A multiple regression method for analysing stage-frequency data

Summary A linear regression method that allows survival rates to vary from stage to stage is described for the analysis of stage-frequency data. It has advantages over previously suggested methods since the calculations are not iterative, and it is not necessary to have independent estimates of stage durations, numbers entering stages, or the rate of entry to stage 1. Simulation is proposed to determine standard errors for estimates of population parameters, and to assess the goodness of fit of models.     

A simplified robust estimate of the birth rate

It is shown that other estimates of the birthrate can be derived from Coale's robust birthrate estimate. Coale's estimate is nearly equal to the birthrate obtainable from reverse survival or reverse projection of the proportion of a population under age 15 (both sexes), or C(15), using a life table corresponding to l5. As a sequel to this, a birth rate estimate was obtained that does not require reference to stable population models and results in computational economy and ease. Taking advantage of the strong linear relation between l5 and 15L0, a simple robust estimate was derived of the birthrate that does not depend upon model stable populations or model life tables. After presenting these methods, their use is illustrated with data from several Asian and African countries. Coale (1981) suggested using the observed C(15) for both sexes and l5 to locate an appropriate stable population from a family of stable models to represent the observed population and to use its birthrate as an estimate of the population under study. The estimate of l5 can be obtained by any of the indirect methods like the Brass method. Coale observed that such methods yield birthrates that are not much affected even when the populations are not stable. He also suggested an adjustment for the stable birthrate for nonstability. To obtain the birthrate, one needs the denominator, namely, the number of persons that lived. This is obtained by using the rate of increase, r, which differs for a stable and a nonstable or observed population. Various methods can be used to obtain the time reference of the mortality estimate, l5, by providing years prior to the survey or census to which the l5 estimate is applicable.     

Correcting missing-data bias in historical demography

Studies on population history are often based on incomplete records of life histories. For instance, in studies using data obtained from family reconstitution, the date of death is right censored (by migration) and the censoring time is never observed. Several methods for the correction of mortality estimates are proposed in the literature, most of which first estimate the number of individuals at risk and then use standard techniques to estimate mortality. Other methods are based on statistical models. In this paper all methods are reviewed, and their merits are compared by applying them to simulated and to seventeenth-century data from the English parish of Reigate. An ad hoc method proposed by Ruggles performs reasonably well. Methods based on statistical models, provided they are sufficiently realistic, give comparable accuracy and allow the estimation of several other quantities of interest, such as the distribution of migration times.     

General growth balance method: A reformulation for populations open to migration

This paper proposes a reformulation of the general growth balance method for estimating census and registration completeness so as to make it applicable even to populations that are affected by migration. It also discusses a new procedure of line fitting that could be useful in countries where the input data are severely affected by age misreporting. The method is applicable to countries where data on age distribution of the population are available for two points in time from either censuses or surveys. Following closely the original proposal of Brass, it involves adjusting the ‘partial’ birth rates for age-specific disturbances from growth and migration rates. Beyond correcting the death rates, the method is useful in inferring the relative completeness of the censuses, and in deriving a robust estimate of birth rate under certain conditions. The application of the method is illustrated using the example of the male population of the Indian state of Uttar Pradesh for the period 1981 to 1991.     

General growth balance method: A reformulation for populations open to migration

This paper proposes a reformulation of the general growth balance method for estimating census and registration completeness so as to make it applicable even to populations that are affected by migration. It also discusses a new procedure of line fitting that could be useful in countries where the input data are severely affected by age misreporting. The method is applicable to countries where data on age distribution of the population are available for two points in time from either censuses or surveys. Following closely the original proposal of Brass, it involves adjusting the 'partial' birth rates for age-specific disturbances from growth and migration rates. Beyond correcting the death rates, the method is useful in inferring the relative completeness of the censuses, and in deriving a robust estimate of birth rate under certain conditions. The application of the method is illustrated using the example of the male population of the Indian state of Uttar Pradesh for the period 1981 to 1991.     

Note on a method for analyzing stage-frequency data

Summary A new method for analyzing stage-frequency data is proposed which is based on the estimation of rates of transition between one stage and the next highest stage in one unit of time, and a unit time survival rate that is assumed to be constant. Once these estimates are calculated it becomes possible to also estimate the mean durations of stages, stage-specific survival rates, and numbers entering stages. An advantage of the method is that it can be applied with any distribution of entry times to stage 1, and any distribution of numbers in stages when sampling begins. Use of the method is illustrated on data from a copepod population in a Canadian lake.     

