioeconomic and demographic factors such as educational level, women's age in years, and religion (P < 0.05) were found to be significant factors in the child's survival status [Table 1]. The environmental factor does not play any significant role in the child's survival status [Table 2]. The proximate and biological factors such as children ever born, births in the last 5 years, number of living children, currently breastfeeding, smoking cigarettes, desire for more children, delivery by cesarean section, ANC visits, and birth order were found to be statistically significant (P < 0.05) [Table 3]. The estimate of the parameters, standard errors, and confidence intervals for Weibull distribution are shown in [Table 4]. In this model, only education and religion out of 13 independent variables were found not to be significant in the under-five child survival data. The estimate of the parameters [Table 5] for Exponential distribution model and this model all the variables found significant except level of education in the under-five child survival data. [Table 6] summarizes the estimates of the parameters for lognormal distribution model in which education, religion, and delivery by cesarean were found to be not significant. [Table 7] summarizes the estimates of the parameters for lognormal distribution model in which education, religion, and delivery by cesarean were found not significant. The Weibull, exponential, log-normal, and log-logistic parametric models have been fitted on the under-five child mortality data. It was found that the Weibull model best fitted as compared to all the other models. Weibull model was found to be with minimum AIC (32985.3) value [Table 8]. All the significant covariates were verified by the Weibull regression model [Table 9].
Table 1: Cox regression analysis of socioeconomic and demographic factors of the child survival status

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Table 2: Cox regression analysis of environment factors of the child survival status

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Table 3: Cox regression analysis of the proximate and biological factors of the child survival status

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Table 4: Estimates of Weibull distribution for under-five child mortality data

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Table 5: Estimates of exponential distribution model for under-five child mortality data

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Table 6: Estimates of log-normal distribution model for under-five child mortality data

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Table 7: Estimates of log-logistic distribution model for under-five child mortality data

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Table 8: Parametric model fitting for under-five child mortality data

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Table 9: Estimates of Weibull regression parameters in under-five child mortality data

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  Discussion Top


Various studies over the past decade have found a positive association between education of mother and child's survival. The risk of under-five mortality is higher in developing countries as compared to developed nations. In this study, the national representative data (NFHS-IV) has been used. The objective is to detect the important factors which are related to under-five child mortality through parametric survival models and find the best parametric model for the study. A Cox proportional model is applied to find the effect of different variables. The variables include socioeconomic, demographic, environmental, and proximate and biological factors.

The Cox regression model is fitted on the time-dependent variables on under-five child mortality data. Similar findings were found in this article. Factors such as education, age, total number of children, and family size were found to be significant.[5] The author analyzed the data through survival analysis approaches and performed Cox proportional hazard model. It is found that mother's education, type of residence, birth order, mother's occupation, and type of birth played a significant role in child survival.[8] These are more or less similar to the findings of our study.

Survival analysis of under-five mortality of children and its associated factors was done by different survival methods such as Kaplan–Meier estimates, Cox proportional hazard regression model, and stratified Cox regression model. Variables such as region, socioeconomic status, contraceptive use, twin child, birth interval, and breastfeeding were found to be significant.[7]

In a recent article on survival analysis for under-five child mortality in Uttar Pradesh done by Saroj et al., the role of significant variables such as educational level, women's age in years, religion, children ever born, births in the last 5 years, number of living children, breastfeeding, smoking cigarettes, desire for more children, size of child at birth, delivery by cesarean section, ANC visits, and birth order was analyzed and found to be significant.[16]

This study is based on the NFHS-IV, and a previous citation[16] is also based on the same data set of Uttar Pradesh. It is clear and verified that almost same variables were found to be significant in both studies. The parametric model fitting is illustrated on the NFHS-IV data. The performance of parametric model is checked by AIC value. The Weibull model is found to be the most suitable model with minimum AIC (32985.3) value among all parametric models. Therefore, the Weibull regression model is preferred to find the role of covariates in under-five child survival status, and it was found that women's age in years, total number of children ever born, births in the last 5 years, number of living children, currently breastfeeding, smoking, desire for more children, size of child, delivery by cesarean section, ANC visits, and birth order covariates were statistically associated with the under-five child mortality.


