How big are educational and racial fertility differentials in the U.S.?

Using pooled data from the 1980, 1985, 1990 and 1995 CPS and 1988 and 1995 NSFG surveys, we show that shifts in fertility timing have occurred disproportionately for the more educated and for whites (compared to the less educated and to African Americans). Such timing shifts imply that the underlying period quantum of fertility is considerably higher for college-educated women and for whites than suggested by the standard total fertility rate. Applying the Bongaarts-Feeney model (1998), we decompose observed racial and educational differences in age-order-specific fertility rates and TFR into tempo and quantum components. We find that a modest part of educational differences and a substantial part of racial difference in period fertility can be attributed to differential changes in tempo. Analysis by race and education shows a clear interaction: higher fertility among African Americans is confined to the less educated.     

Malaria ecology,child mortality & fertility

The broad determinants of fertility are thought to be reasonably well identified by demographers, though the detailed quantitative drivers of fertility levels and changes are less well understood. This paper uses a novel ecological index of malaria transmission to study the effect of child mortality on fertility. We find that temporal variation in the ecology of the disease is well-correlated to mortality, and pernicious malaria conditions lead to higher fertility rates. We then argue that most of this effect occurs through child mortality, and estimate the effect of child mortality changes on fertility. Our findings add to the literature on disease and fertility, and contribute to the suggestive evidence that child mortality reductions have a causal effect on fertility changes.     

Estimating fertility using adults: A method for under-enumerated pre-adult skeletal samples

Objectives

Infant underrepresentation poses a great risk to accurate palaeodemographic findings when analyzing skeletal samples. Empirically derived palaeodemographic methods all require unbiased or minimally biased pre-adult representation for estimating demographic characteristics, including fertility. Currently, there are no reliable methods for estimating palaeodemographic parameters when pre-adults are underrepresented in skeletal samples, consequently such samples are often excluded from palaeodemographic analyses. The aim of this article is to develop a method for estimating total fertility rate (TFR) using reproductive aged adults, specifically for samples with suspected pre-adult under-enumeration.

Methodology

United Nations mortality data and TFR from the World Population Prospects was utilized. The correlation between known fertility and the proportion of individuals in key reproductive years (15–49 years) to total adult sample (15+ years) was assessed as an indirect means to estimate fertility.

Results

It was determined that the proportion of reproductive aged adults is a reasonable proxy for fertility. A significant positive correlation was observed between the TFR and those who died aged 15–49 years of age as a proportion of those who died ≥15 years (D15-49/D15+). SE of the estimate revealed reasonable predictive accuracy. When applied to two modern non-agricultural populations, the method showed some variability in accuracy but good potential for an improved outcome over existing methods when pre-adults are underrepresented.

Conclusion

This research has provided a new method for estimating fertility in archeological skeletal samples with pre-adult under-enumeration. In combination with a contextually focused approach, this provides a significant step toward further use of biased samples in palaeodemography.

     

Social,biological, and political considerations on fertility in Arab populations

In analyzing fertility in the Arab countries, crude birth rate, total fecundity rate, and age specific fertility rates were measured. The data was obtained from United Nations, UNICEF, and the World Bank. In the early 1980's 13 of the countries had birth rates 40/1000. The majority of countries showed a decline in their crude birth rate (CBR) between 1960-83, except Somalia, which increased. The United Arab Emirates (UAE), Tunisia, Lebanon, and Kuwait, had the largest CBR decreases, followed by Morocco, Egypt, and Saudi Arabia. The global fecundity rate (GFR) shows the number of expected births a woman lives through her reproductive period, having children at the prevailing rate for each age. The GFR in these countries is much higher than those of non Moslem countries in the area. Results show that the fertility of Arab countries are in a gradual decline, but remain high, and many have a CBR over 40/1000. In the last 20 years Saudi Arabia, with the largest population of oil producing countries, has had a decreasing CBR. It is not in agreement with its high GFR, but this can be attributed to the large number of immigration workers in the country. The UAE showed a decrease in CBR from 46/1000 to 27/1000, the largest decrease in these countries. This decline coincided with the economic development due to oil production. Kuwait had a 25.5% decrease in CBR but less than Tunisia and Lebanon. The fertility decline in Kuwait intensified in the middle 1970's; the decline in northern Africa began in the late 1960's. There were declines in birth rates in the North African countries in the early 1970's except for Tunisia. The rapid declines in fertility can be attributed to the countries' socioeconomic and political situations.     