Estimatingdendroctonus frontalis (Coleoptera: Scolytidae) daily infestation dynamics

Mathematical procedures are given to estimate infestation totals and daily life stage arrivals, departures, and mortality ofDendroctonus frontalis Zimmermann for an infested tree in the field. These estimates are based on minimal sample data and are designed to utilize all available information. Daily arrival estimates for larvae, pupae, and callow adults are obtained by indirect analysis without direct observation of these stages. The procedures are applied to 147 infested trees, and the results are transformed to a common time basis to obtain daily expectations by life stage for an “average” tree. These expectations suggest optimal times for field sampling or relative times of sampling when optimal times are missed. Expected daily arrival distributions by life stage for a single egg and a single attacking adult are given. Procedures are given for utilizing collateral information to obtain an infestation total and daily arrival estimates for a boundary life stage. The results of this study are applicable to anyD. frontalis field study, and the procedures given are applicable to any bark inhabiting insect having similar habits.     

On the nature of errors involved in estimating stage-specific survival rates by Southwood's method for a population with overlapping stages

Summary This paper has examined the effect of within-stage mortality on the estimation of stage-specific survival rates bySouthwood's (1978, p. 358) method. As pointed out bySouthwood, both the severity and timing of mortality affect the mean duration of a life stage, and consequently the estimate of the number of individuals entering that stage. Knowledge of the form of the survivorship curve permits correction of the estimate under certain circumstances. The use ofSouthwood's method with two overlapping stages having different rates and patterns of mortality leads to complex errors in the estimation of survival for the first stage. The nature of these errors is examined analytically and via a simulation model.Southwood's method is fairly robust, with moderate differences in mortality rates leading to acceptable errors in estimating survival for the first stage. When both the rate and pattern of mortality in both life stages are the same, then the survival estimate is made without error. Precise estimates of stage-specific survival will not usually be possible withSouthwood's method because of the errors introduced by the very parameters being measured. Direct measurement of mortality rates and survivorship patterns (seeSouthwood, 1978, p. 309) is strongly advised, at least in preliminary work.     

Further improvements to a method for analysing stage-frequency data

Summary An iterative procedure for correcting stage-frequency data is described to allow for situations where the period during which a population is sampled begins after some individuals have entered stage 2 or ends before all individuals are dead. The reason for correcting data in this way is to enableKiritani andNakasuji's method for estimating stage-specific survival rates, with extensions proposed byManly (1976, 1977), to be used to analyse the data. The proposed procedure is illustrated on data obtained by sampling a population of the grasshopperChorthippus brunneus passing through four instar stages to reach the adult stage.     

Studies on the spatial distribution pattern of larvae of the mosquito,Anopheles sinensis, in rice fields

Summary The spatial distribution patterns of the population ofAnopheles sinensis larvae were studied in the rice field area in the suburb of Urawa city in Japan, during the summer seasons in 1973 and 1974. The distribution pattern of the larval population within the field, analysed by the m−m regression method, indicated that the basic component of larval distribution was not a group of individuals but a single individual and such components were distributed contagiously over the field. This basic pattern did not change significantly according to developmental stage, census date or field. Therefore, we could describe the distribution pattern of the population in a rice field by the single linear regression, x=0.021+1.339x(r²−0.912). Also, the relation for the whole population in the field area including the five fields could be shown by the linear regression, x=0.049+1.749x(r²−0.959). The value of α remained to be nearly equal to zero, but the value of β became larger than the value for the single-field relation. Such a change in distribution pattern seemed to reflect the greater heterogeneity in conditions among the fields than within individual field. Using the information on the distribution patterns mentioned above, some considerations were given on the sampling plans for mosquito larvae, including samplesize determination and application of sequential methods to estimate population size as well as to classify population level.     

The time response in averted births

Abstract A calculation of the timing of births that are averted may seem a curious exercise, when not only do the births in question not occur, but the corresponding conceptions may never have existed. However, such a calculation may have considerable use. In order to assess the likely direct impact of a contraceptive programme on birth rates it is useful to estimate the number of births that would, in the absence of the programme, have occurred among the couples who accept it. Moreover, some time would necessarily elapse before a new 'steady state' in fertility could be reached, even if the programme and the potentially fertile population did not change in any way; and it is worth while to seek to find the times (for a few years after the start of a programme) when the (averted) births would have occurred in its absence, and to examine any inherent oscillations produced in birth rates by it. This question is considered below only for groups of women aged 20 at marriage (a state which is taken to be the start of regular exposure to the risk of conception), but the same methods are applicable to other ages, (possibly allowing for mortality) and appropriate combinations of age groups and cohorts in the fertile range may be used to estimate changes in fertility and reproduction rates expected from a programme, subject to given conditions, for several years after its start. The methods can also be generalised, by means of convolution, to contraceptive programmes that change with time, but these are not considered further.     