  Conclusions Top


In the present study, under-five child mortality is one of the major issues across the developing countries. Previously many studies have tried to find the factors behind the under-five child mortality through survival statistical model. The finding of this study suggests that female education needs to be enhanced because it contributes significantly in declining under-five child mortality. Therefore, the present study suggests that governments should take proper initiatives to create public awareness about child health. Researchers, clinicians, health policymakers, and other demographers need to implement more programs related to child health, especially for the under-five year children.

Acknowledgment

The authors would like to thank the editor of the journal for the valuable comments and suggestions. Also, the authors specially thank the Ministry of Health and Family Welfare, Government of India, designated by IIPS, Mumbai, for giving opportunities to use data (NFHS-IV) 2016 in the study and also thank the data management staff and their technical assistance also.

Financial support and sponsorship

Nil.

Conflicts of interest

There are no conflicts of interest.

 
  References Top

1.
World Health Organization. Global Health Observatory (GTO) Data. 2017. Available from: https://www.who.int/gho/child_health/mortality/mortality_under_five_text/en/. [Last accessed on 2018 May 03].  Back to cited text no. 1
    
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Saroj RK, Kumar A, Kumar M. Uttar Pradesh statistical approach for finding the determinants of maternal health services in Uttar Pradesh. Int J Adv Res 2016;4:1-7.  Back to cited text no. 4
    
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Ayele DG, Zewotir TT, Mwambi H. Survival analysis of under-five mortality using Cox and frailty models in Ethiopia. J Health Popul Nutr 2017;36:25.  Back to cited text no. 5
    
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Nilima S. Under five child mortality in Bangladesh: Classical and Bayesian approaches to Cox proportion hazard model. Bangladesh J Sci Res 2017;30:45-54.  Back to cited text no. 6
    
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Geachew Y, Bekele S. Survival analysis of under-five mortality of children and its associated risk factors in Ethiopia. J Biosens Bioelectron 2016;7:1-10.  Back to cited text no. 7
    
8.
Nasejje JB, Mwambi HG, Achia TN. Understanding the determinants of under-five child mortality in Uganda including the estimation of unobserved household and community effects using both frequentist and Bayesian survival analysis approaches. BMC Public Health 2015;15:1003.  Back to cited text no. 8
    
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Cox DR, Oakes D. Analysis of Survival Data. London, New York: Chapman and Hall; 1984. p. 201S.  Back to cited text no. 9
    
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Carroll KJ. On the use and utility of the Weibull model in the analysis of survival data. Control Clin Trials 2003;24:682-701.  Back to cited text no. 10
    
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Benjamin E. Exponential distribution and its role in life testing. Ind Qual Control 1958;15:4-9.  Back to cited text no. 11
    
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Weibull W. A statistical distribution function of wide applicability. J Appl Mech 1951;18:293-7.  Back to cited text no. 12
    
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Aitchison J, Brown JA. The Log-Normal Distribution. Cambridge, England: Cambridge University Press; 1957. p. xviii, 176.  Back to cited text no. 13
    
14.
Crow EL, Shimizu K, editors. Log-Normal Distributions: Theory and Application. New York: Dekker; 1988.  Back to cited text no. 14
    
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Akaike H. A new look at the statistical model identification. Automat Contr IEEE Trans 1974;19:716-23.  Back to cited text no. 15
    
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Saroj RK, Murthy KN, Kumar M. Survival analysis for under-five child mortality in Uttar Pradesh. Int J Res Anal Rev 2018;59:782-9.  Back to cited text no. 16
    



 
 
    Tables

  [Table 1], [Table 2], [Table 3], [Table 4], [Table 5], [Table 6], [Table 7], [Table 8], [Table 9]



 

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