Spatial smoothing of low birth weight rate in Bangladesh using Bayesian hierarchical model

The term low birth weight refers an event where a newborn baby has a weight that is less than 2500?g. This is an essential indicator while the interest is in public health issues such as infant mortality, maternal complications, and antenatal care, etc. of a country, particularly, for a developing country like Bangladesh. The regional development programs are in the current priority list of Bangladesh government and other policy makers. Many of such regional development programs may need the spatial distribution of relative risk for low birth weight that can be obtained by mapping the risks over small area domains like the districts of Bangladesh. This study aims to find whether is there any spatial dependence among the relative risks of low birth weight for the districts of Bangladesh. This has been investigated using Moran's I statistic and a significant spatial dependence in the relative risks was found. Then, attempt has been made to rediscover the spatial distribution based on the idea of spatial smoothing. A Bayesian hierarchical model is used considering percent received antenatal care and female labor force participation as covariates to smooth the observed relative risks of low birth weight in 64 districts of Bangladesh. Revised spatial distribution taking the spatial dependence under consideration through intrinsic conditional autoregressive model is derived and showed in choropleth map along with its different behaviors.     

A note on a transient queuing system of a linear birth–immigration process in presence of twin births

In this article, we consider a simple transient queuing system, i.e., a linear birth process with immigration in the presence of twin births. We find the differential-difference equation and also the probability-generating function (p.g.f.) for this process. Again, we generalize it into a linear birth process with immigration in the presence of both single birth or twin births and again for the case of multiple births. From the p.g.f. of linear birth process with immigration in the presence of twin births, we find some particular transient queuing processes like linear birth process with twin births and simple immigration process. Direct derivations of mean and variance of these processes are also discussed without using the generating functions.     

The sex ratio at birth

Several aspects of the disparity in birth ratio of males over females are discussed including variations among different races, variations by order of birth, by age of the parent, and in multiple births. Avenues of statistical exploration are suggested in an attempt to indicate certain peculiarities in nature. The Negro population in the United States has a sex ratio of 102 males to 100 females as opposed to 105:100 for whites, a highly significant difference. Inferences from these statistics are suggested for study of the sex ratios of mixed unions. The group classified as Mulatto show a lower sex ratio and further analysis of this was suggested including examination of slave records. For the white population sex ratio declines from 106.2 to 102.9 between 1st order and 7th order births. This is highly significant. However, nonwhite determinations were more irregular. Data limitations on sex ratio by age of parent prevented conclusive results. Multiple births among whites show a decline from 105.3 for single live births to 103.2 for twins and 86.1 for all other plural deliveries. Among nonwhites these ratios are 102.3, 99.7, and 102.6 respectively. Further information should be developed using the multiple facts relating to the sex ratio at birth.     

Bayesian joint modeling of correlated counts data with application to adverse birth outcomes

In disease mapping, health outcomes measured at the same spatial locations may be correlated, so one can consider joint modeling the multivariate health outcomes accounting for their dependence. The general approaches often used for joint modeling include shared component models and multivariate models. An alternative way to model the association between two health outcomes, when one outcome can naturally serve as a covariate of the other, is to use ecological regression model. For example, in our application, preterm birth (PTB) can be treated as a predictor for low birth weight (LBW) and vice versa. Therefore, we proposed to blend the ideas from joint modeling and ecological regression methods to jointly model the relative risks for LBW and PTBs over the health districts in Saskatchewan, Canada, in 2000–2010. This approach is helpful when proxy of areal-level contextual factors can be derived based on the outcomes themselves when direct information on risk factors are not readily available. Our results indicate that the proposed approach improves the model fit when compared with the conventional joint modeling methods. Further, we showed that when no strong spatial autocorrelation is present, joint outcome modeling using only independent error terms can still provide a better model fit when compared with the separate modeling.     

Fisher Information for a partially observable simple birth process

ABSTRACT

In this paper, we study the Fisher Information for the birth rate of a partially observable simple birth process involving n observations. We suppose that at each observation time, each individual in the population can be observed independently with known fixed probability p. Finding an analytical form of the Fisher Information in general appears intractable. Nonetheless, we find a very good approximation for the Fisher Information by exploiting the probabilistic properties of the underlying stochastic process. Both numerical and theoretical results strongly support the latter approximation and confirm its high level of accuracy.     