A method of estimating the time of marital fertility decline and associated parameters

Significant research attention has been given to historical patterns of marital fertility transitions in currently industrialized countries. Specifically, studies consider the time of the onset of fertility decline and its distribution among populations or population subgroups; the distribution of pre-decline parital fertility levels; and/or the rate of marital fertility decline. Analyses of pre-decline fertility level and its rate of decline, however, depend upon the procedure used to estimate the time of fertility decline. The Princeton European Fertility Project is the most prominent historical fertility study ever conducted. The procedure employed to estimate the timing parameter in these Princeton studies is described. An alternative statistical procedure is then proposed for detecting the onset of the transition from high to low marital fertility; the method may also be used to find the termination point of decline where the sequence of fertility variables is long enough. Both methods produce maximum likelihood least squares estimates, but the form proposed in the text has conceptual advantages.     

A reply to Kim's comment

This reply criticizes Kim's note as incorrectly characterizing the essential feature of the method proposed for life table construction. The method suggested for estimating N(a), the number attaining age 2 during the intercensal period, is to make a separate estimate of the contribution to N (a) made by each single-year cohort that attains 'a' during the period between censuses. Each cohort estimate is constructed by interpolation, utilizing as data the recorded number in the relevant single-year cohorts in the 2 censuses. 2 methods of interpolation were proposed. 1 is an iterative procedure that constructs a preliminary life table by linear interpolation for each cohort and then derives more refined interpolation factors from this preliminary life table. The other procedure derives interpolation factors on the assumption that the proportionate distribution of deaths by age as each cohort moves from the earlier to the later census date is the same as the proportionate distribution of deaths by age over the same age range in a model life table. The advantage of the proposed procedure is that it supplies better estimates of N (a) than do alternative methods. The author concedes that a life table calculated from accurately recorded deaths and an accurately enumerated population would ordinarily be superior. However, he also notes that in the absence of registered deaths data, there is no precise enough conventional method to yield accurate values of average intercensal single-year age-specific mortality rates from nothing more than 2 accurate censuses 11 years apart. A common procedure for calculating life expectation at a very advanced age is to calculate the reciprocal of the death rate among persons over the age in question.     

Criteria for selecting a suitable method for producing post-2000 county population estimates: A case study of population estimates in Illinois

We compared 2000 county population estimates for Illinois against 2000 census counts. Administrative records (ADREC) and ratio correlation (Ratio-CORR) methods were used to produce two sets of controlled county estimates for 2000; a third set represented an average of the estimates reached using these methods. Another set using the ADREC method was not controlled to any estimate. Also, the 2000 estimates were adjusted for undercount in the 1990 census. We compared performance of these methods with the performance of two naive models: (i) do nothing and (ii) constant growth rate. ADREC estimates were more accurate than estimates from the Ratio-CORR or Average method in terms of Mean Absolute Percent (MAPE) or weighted MAPE. Undercount adjustment in general improved the accuracy of the estimates for all three methods. A top-down or bottom-up approach worked equally well. As a single method, ADREC performed best.     

A flexible two-dimensional mortality model for use in indirect estimation

Mortality estimates for many populations are derived using model life tables, which describe typical age patterns of human mortality. We propose a new system of model life tables as a means of improving the quality and transparency of such estimates. A flexible two-dimensional model was fitted to a collection of life tables from the Human Mortality Database. The model can be used to estimate full life tables given one or two pieces of information: child mortality only, or child and adult mortality. Using life tables from a variety of sources, we have compared the performance of new and old methods. The new model outperforms the Coale-Demeny and UN model life tables. Estimation errors are similar to those produced by the modified Brass logit procedure. The proposed model is better suited to the practical needs of mortality estimation, since both input parameters are continuous yet the second one is optional.     