Effect of nuptiality, contraception and breast-feeding on fertility in Bangladesh

The effects of marriage, contraception, and post-partum lactational infecundability on fertility in Bangladesh are assessed by applying Bongaarts' formula to survey data for the period 1975-1985. Marriage is universal and age at marriage is low. Breastfeeding is prolonged and has a pronounced effect on fertility. The fertility-reducing effect of contraception increased over the period through increased use of modern methods. The total fertility rate (TFR) declined by 24% from 1975 to 1985. This study shows that the 3 major proximate determinants cannot account completely for variation in national fertility levels.     

Order-restricted inference for clustered ROC data with application to fingerprint matching accuracy

Receiver operating characteristic (ROC) curve is commonly used to evaluate and compare the accuracy of classification methods or markers. Estimating ROC curves has been an important problem in various fields including biometric recognition and diagnostic medicine. In real applications, classification markers are often developed under two or more ordered conditions, such that a natural stochastic ordering exists among the observations. Incorporating such a stochastic ordering into estimation can improve statistical efficiency (Davidov and Herman, 2012). In addition, clustered and correlated data arise when multiple measurements are gleaned from the same subject, making estimation of ROC curves complicated due to within-cluster correlations. In this article, we propose to model the ROC curve using a weighted empirical process to jointly account for the order constraint and within-cluster correlation structure. The algebraic properties of resulting summary statistics of the ROC curve such as its area and partial area are also studied. The algebraic expressions reduce to the ones by Davidov and Herman (2012) for independent observations. We derive asymptotic properties of the proposed order-restricted estimators and show that they have smaller mean-squared errors than the existing estimators. Simulation studies also demonstrate better performance of the newly proposed estimators over existing methods for finite samples. The proposed method is further exemplified with the fingerprint matching data from the National Institute of Standards and Technology Special Database 4.     

Phylogeny reconstruction: increasing the accuracy of pairwise distance estimation using Bayesian inference of evolutionary rates

Distance-based methods for phylogeny reconstruction are the fastest and easiest to use, and their popularity is accordingly high. They are also the only known methods that can cope with huge datasets of thousands of sequences. These methods rely on evolutionary distance estimation and are sensitive to errors in such estimations. In this study, a novel Bayesian method for estimation of evolutionary distances is developed. The proposed method enables the use of a sophisticated evolutionary model that better accounts for among-site rate variation (ASRV), thereby improving the accuracy of distance estimation. Rate variations are estimated within a Bayesian framework by extracting information from the entire dataset of sequences, unlike standard methods that can only use one pair of sequences at a time. We compare the accuracy of a cascade of distance estimation methods, starting from commonly used methods and moving towards the more sophisticated novel method. Simulation studies show significant improvements in the accuracy of distance estimation by the novel method over the commonly used ones. We demonstrate the effect of the improved accuracy on tree reconstruction using both real and simulated protein sequence alignments. An implementation of this method is available as part of the SEMPHY package.     

Canadian fertility trends in perspective

This paper examines the broad movements of Canadian period and cohort fertility over the past 100 years, and compares them with corresponding trends in the US and other industrialized countries. The main movement in Canada was a decline in fertility extending from the 19th century to the present, interrupted in the 1940s and 1950s by a baby boom. Between 1871 and 1937 the total fertility rate (TFR) fell at about an average of 1.4% annually. The rate of fall in the US was similar, with the result that in the late 1930s the Canadian TFR was about 20% that of the US. The fertility boom that followed was steeper in the US than in Canada, and in the downswing that later followed, the rate of decline was similar in the 2 countries (3.4-4% annual average). But, the decline continued longer-- indeed still continues--in Canada, whereas the TFR in the US reached its lowest point in 1976. Moreover, the recent decline in fertility has been more severe in Canada than in almost any other industrialized country. The TFR relates to fertility in a single year and is highly sensitive to short-term changes in the timing of births. For the purposes of understanding and explaining long-term trends in fertility, the completed fertility rate (CFR) is a better index because it measures the ultimate family size of cohorts. Cohort fertility can be seen to fluctuate much less than does period fertility. In both the US and Canada, the peak cohorts, born in the early 1930s, had roughly the same completed fertility, and later cohorts continued to remain closely in step as the CFR fell sharply. In Canada the fall continues, though at a reduced rate, in the latest cohorts for which there is information. Apart from differences in amplitude, the dates of turning points and the shapes of the TFR and CFR curves of Canadian fertility are fairly similar. The long decline in cohort fertility is largely explained by the decrease in the proportions of families of 6 or more children. During the baby boom, for Catholics and non-Catholics alike, the proportion of ever-married women remaining childless fell by about 40%, the proportion having 2 children changed little, and the proportions having 3,4 and 5 children tended to increase substantially. The crucial difference between the 2 groups was in the proportions of women having 6 or more children. For non-Catholics, the proportion fell by over 4% from a high level. For non-Catholics, on the other hand, the proportion rose somewhat, though even after the rise, it was barely more than 1/2 the level to which the Catholic proportion had declined. Among Catholics, the effect of the massive decline in the proportion of women having 6 or more children was to swamp the effects of the increase in the proportions of women having 3, 4 and 5 children. The net effect was that fertility declined. Among non-Catholics, however, the comparable increases in the proportions of families of 3, 4 and 5 children, were not offset by any fall in the proportion of larger families, with the result that a baby boom occurred.     