Semi-parametric survival analysis via Dirichlet process mixtures of the First Hitting Time model

Time-to-event data often violate the proportional hazards assumption inherent in the popular Cox regression model. Such violations are especially common in the sphere of biological and medical data where latent heterogeneity due to unmeasured covariates or time varying effects are common. A variety of parametric survival models have been proposed in the literature which make more appropriate assumptions on the hazard function, at least for certain applications. One such model is derived from the First Hitting Time (FHT) paradigm which assumes that a subject’s event time is determined by a latent stochastic process reaching a threshold value. Several random effects specifications of the FHT model have also been proposed which allow for better modeling of data with unmeasured covariates. While often appropriate, these methods often display limited flexibility due to their inability to model a wide range of heterogeneities. To address this issue, we propose a Bayesian model which loosens assumptions on the mixing distribution inherent in the random effects FHT models currently in use. We demonstrate via simulation study that the proposed model greatly improves both survival and parameter estimation in the presence of latent heterogeneity. We also apply the proposed methodology to data from a toxicology/carcinogenicity study which exhibits nonproportional hazards and contrast the results with both the Cox model and two popular FHT models.

     

THE CASE FOR PARITY AND BIRTH-ORDER STATISTICS

Parity refers to the number of (live) births that a woman (or man) has had. Birth order refers to whether a birth is the first, second, third or higher‐order birth of the parent. In the context of low and shifting fertility, parity and birth‐order statistics are becoming increasingly important for understanding fertility trends and patterns, for policy, and for carrying out projections of future fertility. In Australia, the main sources of demographic data are birth, death and marriage registers, and the five‐yearly national census. Both the birth registers and the census are ideally placed to collect data required to calculate parity and birth‐order statistics. However not all Australian states and territories collect or code the necessary information in the birth registers, and the parity question ‘For each female, how many babies has she ever had?’ is only asked every second census; that is, once every 10 years. In this paper, we outline the importance and uses of parity and birth‐order statistics. We discuss the Australian data available at present and their gaps and shortcomings. We then describe the ‘gold standard’ of parity and birth‐order statistics and how Australia can achieve this standard through some minor changes to the data collection process.     

Mixture modelling of recurrent event times with long-term survivors: Analysis of Hutterite birth intervals

We propose a mixture model that combines a discrete-time survival model for analyzing the correlated times between recurrent events, e.g. births, with a logistic regression model for the probability of never experiencing the event of interest, i.e., being a long-term survivor. The proposed survival model incorporates both observed and unobserved heterogeneity in the probability of experiencing the event of interest. We use Gibbs sampling for the fitting of such mixture models, which leads to a computationally intensive solution to the problem of fitting survival models for multiple event time data with long-term survivors. We illustrate our Bayesian approach through an analysis of Hutterite birth histories.     

Assessing the use of sample selection models in the estimation of fertility postponement effects

Several studies have shown that at the individual level there exists a negative relationship between age at first birth and completed fertility. Using twin data in order to control for unobserved heterogeneity as possible source of bias, Kohler et al. (2001) showed the significant presence of such "postponement effect" at the micro level. In this paper, we apply sample selection models, where selection is based on having or not having had a first birth at all, to estimate the impact of postponing first births on subsequent fertility for four European nations, three of which have now lowest-low fertility levels. We use data from a set of comparative surveys (Fertility and Family Surveys), and we apply sample selection models on the logarithm of total fertility and on the progression to the second birth. Our results show that postponement effects are only very slightly affected by sample selection biases, so that sample selection models do not improve significantly the results of standard regression techniques on selected samples. Our results confirm that the postponement effect is higher in countries with lowest-low fertility levels.     

Frailty modeling for clustered survival data: an application to birth interval in Bangladesh

The present work demonstrates an application of random effects model for analyzing birth intervals that are clustered into geographical regions. Observations from the same cluster are assumed to be correlated because usually they share certain unobserved characteristics between them. Ignoring the correlations among the observations may lead to incorrect standard errors of the estimates of parameters of interest. Beside making the comparisons between Cox's proportional hazards model and random effects model for analyzing geographically clustered time-to-event data, important demographic and socioeconomic factors that may affect the length of birth intervals of Bangladeshi women are also reported in this paper.     