Application of a marking-and-recapture method for the analysis of larval-adult populations of an insect,Nezara viridula (Hemiptera: Pentatomidae)

Summary Difficulty arises in applying marking-and-recapture methods to insects when the probability of recapture of marked individuals is changed with advancing age, either due to detachment of the mark by moulting (in the case of larvae) or to changes in their survival rate or their behaviour. A modification of the re-recapture method (Leslie et al., 1953) has been devised to analyze the capture-recapture data of the 5th-instar larvae and adults ofNezara viridula L. Estimation of the rate of moulting to the adult stage is made with the aid of additional information on larval survival. Migration rates of the larvae between the two halves of the census field is estimated byIwao's (1963) method. Through these analyses, the dynamic feature of the population during transition from the 5th instar to, adult is revealed. Several problems involved in the application of marking-and-recapture methods to insect populations are discussed. Contribution from the Entomological Laboratory, Kyoto University No. 392.     

Living Environment Preferences of the Inhabitants of Istanbul: A Modified Hierarchical Information Integration Model

This paper presents a two-stage research to model the different priorities and expectations about living environment preferences of the inhabitants of Istanbul, Turkey's largest metropolitan with a population of 10 million. In the first stage, a modified hierarchical information integration approach was used to estimate the utilities of different attributes for each individual sampled from the inhabitants of Istanbul. This is a decompositional approach and involves measuring individual preferences. In this study, not only aggregate results are reported but also a segmentation study is carried out to explore the heterogeneity in respondents' preferences. Identification of such segments would help planner offer different planning options to groups with different preferences. Thus, the second stage of this study consists of identifying distinct groups of inhabitants with different preference structures by using cluster analysis. The resulting information is believed to be more useful especially to understand diverging demands of inhabitants of Istanbul.     

A method for deriving mortality estimates from incomplete vital Statistics

Summary Although they are available in many developing countries vital registration records are very little used for mortality estimation which is still mainly based on census returns. However, defective death records may yield accurate estimations of mortality. This procedure requires few data only; a sex-age distribution of the population (preferably at the middle of a period) and a sexage distribution of deaths, either derived from vital records or from census returns to questions relating to deaths during the preceding twelve months. This method is based on the observation that for a fixed age structure of the population, there is a one-one relation between the age structure of deaths (measured by the proportion of deaths at older ages) and the level of mortality (measured by the death rate above a certain minimum age). It is assumed that at ages above this minimum the rate of underregistration of deaths does not vary significantly with age. Therefore, the age distribution of registered deaths makes it possible to estimate the true proportion of deaths at older ages. This in its turn will permit the estimation of the true level of mortality, because of the relation which exists between age structure of deaths and level of mortality. The true level is then compared with the observed, to estimate the rate of underregistration, and observed age-specific death rates can be adjusted in the light of this knowledge.     

Obtaining multistate life table distributions for highly refined subpopulations from cross-sectional data: A bayesian extension of sullivan’s method

Multistate life table methods are often used to estimate the proportion of remaining life that individuals can expect to spend in various states, such as healthy and unhealthy states. Sullivan’s method is commonly used when panels containing data on transitions are unavailable and true multistate tables cannot be generated. Sullivan’s method requires only cross-sectional mortality data and cross-sectional data indicating prevalence in states of interest. Such data often come from sample surveys, which are widely available. Although the data requirements for Sullivan’s method are minimal, the method is limited in its ability to produce estimates for subpopulations because of limited disaggregation of data in cross-sectional mortality files and small cell sizes in aggregated survey data. In this article, we develop, test, and demonstrate a method that adapts Sullivan’s approach to allow the inclusion of covariates in producing interval estimates of state expectancies for any desired subpopulation that can be specified in the cross-sectional prevalence data. The method involves a three-step process: (1) using Gibbs sampling to sample parameters from a bivariate regression model; (2) using ecological inference for producing transition probability matrices from the Gibbs samples; (3) using standard multistate calculations to convert the transition probability matrices into multistate life tables.     

A census-based method for estimating adult mortality

Abstract A simple method is presented for converting an age distribution in any closed population into the stationary population corresponding to its current mortality conditions. The conversion only requires a set of age-specific growth rates, which will normally be available from successive censuses. From the stationary population, any life table mortality measure of interest can be computed. The index most robust to normal data errors in developing countries is life expectancy, and the paper focuses on its calculation. The sensitivity of results to various forms of data error is considered, and procedures are proposed for removing errors resulting from differential census coverage completeness and from age misstatement at older ages. Applications of the procedures are made to data from Sweden, India and South Korea. Because of the absence of a radix, estimation of life expectancy usually will begin at the fifth birthday.