Microsatellite mutations during the polymerase chain reaction: mean field approximations and their applications

We develop a novel mathematical model for microsatellite mutations during polymerase chain reaction (PCR). Based on the model, we study the first- and second-order moments of the number of repeat units in a randomly chosen molecule after n PCR cycles and their corresponding mean field approximations. We give upper bounds for the approximation errors and show that the approximation errors are small when the mutation rate is low. Based on the theoretical results, we develop a moment estimation method to estimate the mutation rate per-repeat-unit per PCR cycle and the probability of expansion when mutations occur. Simulation studies show that the moment estimation method can accurately recover the true mutation rate and probability of expansion. Finally, the method is applied to experimental data from single-molecule PCR experiments.     

Quantifying Population Genetic Differentiation from Next-Generation Sequencing Data

Over the past few years, new high-throughput DNA sequencing technologies have dramatically increased speed and reduced sequencing costs. However, the use of these sequencing technologies is often challenged by errors and biases associated with the bioinformatical methods used for analyzing the data. In particular, the use of naïve methods to identify polymorphic sites and infer genotypes can inflate downstream analyses. Recently, explicit modeling of genotype probability distributions has been proposed as a method for taking genotype call uncertainty into account. Based on this idea, we propose a novel method for quantifying population genetic differentiation from next-generation sequencing data. In addition, we present a strategy for investigating population structure via principal components analysis. Through extensive simulations, we compare the new method herein proposed to approaches based on genotype calling and demonstrate a marked improvement in estimation accuracy for a wide range of conditions. We apply the method to a large-scale genomic data set of domesticated and wild silkworms sequenced at low coverage. We find that we can infer the fine-scale genetic structure of the sampled individuals, suggesting that employing this new method is useful for investigating the genetic relationships of populations sampled at low coverage.     

A General Approach for Haplotype Phasing across the Full Spectrum of Relatedness

Many existing cohorts contain a range of relatedness between genotyped individuals, either by design or by chance. Haplotype estimation in such cohorts is a central step in many downstream analyses. Using genotypes from six cohorts from isolated populations and two cohorts from non-isolated populations, we have investigated the performance of different phasing methods designed for nominally ‘unrelated’ individuals. We find that SHAPEIT2 produces much lower switch error rates in all cohorts compared to other methods, including those designed specifically for isolated populations. In particular, when large amounts of IBD sharing is present, SHAPEIT2 infers close to perfect haplotypes. Based on these results we have developed a general strategy for phasing cohorts with any level of implicit or explicit relatedness between individuals. First SHAPEIT2 is run ignoring all explicit family information. We then apply a novel HMM method (duoHMM) to combine the SHAPEIT2 haplotypes with any family information to infer the inheritance pattern of each meiosis at all sites across each chromosome. This allows the correction of switch errors, detection of recombination events and genotyping errors. We show that the method detects numbers of recombination events that align very well with expectations based on genetic maps, and that it infers far fewer spurious recombination events than Merlin. The method can also detect genotyping errors and infer recombination events in otherwise uninformative families, such as trios and duos. The detected recombination events can be used in association scans for recombination phenotypes. The method provides a simple and unified approach to haplotype estimation, that will be of interest to researchers in the fields of human, animal and plant genetics.     