Seasonal patterns of fertility measures: theory and data

The distribution of births by month exhibits a seasonal pattern in most populations. The monthly marital fertility rate for an area of Bangladesh provides a good example of the seasonal periodicity. Seasonal patterns of measures of reproduction in a population of married women are considered. Equations are developed that predict the seasonal patterns of these alternative measures under the assumption that the fertility rate (R) follows a trigonometric curve. This is followed by an empirical analysis of the measures in a Bangladesh population that has a pronounced seasonal fertility. The investigation is intended both to validate the theoretical framework developed in the 1st part of the paper as well as to determine whether seasonal variation in actual populations is sufficiently large to affect the alternative measures significantly. 4 measures are considered: pregnancy prevalence (PP)--the proportion of married women who are pregnant at the survey date; mean open birth interval (MOI)--the time from the last live birth to the date of the survey for parous women and from the time of marriage to the date of the survey for nulliparous women; mean closed interval-birth (MCIB)--the mean interval between the last 2 live births for married women who have a birth in the period immediately preceding the survey date; and mean closed interval-woman (MCIW)--the mean interval between the last 2 live births for women who have had at least 2 children by the time of the survey. It is assumed that the seasonal pattern of the fertility rate of a population follows a cosine curve and that there is no trend in annual fertility from year to year. The lag and relative variability of the other measures are considered in comparison with the fertility rate curve. The predictions from this theoretical effort, when compared with observed patterns and trigonometric regression results for each measure in data from Bangladesh, are shown to be quite accurate. The figure and regression results show that R, PP, and MOI have definite seasonal periodicity, but MCIB and MCIW do not display any seasonal patterns. If there is a secular trend in fertility in addition to seasonality, these relationships between the seasonal patterns of the measures may no longer hold. There is a disadvantage to using closed interval measures, for they are unable to detect effects of limiting of childbearing in a population since they are based only on information from women who have births.     

ARIMA modelling of birth data

In this article the fitting of ARIMA models to time series relating to the births at Edendale Hospital in Natal, South Africa, over a 16-year period is discussed. The model (011)X(011)12 provides andexcellent fit to the monthly totals of mothers delivered but serious discrepancies between estimates of the moving average parameters obtained by the method of unconditional least squares using various statistical computer packages were observed. These can be ascribed to the fact that certain of the packages use the method of backcasting to calculate the unconditional sum-of-squares function in the estimation procedure and this approach breaks down for values of the moving average parameters close to the invertibility boundary. A simulation study to compare the different methods of estimation for the model (011) X (011)12 and to assess the seriousness of discrepancies in the ULS estimates is described. ARIMA models which provided the best fit to the series of monthly totals of caesarean sections performed, breechs births and instrumental deliveries are non-seasonal and reflect a dependence of present on past observations. In contrast the series involving stillbirths and neonatal deaths are white noise indicating that perinatal deaths are random events.     

A discrete distribution associated with a pure birth process

A discrete distribution associated with a pure birth process starting with no individuals, with birth rates λ ⁿ =λ forn=0, 2, …,m−1 and λ ⁿ forn≥m is considered in this paper. The probability mass function is expressed in terms of an integral that is very convenient for computing probabilities, moments, generating functions and others. Using this representation, the mean and the k-th factorial moments of the distribution are obtained. Some nice characterizations of this distribution are also given.     

On an application of the diffusion approximation of the generalized birth and death process for stochastic population projection

Assuming that both birth and death rates are density and time dependent, a diffusion approximation of the generalized birth and death process has been considered in this paper to obtain a suitable stochastic population model describing the population size and its moments. A simple method of estimating the parameters of the model Is discussed. The predictions of the expected size of the population, and the variance are made and compared with the corresponding census figures as well as with another deterministic projection series made for the corresponding period.     

Bayesian meta-analysis using skewed elliptical distributions

Meta-analysis refers to a quantitative method for combining results from independent studies in order to draw overall conclusions. We consider hierarchical models including selection models under a skewed heavy tailed error distribution proposed originally by Chen, Dey, and Shao [M. H. Chen, D. K. Dey, Q. M. Shao, A new skewed link model for dichotomous quantal response data, J. Amer. Statist. Assoc. 94 (1983), pp. 1172–1186.] and Branco and Dey [D. Branco and D.K. Dey, A general class of multivariate skew-elliptical distributions, J. Multivariate Anal. 79, pp. 99–113.]. These rich classes of models combine the information of independent studies, allowing investigation of variability both between and within studies and incorporating weight functions. We constructed a detailed computational scheme under skewed normal and skewed Student's t distribution using the MCMC method. Bayesian model selection was conducted by Bayes factor under a different skewed error. Finally, we illustrated our methodology using a real data example taken from Johnson [M.F. Johnson, Comparative efficacy of Naf and SMFP dentifrices in caries prevention: a meta-analysis overview, J Eur. Organ. Caries Res. 27 (1993), pp. 328–336.].     

