Inference with bivariate truncated data.

In this paper we build on previous work for estimation of the bivariate distribution of the time variables T1 and T2 when they are observable only on the condition that one of the time variables, say T1, is greater than (left-truncation) or less than (right truncation) some observed time variable C1. In this paper, we introduce several results based on the Influence Curve (which we derive in this paper) of the NPMLE of the distribution F of (T1, T2) developed by van der Laan (van der Laan, 1996). Specifically we will: prove that the NPMLE is asymptotically equivalent to an estimator developed by Gürler (Gürler, 1997), derive the asymptotic distribution of the NPMLE based on its Influence Curve, present tests to determine the amount of dependence between T1 and T2, present the results of simulation studies that compare the NPMLE and Gürler's estimator and evaluate the performance of both the above mentioned tests and confidence intervals of F based on the asymptotic distribution of the NPMLE, and finally we will apply the methods in a data analysis in which we also point out practical issues that arise in the implementation of the estimator.

Rate of caffeine metabolism and risk of spontaneous abortion.

In a case-control study of 73 women with and 141 women without spontaneous abortion, the authors determined the activity of the three principal caffeine-metabolizing enzymes--cytochrome P-4501A2 (CYP1A2), xanthine oxidase, and N-acetyltransferase 2--by measuring levels of caffeine metabolites in urine. After examining the effect of enzyme activity and different levels of caffeine intake, they concluded that there was no evidence that an interaction between enzyme activity and caffeine intake during pregnancy resulted in risk of spontaneous abortion. In a subsample comparing 24 cases with recurrent (two or more) spontaneous abortions and 21 controls with two or more livebirths and no previous spontaneous abortions, the unadjusted odds ratio for low CYP1A2 enzyme activity (below the median) was 0.92 (95% confidence interval (CI) 0.28-3.04) compared with higher CYP1A2 activity. The odds ratio for risk of recurrent spontaneous abortion and low xanthine oxidase activity (below the median) versus higher activity was 0.37 (95% CI 0.10-1.29). Phenotypically slow acetylators (N-acetyltransferase 2 index <0.37) had an odds ratio of 1.58 (95% CI 0.48-5.13) for recurrent loss compared with rapid acetylators. Thus, some association of the latter two caffeine-metabolizing enzymes with recurrent spontaneous abortion is suggested but may also be due to chance.

Caffeine consumption and menstrual function.

The relation between caffeine intake and menstrual function was examined in 403 healthy premenopausal women who belonged to Kaiser Permanente Medical Care Program in 1990-1991. A telephone interview collected information about caffeinated beverage intake as well as other lifestyle, demographic, occupational, and environmental factors. Subjects collected daily urine samples and completed a daily diary for an average of five menstrual cycles. Metabolites of estrogen and progesterone were measured in the urine, each cycle was characterized as anovulatory or ovulatory, and a probable day of ovulation was selected when appropriate. Logistic regression and repeated measures analyses were performed on menstrual parameters. Women whose caffeine consumption was heavy (>300 mg of caffeine per day) had less than a third of the risk for long menses (> or =8 days) compared with women who did not consume caffeine (adjusted odds ratio = 0.30, 95% confidence interval 0.14-0.66). Those whose caffeine consumption was heavy also had a doubled risk for short cycle length (< or =24 days) (adjusted odds ratio = 2.00, 95% confidence interval 0.98-4.06); this association was also evident in those whose caffeine consumption was heavy who did not smoke (adjusted odds ratio = 2.11, 95% confidence interval 1.03-4.33). Caffeine intake was not strongly related to an increased risk for anovulation, short luteal phase (< or =10 days), long follicular phase (> or =24 days), long cycle (> or =36 days), or measures of within-woman cycle variability.