Proximate determinants of fertility in the Kathmandu Valley, Nepal: an anthropological case study

The analytical model of Bongaarts and Potter is employed to compare the proximate determinants of fertility among 3 populations in Nepal's Kathmandu valley. 3 sub-groups are studied: high caste (Brahmin and Chetri) urban residents, high caste urban fringe residents, and low caste untouchables (Sarki). Both survey and anthropological methods are employed. According to the analytical model, the transition in fertility follows 4 phases. The changes in fertility levels from Phase 1 to Phase 4 generally indicate that the transition from natural to controlled fertility is characterized by declines in the proportions of women married and the duration of postpartum infecundability, and a substantial increase in the prevalence and effectiveness of contraceptive practices. The results of this study show that Nepal as a whole is entrenched in Phase 1 of the fertility transition. However, data from the 3 populations reported here clearly indicate that each has begun to experience a demographic transition to different degrees. The Sarkis in this study fall between Phases 2 and 3, as indicated by the total fertility rate (TFR). The rural high castes most closely approximate a population in Phase 3, while urban high castes included in this study are approaching Phase 4. Each of the 3 populations is characterized by a decline in the proportion of women married when compared to all of Nepal. It is also apparent that the relative use-effectiveness of contraceptive methods currently employed is high. Gains in the reduction of fertility, then, will have to be made from increasing and retaining the number of acceptors and in reducing the desired family size of those at reproductive risk.     

Robust approach to combining multiple markers to improve surrogacy

Identifying effective and valid surrogate markers to make inference about a treatment effect on long-term outcomes is an important step in improving the efficiency of clinical trials. Replacing a long-term outcome with short-term and/or cheaper surrogate markers can potentially shorten study duration and reduce trial costs. There is sizable statistical literature on methods to quantify the effectiveness of a single surrogate marker. Both parametric and nonparametric approaches have been well developed for different outcome types. However, when there are multiple markers available, methods for combining markers to construct a composite marker with improved surrogacy remain limited. In this paper, building on top of the optimal transformation framework of Wang et al. (2020), we propose a novel calibrated model fusion approach to optimally combine multiple markers to improve surrogacy. Specifically, we obtain two initial estimates of optimal composite scores of the markers based on two sets of models with one set approximating the underlying data distribution and the other directly approximating the optimal transformation function. We then estimate an optimal calibrated combination of the two estimated scores which ensures both validity of the final combined score and optimality with respect to the proportion of treatment effect explained by the final combined score. This approach is unique in that it identifies an optimal combination of the multiple surrogates without strictly relying on parametric assumptions while borrowing modeling strategies to avoid fully nonparametric estimation which is subject to the curse of dimensionality. Our identified optimal transformation can also be used to directly quantify the surrogacy of this identified combined score. Theoretical properties of the proposed estimators are derived, and the finite sample performance of the proposed method is evaluated through simulation studies. We further illustrate the proposed method using data from the Diabetes Prevention Program study.     

High-Dimensional Heteroscedastic Regression with an Application to eQTL Data Analysis

We consider the problem of high-dimensional regression under non-constant error variances. Despite being a common phenomenon in biological applications, heteroscedasticity has, so far, been largely ignored in high-dimensional analysis of genomic data sets. We propose a new methodology that allows non-constant error variances for high-dimensional estimation and model selection. Our method incorporates heteroscedasticity by simultaneously modeling both the mean and variance components via a novel doubly regularized approach. Extensive Monte Carlo simulations indicate that our proposed procedure can result in better estimation and variable selection than existing methods when heteroscedasticity arises from the presence of predictors explaining error variances and outliers. Further, we demonstrate the presence of heteroscedasticity in and apply our method to an expression quantitative trait loci (eQTLs) study of 112 yeast segregants. The new procedure can automatically account for heteroscedasticity in identifying the eQTLs that are associated with gene expression variations and lead to smaller prediction errors. These results demonstrate the importance of considering heteroscedasticity in eQTL data analysis.     

