Analytical approximations for iterated bootstrap confidence intervals

Standard algorithms for the construction of iterated bootstrap confidence intervals are computationally very demanding, requiring nested levels of bootstrap resampling. We propose an alternative approach to constructing double bootstrap confidence intervals that involves replacing the inner level of resampling by an analytical approximation. This approximation is based on saddlepoint methods and a tail probability approximation of DiCiccio and Martin (1991). Our technique significantly reduces the computational expense of iterated bootstrap calculations. A formal algorithm for the construction of our approximate iterated bootstrap confidence intervals is presented, and some crucial practical issues arising in its implementation are discussed. Our procedure is illustrated in the case of constructing confidence intervals for ratios of means using both real and simulated data. We repeat an experiment of Schenker (1985) involving the construction of bootstrap confidence intervals for a variance and demonstrate that our technique makes feasible the construction of accurate bootstrap confidence intervals in that context. Finally, we investigate the use of our technique in a more complex setting, that of constructing confidence intervals for a correlation coefficient.     

Contraceptive Method Choice Among Youth in the United States: The Importance of Relationship Context

We examine the relationship characteristics associated with contraceptive method choice within young people’s nonmarital sexual relationships, using data from retrospective relationship histories available in the third wave (2001–2002) of the National Longitudinal Study of Adolescent Health. Data-reduction techniques produce a detailed multidimensional characterization of relationship commitment for nonmarital sexual relationships. We then use multilevel analysis to estimate associations between two key relationship characteristics—relationship commitment and couple heterogamy—and the type of contraceptive method used at last sexual intercourse within each relationship. Results indicate that for a given individual, contraceptive method choice varies across relationships as a function of these characteristics, even after we account for important individual and family characteristics and prior relationship experiences.     

A Simple Analysis of the Exact Probability Matching Prior in the Location-Scale Model

It has long been asserted that in univariate location-scale models, when concerned with inference for either the location or scale parameter, the use of the inverse of the scale parameter as a Bayesian prior yields posterior credible sets that have exactly the correct frequentist confidence set interpretation. This claim dates to at least Peers, and has subsequently been noted by various authors, with varying degrees of justification. We present a simple, direct demonstration of the exact matching property of the posterior credible sets derived under use of this prior in the univariate location-scale model. This is done by establishing an equivalence between the conditional frequentist and posterior densities of the pivotal quantities on which conditional frequentist inferences are based.     

Sexual Activity and Weekly Contraceptive Discontinuation and Selection Among Young Adult Women in Michigan

Understanding young women’s contraceptive and pregnancy prevention behaviors is important for helping women and their partners control if and when they have children. Prior research on associations between patterns of sexual activity and contraceptive behaviors is limited. We assessed the influence of recent sexual activity on discontinuation and selection of specific contraceptive methods. We used weekly data from the Relationship Dynamics and Social Life (RDSL) study, a longitudinal 2.5-year population-based project that sampled woman ages 18 and 19 (N = 1,003) in one Michigan county. We estimated logistic and multinomial regression models that accounted for clustering of weekly observations within partnerships and women. Weekly discontinuation of longer-acting methods declined with increasing sexual activity in the past month, as did discontinuation of shorter-acting hormonal methods. Sexual activity was associated with decreased selection of condoms relative to other methods. Future research into life events that lead to changes in the frequency of sexual activity may provide insight into times when women are at risk of contraceptive discontinuation. These findings underscore the importance of anticipatory guidance in contraceptive counseling so that when women change their contraceptive behavior they are equipped in advance with resources to make safe transitions between methods.     