Comparison of dichotomized and distributional approaches in rare event clinical trial design: a fixed Bayesian design

This research was motivated by our goal to design an efficient clinical trial to compare two doses of docosahexaenoic acid supplementation for reducing the rate of earliest preterm births (ePTB) and/or preterm births (PTB). Dichotomizing continuous gestational age (GA) data using a classic binomial distribution will result in a loss of information and reduced power. A distributional approach is an improved strategy to retain statistical power from the continuous distribution. However, appropriate distributions that fit the data properly, particularly in the tails, must be chosen, especially when the data are skewed. A recent study proposed a skew-normal method. We propose a three-component normal mixture model and introduce separate treatment effects at different components of GA. We evaluate operating characteristics of mixture model, beta-binomial model, and skew-normal model through simulation. We also apply these three methods to data from two completed clinical trials from the USA and Australia. Finite mixture models are shown to have favorable properties in PTB analysis but minimal benefit for ePTB analysis. Normal models on log-transformed data have the largest bias. Therefore we recommend finite mixture model for PTB study. Either finite mixture model or beta-binomial model is acceptable for ePTB study.     

A NOTE ON THE DEMOGRAPHIC IMPACT OF CONTRACEPTION IN A MATHEMATICAL MODEL OF HUMAN REPRODUCTION

The application of mathematical models of human reproduction to the study of reproductive behaviour as a function of contraceptive behaviour was pioneered by Perrin and Sheps (1963). More recent work in this area continues to focus on an examination of the birth rate as the principal dependent variable. This note suggests an alternative procedure for studying the demographic impact of contraception through the analysis of birth intervals. A mathematical model is formulated for the waiting time between successive live births, and a procedure is described for incorporating into the model certain contraceptive parameters. A controlled experiment is then performed to determine the effect of these parameters on expected child spacing patterns.     

Non-homogeneous Pólya-Aeppli process

Abstract

In this paper we suppose that the intensity parameter of the Pólya-Aeppli process is a function of time t and call the resulting process a non-homogeneous Pólya-Aeppli process (NHPAP). The NHPAP can be represented as a compound non-homogeneous Poisson process with geometric compounding distribution as well as a pure birth process. For this process we give two definitions and show their equivalence. Also, we derive some interesting properties of NHPAP and use simulation the illustrate the process for particular intensity functions. In addition, we introduce the standard risk model based on NHPAP, analyze the ruin probability for this model and include an example of the process under exponentially distributed claims.     

Birth forecasting based on birth order probabilities,with application to U.S. data

"A model for birth forecasting based on prediction of the so-called 'birth order probabilities' is constructed. The relation between this model and recent models of fertility prediction is derived. Birth forecasts with approximate probability limits for the U.S. for the period 1983-1997 are generated. The performance of the proposed model in predicting future fertility is tested by fitting time series models to part of the available series (1917-1982) and ultimately generating birth forecasts for the remainder of the period, then comparing these forecasts with the actual data." The accuracy of the fertility forecasts made are compared with those made by other methods.     

Truncation effect in closed and open birth interval data

A numerical investigation using a flexible simulation model to establish interval analysis as an index for changing natality patterns. Such an index should reflect parity distribution, the age at which women start reproduction, and the spacing of their births. The simulated statistical results illustrate the truncation effect that reflects a negative correlation between parity and the length of closed and open intervals in a birth or marriage cohort. Truncation is related to the duration of marriage at survey, but this duration interacts with other assumptions. Holding duration constant does not ensure that the data on intervals will reflect postulated changes in the distributions. For complete birth orders, this analysis does reflect patterns of child spacing. However, it ignores changes in the parity distribution, whether produced by deliberate limitation of family size or by the onset of secondary sterility. This difficulty is not overcome by life table analysis except under highly restrictive assumptions. It is doubtful whether the current emphasis on securing such data is justified. Further investigation is needed to provide a better basis for the definition and analysis of interval data if they are to be used.