Finding confidence limits on population growth rates

Recent concern with the survival of endangered species has renewed interest in estimating the growth rates of natural populations. Estimates of population growth rate are subject to uncertainties because of both sampling and experimental errors incurred when estimating rates of fecundity and survivorship. In recent years, a variety of methods have been proposed for placing confidence limits on estimated growth rates. The commonly used analytical approximation assumes that errors are relatively small. There are several computer-intensive methods, including methods based on jackknife and bootsrap procedures, that test the robustness of that approximation. In addition, several computer simulations of hypothetical populations have led to some generalizations about the performance of different methods. In general, it is possible to find confidence intervals for estimates of population growth rates but the appropriate method for doing so depends on the kind of data available and on the magnitude and correlation structure of the errors.     

A population pharmacokinetic model with time-dependent covariates measured with errors

We propose a population pharmacokinetic (PK) model with time-dependent covariates measured with errors. This model is used to model S-oxybutynin's kinetics following an oral administration of Ditropan, and allows the distribution rate to depend on time-dependent covariates blood pressure and heart rate, which are measured with errors. We propose two two-step estimation methods: the second-order two-step method with numerical solutions of differential equations (2orderND), and the second-order two-step method with closed form approximate solutions of differential equations (2orderAD). The proposed methods are computationally easy and require fitting a linear mixed model at the first step and a nonlinear mixed model at the second step. We apply the proposed methods to the analysis of the Ditropan data, and evaluate their performance using a simulation study. Our results show that the 2orderND method performs well, while the 2orderAD method can yield PK parameter estimators that are subject to considerable biases.     

A Reliability-Based Track Fusion Algorithm

The common track fusion algorithms in multi-sensor systems have some defects, such as serious imbalances between accuracy and computational cost, the same treatment of all the sensor information regardless of their quality, high fusion errors at inflection points. To address these defects, a track fusion algorithm based on the reliability (TFR) is presented in multi-sensor and multi-target environments. To improve the information quality, outliers in the local tracks are eliminated at first. Then the reliability of local tracks is calculated, and the local tracks with high reliability are chosen for the state estimation fusion. In contrast to the existing methods, TFR reduces high fusion errors at the inflection points of system tracks, and obtains a high accuracy with less computational cost. Simulation results verify the effectiveness and the superiority of the algorithm in dense sensor environments.     

Progress curve analysis for enzyme and microbial kinetic reactions using explicit solutions based on the Lambert W function

We present a simple method for estimating kinetic parameters from progress curve analysis of biologically catalyzed reactions that reduce to forms analogous to the Michaelis-Menten equation. Specifically, the Lambert W function is used to obtain explicit, closed-form solutions to differential rate expressions that describe the dynamics of substrate depletion. The explicit nature of the new solutions greatly simplifies nonlinear estimation of the kinetic parameters since numerical techniques such as the Runge-Kutta and Newton-Raphson methods used to solve the differential and integral forms of the kinetic equations, respectively, are replaced with a simple algebraic expression. The applicability of this approach for estimating Vmax and Km in the Michaelis-Menten equation was verified using a combination of simulated and experimental progress curve data. For simulated data, final estimates of Vmax and Km were close to the actual values of 1 microM/h and 1 microM, respectively, while the standard errors for these parameter estimates were proportional to the error level in the simulated data sets. The method was also applied to hydrogen depletion experiments by mixed cultures of bacteria in activated sludge resulting in Vmax and Km estimates of 6.531 microM/h and 2.136 microM, respectively. The algebraic nature of this solution, coupled with its relatively high accuracy, makes it an attractive candidate for kinetic parameter estimation from progress curve data.     

Conditional-cumulant-of-exposure method in logistic missing covariate regression

We consider estimation in logistic regression where some covariate variables may be missing at random. Satten and Kupper (1993, Journal of the American Statistical Association 88, 200-208) proposed estimating odds ratio parameters using methods based on the probability of exposure. By approximating a partial likelihood, we extend their idea and propose a method that estimates the cumulant-generating function of the missing covariate given observed covariates and surrogates in the controls. Our proposed method first estimates some lower order cumulants of the conditional distribution of the unobserved data and then solves a resulting estimating equation for the logistic regression parameter. A simple version of the proposed method is to replace a missing covariate by the summation of its conditional mean and conditional variance given observed data in the controls. We note that one important property of the proposed method is that, when the validation is only on controls, a class of inverse selection probability weighted semiparametric estimators cannot be applied because selection probabilities on cases are zeroes. The proposed estimator performs well unless the relative risk parameters are large, even though it is technically inconsistent. Small-sample simulations are conducted. We illustrate the method by an example of real data analysis.