Estimating Infant Mortality with Special Reference to Nepal: An Alternative Approach

Transcription

1 Nepal Journal of Science andtechnology 5(3) Estimating Infant Mortality with Special Reference to Nepal: n lternative pproach S.P. Pate1 Thakur Multiple Campus Tribhuvan University, Birgunj bstract The estimates of infant mortality rate (IMR) so far available in the country were computed from the census or survey data employing costly and sophisticated indirect techniques borrowed from foreign countries.the present study has been designed to estimate IMR for Nepal from the estimated values of minimum relevant parameters (e.g. eo and el ) without using any census or survey data and model life tables.the estimates of eo required for estimating IMR have been extracted from various sources whereas estimates of el are obtained from a suitable model developed in this paper. The validity of the models was ascertained by applying the models to obtain estimates for Nepal, comparing the estimated IMRs with those from other sources and by computing relevant tests of model adequacy whenever possible. The model was found to provide satisfactory estimates of IMR for Nepal. For instance, the model provided the most plausible estimate of IMR of 7.6 (per thousand live births) for Nepal for the year 3, which may be considered close and consistent to the IMR of 7. (per thousand live births) provided by the ESCP (3). Key words: development indicator, health indicator, life expectancy at birth, life expectancy at age one, regression Introduction Infant mortality rate (IMR) is an important indicator of development. It is widely used for assessing the socio-economic and health situation in developing countries (Chandrasekhar 197). If vital registration is complete, IMR for each year can be calculated in the conventional manner directly from the system's data (Hill 199 1). Unfortunately, complete vital registration system is practically non-existent in Nepal (Karki 1989). In the absence of complete vital registration system, indirect techniques proposed by Brass (1964), Trussell (1975), Palloni and Heligman (1986) and others have been employed for estimating IMR for Nepal using the census or survey data. The estimation of IMR by these techniques needs accurate birth history data to be collected from census or survey; reliable and adequate age patterns of child mortality for selecting an appropriate method and model life table; and lastly, many assumptions to be satisfied by the population under study But irony is that the birth and death data collected from the censuses or surveys of Nepal are highly inaccurate (Pant 1996). Further, many assumptions underlying the models are not justifiable in the population under study (Hill & Yazbek 1993). Moreover, there is no reliable age distribution of mortality for Nepal to use in deciding the right family that fits (CBS 1995). part from this, collection of census or survey data with fair accuracy needs a lot of time, money and highly skilled manpower. But reality is that Nepal is a poor country where 4 percent of her people still live below the poverty line, and the half of the population can not yet read or write (UNDP 1). Most enumerators of censuses or surveys are found to fill their questionnaires at home without bothering to contact the real respondents. Keeping in view the socio-economic and demographic realities of our own country, this paper presents a simple model for estimating IMR for Nepal from the minimum relevant parameters i.e. life expectancy at birth (eo) and life expectancy at age one (el ). The model is applied to obtain levels and trends of IMR for Nepal. The estimates of eo for the purpose are derived from various reliable sources whereas estimates of el are obtained from a suitable regression model presented in this paper Life expectancy at birth (eo ) has been selected as a key relevant parameter needed for estimating IMR because it represents the "end result" of development;

2 S.P. PateVNepal Journal of Science andtechnology (3) can be easily obtained from either suitable models or various publications; is independent of age structure of age structure of population; and more importantly it is strongly correlated with the level of IMR ( UNICEF 1989; Woods 1993). nother parameter i.e. el can be obtained from eo using suitable models. The validity of the model is ascertained by applying the model to obtain the estimates of IMR for Nepal; comparing the estimated IMRs for Nepal with the other estimates available to the country; and by computing relevant tests for model adequacy whenever possible. Methodology The proposed methodology attempts to relate IMR with eo and el by the help of usual life table functions. n expression for life expectancy at birth is given by: [For derivation of the equation see Pressat, R Where the symbols have the following meanings: eo = Life expectancy at birth; l() = radix of life table usually round number 1,1 or 1; w = last age attained. With simple adjustments and using some other life table functions, the above equation can be written as: l() + 1(3)+... +l(w) where el =... (1.3) l(1) indicates curate expectancy of life at age one. Since q is not in common practice, the following expression may be used for the purpose: [For derivation of the equation see Biswas 1988: 111 Now with help of this and some other life table functions, the equation () can be written as: 1 when - q (1) is very small. Simplifying the equation (1.5) and multiplying the right hand side by 1, the model for estimating IMR can be written as: where q (1) = Estimated IMR [per thousand live births]; e = Life expectancy at birth (years); el = Life expectancy at age one (years). This model can be used to obtain reliable estimates of IMR for Nepal if accurate estimates of e: and ep are available. Data Required for Estimating IMR The estimates of eo required for estimating IMR for Nepal can be easily obtained from either suitab!. models or various publicztions. But it is not easy to obtain timely and reliable estimates of e, for Nepal. To solve this problem, an attempt is made here to obtain timely and reliable estimates of el from eo. Since several empirical studies show almost a linear relationship between el and eo, it was decided to fit a regression model of type: Y=a+bX+e... (.1) where Y = el (years) ; X = eo (years); e = random error term; and 'a' and 'b' parameters to be estimated. The parameters are estimated by using the following set of data extracted from the "General pattern" of the United Nations (198) model life tables which is assumed to exhibit mortality patterns close similar the "West" pattern of Coale and Demeny (1966) model life tables:

