China's Below‐Replacement Fertility: Recent Trends and Future Prospects

Between 1970 and 1990, China experiencoed a rapid and sharp fertility decline—from total fertility rates of approximately six births to two. The degree to which Chinese fertility has continued to fall after 1990 is controversial. We use survey data from the 1997 National Population and Reproductive Health Survey and from the 2001 Reproductive Health and Family Planning Survey to document recent trends in Chinese fertility. Our estimates provide further evidence that China's fertility is well below‐replacement level at the turn of the twenty‐first century—with TFR levels of approximately 1.5 children per woman. Trends in parity‐specific cohort fertility by age also suggest below replacement completed fertility for cohorts still in the childbearing years. In the article's second section, we identify key components of low period fertility in order to frame our discussion of two questions: 1) in what ways is Chinese low fertility different from/similar to that in other low‐fertility countries? And 2) what are the likely future trends in Chinese fertility?     

The Correspondence Between Fertility Intentions and Behavior in the United States

Using data from the 1979 National Longitudinal Survey of Youth, we describe the correspondence between intended family size and observed fertility for US men and women in the 1957–64 birth cohorts. Mean fertility intentions calculated from reports given in the mid‐20s modestly overstate completed fertility. But discrepancies between stated intent and actual fertility are common—the stated intent at age 24 (for both women and men) is more likely to miss than to match completed fertility. We focus on factors that predict which women and men will have fewer or more children than intended. Consistent with life‐course arguments, those unmarried, childless, or (for women) still in school at approximately age 24 were most likely to underachieve their intended parity (i.e., had fewer children than intended at age 24). We discuss how such discrepancies between intentions and behavior may cumulate to produce sizable cross‐group fertility differences.     

White and nonwhite trends in first birth timing: Comparisons using vital registration and current population surveys

The magnitude of racial differences in first birth timing vary greatly depending upon the data sources from which they are estimated. Vital registration data (Heuser 1976; with updates from the National Center for Health Statistics 1974–1990) show that in recent years nonwhites have higher risks of a first birth at virtually all ages compared to whites. As a result very large and historically novel differentials in childlessness are forecast using these data (see Rindfuss et al. 1988; Chen & Morgan 1991; Morgan & Chen 1992). However, retrospective fertility history data collected from the 1980, 1985 and 1990 Current Population Surveys (CPS) suggest much smaller racial differences in completed childlessness and isolate racial differences in probabilities of first births at young ages. Differences also exist between theses two series for whites prior to the mid-1960s but not afterwards. Reasons for these differing estimates are suggested and examined. We conclude that a substantial portion of the differences result from an accumulation of biases in the vital registration estimates that affect primarily estimates of first birth timing. Thus, the CPS data provide a more firm basis for racial comparisons of first birth timing.     

Response‐adaptive designs for binary responses: How to offer patient benefit while being robust to time trends?

Response‐adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not either feasible or ethically questionable. In this paper, we discuss and address a major criticism levelled at RAR: namely, type I error inflation due to an unknown time trend over the course of the trial. The most common cause of this phenomenon is changes in the characteristics of recruited patients—referred to as patient drift. This is a realistic concern for clinical trials in rare diseases due to their lengthly accrual rate. We compute the type I error inflation as a function of the time trend magnitude to determine in which contexts the problem is most exacerbated. We then assess the ability of different correction methods to preserve type I error in these contexts and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations as to which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the 2‐armed and the multi‐armed case. We further propose a RAR design for multi‐armed clinical trials, which is computationally efficient and robust to several time trends considered.     

Sampling schemes for price index construction: a performance comparison across the classification of individual consumption by purpose food groups

Five sampling schemes (SS) for price index construction – one cut-off sampling technique and four probability-proportional-to-size (pps) methods – are evaluated by comparing their performance on a homescan market research data set across 21 months for each of the 13 classification of individual consumption by purpose (COICOP) food groups. Classifications are derived for each of the food groups and the population index value is used as a reference to derive performance error measures, such as root mean squared error, bias and standard deviation for each food type. Repeated samples are taken for each of the pps schemes and the resulting performance error measures analysed using regression of three of the pps schemes to assess the overall effect of SS and COICOP group whilst controlling for sample size, month and population index value. Cut-off sampling appears to perform less well than pps methods and multistage pps seems to have no advantage over its single-stage counterpart. The jackknife resampling technique is also explored as a means of estimating the standard error of the index and compared with the actual results from repeated sampling.     

A new mixture model for capture heterogeneity

Summary.  We propose a mixture of binomial and beta–binomial distributions for estimating the size of closed populations. The new mixture model is applied to several real capture–recapture data sets and is shown to provide a convenient, objective framework for model selection. The new model is compared with three alternative models in a simulation study, and the results shed light on the general performance of models in this area. The new model provides a robust flexible analysis, which automatically deals with small capture probabilities.     

E-optimal designs for three treatments

E-optimality is studied for three treatments in an arbitrary n-way heterogeneity setting. In some cases maximal trace designs cannot be E-optimal. When there is more than one E-optimal design for a given setting, the best with respect to all reasonable criteria is determined.