Effects of intensive longitudinal data collection on pregnancy and contraceptive use

We use an experiment based on the relationship dynamics and social life study of sexual behavior, pregnancy, and contraceptive use to investigate whether participation in weekly self-reports over one year result in differential effects on related behaviors and attitudes, compared to participation in a one-time follow-up interview requiring retrospective self-reporting for the prior year. We randomly assigned 200 subjects to either a control group or a journal group. All subjects were interviewed at the beginning of the study (baseline interview) and 12 months later (closeout interview). Subjects in the journal group also completed a five-minute web- or phone-based survey every week during the 12-month study period. We found no statistically significant difference in pregnancy rates across the two groups at closeout. Contrary to our expectation, the control group experienced a slightly larger increase in having ever used a contraceptive method, although this was mainly due to increases in the least effective methods, such as condoms and withdrawal. Respondents in the weekly interview group became slightly more positive toward childbearing in terms of one specific attitude measure, but not for the vast majority of measures. We conclude that intensive longitudinal data collection does not appear to have a large or consistent impact on respondents’ pregnancy, contraceptive use, or related attitudes, relative to the more standard longitudinal approach.     

Use of Biological Markers in Risk Assessment1

Measurements of intermediate end points in the carcinogenic process may reduce uncertainty in human risk assessment from bioassay data, by identifying sources of interspecies variation and dose nonlinearity. This paper describes desirable properties of such markers: persistence, predictive power, temporal relevance, and consistency across dose rate and species. We illustrate these properties by evaluating markers for squamous cell nasal carcinoma in rodents exposed to formaldehyde. We also discuss design issues for bioassays that evaluate markers and tumors simultaneously at necropsy.     

Sexual activity and weekly contraceptive use among young adult women in Michigan

Past studies on the influence of sexual activity on contraceptive behaviours are inconclusive, relying heavily on cross-sectional data. We used a population-based longitudinal sample of young women in Michigan to evaluate weekly associations between sexual activity and contraceptive use at three levels of measurement: comparing between women, among individual women’s partnerships, and from week to week within partnerships. We used multinomial logistic regression accounting for correlations within partnerships and women. Relative to use of least effective methods, weekly sexual activity was significantly associated with increased use of condoms, pills, and highly effective methods. For pills and highly effective methods, partnership-, woman-, and week-level effects were similar. For condoms, there was no significant woman-level effect. Evidence of immediate effects of sexual activity on contraceptive use highlights the importance of longitudinal data. These dynamics may be diluted or missed altogether when relying on cross-sectional data approaches that compare groups of individuals.     

Testing for sub-models of the skew <Emphasis Type="Italic">t</Emphasis>-distribution

The skew t-distribution includes both the skew normal and the normal distributions as special cases. Inference for the skew t-model becomes problematic in these cases because the expected information matrix is singular and the parameter corresponding to the degrees of freedom takes a value at the boundary of its parameter space. In particular, the distributions of the likelihood ratio statistics for testing the null hypotheses of skew normality and normality are not asymptotically \(\chi ^2\). The asymptotic distributions of the likelihood ratio statistics are considered by applying the results of Self and Liang (J Am Stat Assoc 82:605–610, 1987) for boundary-parameter inference in terms of reparameterizations designed to remove the singularity of the information matrix. The Self–Liang asymptotic distributions are mixtures, and it is shown that their accuracy can be improved substantially by correcting the mixing probabilities. Furthermore, although the asymptotic distributions are non-standard, versions of Bartlett correction are developed that afford additional accuracy. Bootstrap procedures for estimating the mixing probabilities and the Bartlett adjustment factors are shown to produce excellent approximations, even for small sample sizes.     

On expected volumes of multidimensional confidence sets associated with the usual and adjusted likelihoods

We consider a general multiparameter set-up, where both the interest and the nuisance parameters are possibly vector valued. We derive an explicit higher order asymptotic formula to compare the expected volumes of confidence sets given by likelihood ratio statistics arising from the usual profile likelihood and various adjustments thereof. Our general framework also allows us to include highest posterior density regions, with approximate frequentist validity, in the study. The fact that our interest parameter is possibly vector valued complicates the derivation and warrants the development of special tools and techniques.