3 S.P. PateVNepal Journal of Science andtechnology (3) o o Results Table 1. ~stimates of el and eo extracted frorn the model that fails in diagnostic checking for model "General Pattern" of the UN (198) Model Lifexbles adequacy will always remain a suspect and little faith can be put in the results (Kerlinger 1998).Therefore, Males Females it is essential that the model fitted for estimation x(=e) y(=e1) x(=e) ~(=e,) purpose should satisfy the important tests of model adequacy. The first part discusses adequacy of the model proposed for estimating whereas the second part discusses adequacy of the model proposed for estimating IMR for Nepal. Models for Estimating ep and Discussions In this part, diagnostic checking for model adequacy is done by applying the model in Nepal's context; and by computing major relevant tests of model adequacy whenever possible. The estimated el s for Nepal shows close agreement with the limited estimates available to the country. For instance, the estimated values of ep for males and females for the year are 56.1 and 53. years respectively which may be This table gives the following values of constants considered close consistent to ep of and needed for estimating the parameters: years provided by the CBS (1987a). The results of For males: major tests of model adequacy presented by the EX = 848 CY = CXY = following table also indicate the suitability of the model. For females: EX = 848 ZY = CXY = C? = 55 ZY* = n=15 Using these data, simple regression approach gives the following estimated regression model for computing e, el (life expectancy at age one) for Nepal: For males: Y = X... (.) n = 15, R = 99.95%, S.E. (Y) =.179 For females: Y = X...(.3) n = 15, R = 99.65%, S.E. (Y) =.359 ~~~~~i~~ the equations (.)and (.31, the model for estimating ep for both sexes can be written as: Consider the diagnostic checking of the model adequacy for males. The high value of coefficient of determination R (= 99.94%) clearly indicates the goodness of fit. Similarly, the small value of S.E. of estimates (=.179) indicates the high reliability of the model. The goodness of fit of a regression model is mostly affected by the estimated values of the parameters. The estimated parameters may be considered significant at P<.5 and PC.1 as they satisfied the 't' test. For instance, the parameter d may be considered significant at PC.5 and P<.1 as the calculated value of It1 statistic ford is.74 which is greater than the tabulated values t* (=.16) and t** (= 1.771) for n - (= 13) degrees of freedom.this is also true for the other remaining pararneters.nother way to test the significance of the regression model is to compute the 'F test. The calculated value of 'F ratio' (= ) is evidently greater than the tabulated values F* (= 4.67) and F** (= 9.9) for (l,13) degrees of freedom and therefore, the regression model may Forbothsexes:Y= X... (.4) be considered significant. The model for females also o o satisfies all these tests described above. However the where '= Estimated el (years); = (years) main problem is that the results show presence of provided. autocorrelation in the residuals, which may be

4 S.F? PateVNepal Journal of Science andtechnology (3) Table. Tests computed for diagnostic checking for model adequacy Tests for Model dequacy Results 1. Tests for Goodness of fit: i. Based on coefficient of determination: R (%) r. S.E. of parameters: # n S.E. (YE) S.E. ( a~) S.E. ( b~) 3. Tests of significance: i. Based on 't' test: For : It1 For b: It1 For r: It1 Tabulated t* Tabulated t** ii. Based on NOV and 'F Ratio': TSS SSR SSE Calculated 'F Ratio' Tabulated F* Tabulated F** iii. Based on PE. (r): P.E. (r) 4. D-W test for utocorrelation: d statistic. P du* dl* d,** dl** Notes: * p<.5. ** p<o.ol # Refers to the results of tests computed for the model (.). ## Refers to the results of tests computed for the model (.3). ## Results attributed to several reasons (Gujarati 985). In summary, the models may be used to compute timely and reliable estimates of ep for Nepal. Model for Estimating IMR and Discussions In this part, diagnostic checking for model adequacy is done by applying the model in Nepal's context; and by comparing the estimated IMRs for Nepal with other estimates available to the country from the national and international publications (e.g. Singh 1979; CBS, 1987a, 1995, UNDP, WB 3, ESCP 3) possibly over a wide range of periods. The following table and figure show the comparison of the estimated IMRs for Nepal with the other estimates available to the country: The findings of the study are presented systematically. The following table and figure summarize the results computed for testing the model adequacy. Table 3. Comparison of the estimated IMRs for Nepal with the other estimates Estimates of other sources Present study Years en IMR 3vi Source: Singh, M.L. (1979); CBS (1987a, 1995): UNDP (); WB (3); ESCP(3).

