Rafiqul I. Chowdhury

Anaemia and iron deficiency in rural bangladeshi pregnant women living in areas of high and low iron in groundwater

BACKGROUNDnRecent studies found a low rate of iron deficiency in Bangladeshi non-pregnant and non-lactating women. This was attributed to high iron concentrations in drinking water. However, there are limited data on iron deficiency among pregnant women in Bangladesh.nnnOBJECTIVESnOur aim was to investigate the prevalence of anemia, iron deficiency, and iron deficiency anemia (IDA) among rural pregnant women and explore the association of groundwater iron concentration with anemia and iron deficiency in this group.nnnMETHODSnThis study used data from a baseline assessment of an intervention study on rural pregnant women (nu2009=u2009522), gestational age ≤20u2009wk, living in areas of low and high iron in groundwater.nnnRESULTSnOverall, 34.7% of the pregnant women had anemia, 27% had iron deficiency, and 13.4% had IDA. Prevalence of anemia, iron deficiency, and IDA among the pregnant women living in low-groundwater-iron areas was significantly higher than among the pregnant women from high-groundwater-iron areas. The odds of iron deficiency were significantly lower among pregnant women in the higher quartiles of daily iron intake from drinking water.nnnCONCLUSIONSnThis study found a differential prevalence of anemia and iron deficiency among pregnant women living in areas of high and low groundwater iron. Iron status was independently associated with daily iron intake from drinking water. However, a significant proportion of the anemia could not be attributed to iron deficiency. Further research to identify other nutritional and non-nutritional contributors to anemia in Bangladesh is needed to formulate effective prevention and control programs for anemia.

Analysis of Repeated Measures Data

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Exponential Family of Distributions

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Multistate and Multistage Models

The role of exponential family of distributions has become increasingly important for developing generalized linear models that can be extended to repeated measures data as well. Chapter 3 provides an introduction to the exponential family of distribution with several examples. Some important properties are also shown.

Generalized Estimating Equation

The longitudinal data analysis generally involves the special challenges methodologically with censoring and repeated observations. A subject is followed longitudinally over time and change is recorded in status of the event. In longitudinal studies, generally data on time to occurrence of events may be either complete or incomplete. The partially incomplete data pose special type of challenge to statistical modeling and which has been a focus of research for a long time. In Chapter 16, multistate and multistage hazards models are described, estimation and test procedures are shown for repeated measures data. The techniques are illustrated with examples.

Bivariate Exponential Model

The generalized estimating equation (GEE) uses a quasi-likelihood approach for analyzing data with correlated outcomes. This is an extension of GLM and uses quasi-likelihood method for cluster or repeated outcomes. If observations on outcome variable are repeated, it is likely that the observations are correlated. In addition, non-normality of outcome variables is a common phenomenon in real-life problems. In such situations, use of quasi-likelihood estimating equations provides necessary methodological support for estimating parameters of a regression model. The GEE is a marginal model approach for analyzing repeated measures data developed by Zeger and Liang (1986) and Liang and Zeger (1986). This approach can be considered as a semiparametric approach because it does not require full specification of the underlying joint probability distribution for repeated outcome variables rather assumes likelihood for marginal distribution and a working correlation matrix. The correlation matrix represents the correlation between observations in clusters observed from panel, longitudinal, or family studies. In this chapter, an overview of GEE is presented.

Models for Bivariate Count Data: Bivariate Poisson Distribution

The exponential distribution is considered as one of the most important distributions in reliability as well as other lifetime-related problems. It is applied in many instances for its mathematical and statistical ease and convenience attributable to memoryless property. Bivariate generalization of the exponential distribution has been of prime importance due to dependence in failure times. Some fundamental developments in the bivariate exponential distribution are discussed in this chapter. Two bivariate generalized exponential regression models are presented in this chapter with examples.

Modeling Bivariate Binary Data

The dependence in the count outcome variables is observed in many instances in the fields of health sciences, traffic accidents, economics, actuarial science, social sciences, environmental studies, etc. A typical example of such dependence arises in the traffic accidents where the extent of physical injuries may lead to fatalities. The bivariate Poisson distribution has been developed following various assumptions. In this chapter, several bivariate Poisson models including bivariate GLM for Poisson–Poisson, generalized zero-truncated bivariate Poisson, right-truncated bivariate Poisson, and bivariate double Poisson are discussed. The generalized linear models are shown for analyzing bivariate count data and the over- or underdispersion problems are also discussed. The problem of truncation for bivariate count data is also highlighted in this chapter. Tests for over- or underdispersion as well as tests for goodness of fit are illustrated with examples.

Analysing Data Using R and SAS

The Bernoulli distribution is a very important discrete distribution with extensive applications to real-life problems. This distribution can be linked with univariate distributions such as binomial, geometric, negative binomial, Poisson, gamma, hypergeometric, exponential, normal, etc., either as a limit or as a sum or other functions. On the other hand, some distributions can be shown to arise from bivariate Bernoulli distribution as well. Since the introduction of the generalized linear model and generalized estimating equations, we observed a very rapid increase in the use of linear models based on binary outcome data. However, as the generalized linear models are proposed only for univariate outcome data and GEE is based on the marginal model, the utility of bivariate relationship cannot be explored adequately. It may be noted here that repeated measures data comprise of two types of associations: (i) association between outcome variables, and (ii) association between explanatory variables and outcome variables. Hence, correlated outcomes pose difficulty in estimating parameters of models for outcome and explanatory variables. In this chapter, regression models for correlated binary outcomes are introduced. A joint model for bivariate Bernoulli is obtained by using marginal and conditional probabilities using two approaches. In the first approach, estimates are obtained using the traditional likelihood method and the second approach provides a generalized bivariate binary model by extending the univariate generalized linear model for bivariate data. Tests for independence and goodness of fit of the model are shown. Section 6.2 reviews the bivariate Bernoulli distribution and defines the joint mass function in terms of conditional and marginal probabilities. Section 6.3 introduces the covariate dependence and shows the logit functions for both conditional and marginal probabilities. The likelihood function and estimating equations are shown. Some measures of dependence in outcomes as well as tests for model, parameters, and dependence are presented in Sect. 6.4. A recently introduced generalized bivariate Bernoulli model is discussed in Sect. 6.5. In this section, the bivariate Bernoulli mass function is expressed in an exponential family of distributions and link functions are obtained for correlated outcome variables as well as for association between two outcomes. Estimating equations are shown using a bivariate generalization of GLM and test for dependence is discussed. Section 6.6 summarizes some alternative procedures for binary repeated measures data. Examples are displayed in Sect. 6.7.

Bivariate Negative Binomial and Multinomial Models

In this chapter, we provided computer programs for carrying out most of the analyses described in this text.