5 S.P. PateVNepal Journal of Science andtechnology (3) Notes: i iv v vi Refers to the estimates of Baidyanathan and Gaige (1973), PI? Refers to the estimates of Singh, (1 979), p. 17. Refers to the estimates ofthe NE (1 986). Refers to the estimates of the CBS (1 999, p.16. Refers to the estimates of the UNDP (), p Refers to the estimates of the ESCP(3). Refers to the average estimates of males and females. Refers to the estimates ofthe WB (3), p. 35. Refers to the estimates ofthe model (.4). Refers to the estimates of the model (I.6). accuracy of data.the main problem with this model is that it requires accurate estimates of eo and e, which are not available developing countries like Nepal. In summary, the model seems to provide satisfactory estimates of IMR for Nepal over a wide range of periods. Conclusions The advantages of the indirect techniques in mortality estimation cannot be over emphasized in developing countries like Nepal. The proposed model is very simple and easy to apply; does not require census or survey data and model life tables for estimation of IMR; and gives approximately reliable estimates for Nepal. The results indicate that the model is effective in providing approximately reliable estimates of IMR for Nepal over a wide range of periods. Conclusively, the model may be'considered suitable for estimating IMR for Nepal for over a wide range of periods of practical interest whenever accurate estimates of eo and el are available Years Fig.1. Comparison of the estimated IMRs for Nepal with the other estimates. Figure 1 shows declining trends of IMR for Nepal as is usually expected. More importantly, it shows strong agreement betwen the estimated IMRs and the other estimates available to the country from different sources over a wide range of periods. Howeveq it also shows little difference in the estimated IMRs and the other estimates at distant past, which may be attributed to the limitations of the data sources.the model is further enhanced because it is based on few assumptions, does not necessarily require census or survey data and model life tables for estimation of MR. The key assumption underlying the model is that it uses life expectancy at birth, which is independent of age structure of population and is not affected by extraneous factors. Despite the advantages the model has some limitations too. The model seems to provide better estimates for more recent periods than for distant past. The model seems to be highly affected by cknowledgement The author is thankful to Dr. Mrigendra La1 Singh, Professor of Statistics at Central Department of Statistics, Tribhuvan University, Kirtipur, Kathmandu. The study was conducted with the grant support of University Grant Commission (UGC), Kathmandu. References Baidyanathan, K.E. and EH. Gaige Estimates of abridged life tables, corrected sex-age distribution and Birth and Death Rates for Nepal, 1954.Demography India (): Biswas, Suddhendu Stochastic Processes in Demography andpplications. Wiley Eastern Limited, India. Brass, W Uses of census andsuwey data for estimation of vital rates. Paper Presented for thefrican Seminar on Vital Statistics, ddis baba. CBS.1987a. Population Monograph of NepaL Central Bureau of Statistics, Kathmandu. CBS Population Monograph of Nepal Central Bureau of Statistics, Kathmandu. Chandrasekhar, S Infant Moflalify, Population Gmwth and Family Planning in India George llene and Unwine Ltd. London. Code,.J. and I? Demeny, Regional Model Life Tables and Stable Population Princeton University Press, Princeton.

6 S.P. PateVNepal Journal of Science andtechnology (3) ESCP. 3. Population and Development Indicators for sia and the Pacijic 3. ESCP, Bangkok. Gujarati, D Basic Econometrics. McGraw-Hill Book Company, Hill, K pproaches to the measurement of childhood mortality: comparative review. Population Index.57(3): Hill, K. and.yazbek Trends in Child Mortali~ : Estimates for 83 Developing Countries United Nations Children's Fund, NewYork. Karki, Y.B Vital registration system in Nepal. In: National Seminar on Social Statistics Central Bureau of Statistics, HMGNepal, Kathmandu. Kerlinger, EN Foundations of Behavioral Research. Surjeet Publications, Delhi. NE Nepal Fertility and Mortality Survey: Preliminary Report. New Era, Kathmandu. Palloni,. and L.Heligman Re-estimation of structural parameters to obtain estimates of mortality in developing countries. Population Bulletin of the United Nations 18: Pant, P.D The quality of the reported age of mother date of birth and death of children in the 1976 NFS and 1986 NFFS data Nepal Population Journal 5(4): 1-8. Singh, M.L Population Dynamics of Nepa1:n nalytic Study. Ph.D. Thesis. Tribhuvan University. Kathmandu. Trussel1,T.J re-estimation of the multiplying factors for the Brass Technique for determining childhood survivorship rates Population Studies9(1): UNDP 1. Human Development Repoc 1. Poverty Reduction and Governance, Kathmandu. UNDP.. Human Development Report. Oxford University Press, New York. UNICEF The State of World's Children. Oxford University Press, NewYork UN Model life tables for developing countries Population Studies No. ZI, New York. WB. 3. World Development Repot?. Washington D.C., US. Woods, R On the historical relationship between infant and adult morali ty Population Studies47():