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The two-stage design involves sample size recalculation using an interim variance estimate. Stein proposed the design in 1945; biostatisticians recently have shown renewed interest in it. Wittes and Brittain proposed a modiÿcation aimed at greater e ciency; Gould and Shih proposed a similar procedure, but with a di erent interim variance estimate based on blinded data. We compare the power of Stein's original test, an idealized version of the Wittes-Brittain test, and a theoretical optimal test which can be approximated in practice. We also compare two procedures that control the conditional type I error rate given the actual ÿnal sample size: Gould and Shih's procedure and a newly proposed 'second segment' procedure. The comparison among the ÿrst three procedures indicates that the Stein test is, unexpectedly, the test of choice under the original design alternative, whereas the approximate-optimal and Wittes-Brittain procedures appear to have superior power for detecting smaller treatment di erences. As between the latter two procedures, the second segment procedure is more powerful when many observations are likely to be taken after the interim resizing, whereas otherwise the Gould-Shih procedure is superior.

When sample size is recalculated using unblinded interim data, use of the usual t‐test at the end of a study may lead to an elevated type I error rate. This paper describes a numerical quadrature investigation to calculate the true probability of rejection as a function of the time of the recalculation, the magnitude of the detectable treatment effect, and the ratio of the guessed to the true variance. We consider both ‘restricted’ designs, those that require final sample size at least as large as the originally calculated size, and ‘unrestricted’ designs, those that permit smaller final sample sizes than originally calculated. Our results indicate that the bias in the type I error rate is often negligible, especially in restricted designs. Some sets of parameters, however, induce non‐trivial bias in the unrestricted design. Copyright © 1999 John Wiley & Sons, Ltd.

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Summary The use of instrumental variables for estimating the effect of an exposure on an outcome is popular in econometrics, and increasingly so in epidemiology. This increasing popularity may be attributed to the natural occurrence of instrumental variables in observational studies that incorporate elements of randomization, either by design or by nature (e.g., random inheritance of genes). Instrumental variables estimation of exposure effects is well established for continuous outcomes and to some extent for binary outcomes. It is, however, largely lacking for time-to-event outcomes because of complications due to censoring and survivorship bias. In this paper, we make a novel proposal under a class of structural cumulative survival models which parameterize time-varying effects of a point exposure directly on the scale of the survival function; these models are essentially equivalent with a semi-parametric variant of the instrumental variables additive hazards model. We propose a class of recursive instrumental variable estimators for these exposure effects, and derive their large sample properties along with inferential tools. We examine the performance of the proposed method in simulation studies and illustrate it in a Mendelian randomization study to evaluate the effect of diabetes on mortality using data from the Health and Retirement Study. We further use the proposed method to investigate potential benefit from breast cancer screening on subsequent breast cancer mortality based on the HIP-study.

BACKGROUND AND OBJECTIVE: Worldwide, roughly 40% of children are exposed to the damaging and sometimes deadly effects of tobacco smoke. Interventions aimed at reducing child tobacco smoke exposure (TSE) have shown mixed results. The objective of this study was to perform a systematic review and meta-analysis to quantify effects of interventions aimed at decreasing child TSE.METHODS: Data sources included Medline, PubMed, Web of Science, PsycNet, and Embase. Controlled trials that included parents of young children were selected. Two reviewers extracted TSE data, as assessed by parentally-reported exposure or protection (PREP) and biomarkers. Risk ratios and differences were calculated by using the DerSimonian and Laird random-effects model. Exploratory subgroup analyses were performed.RESULTS: Thirty studies were included. Improvements were observed from baseline to follow-up for parentally-reported and biomarker data in most intervention and control groups. Interventions demonstrated evidence of small benefit to intervention participants at follow-up (PREP: 17 studies, n = 6820, relative risk 1.12, confidence interval [CI] 1.07 to 1.18], P , .0001). Seven percent more children were protected in intervention groups relative to control groups. Intervention parents smoked fewer cigarettes around children at follow-up than did control parents (P = .03). Biomarkers (13 studies, n = 2601) at follow-up suggested lower child exposure among intervention participants (RD 20.05, CI 20.13 to 0.03, P = .20).CONCLUSIONS: Interventions to prevent child TSE are moderately beneficial at the individual level. Widespread child TSE suggests potential for significant population impact. More research is needed to improve intervention effectiveness and child TSE measurement. KEY WORDS secondhand smoke exposure, tobacco smoke exposure, metaanalysis, systematic review, child ABBREVIATIONS CCR-cotinine/creatinine ratio CI-confidence interval CT-controlled trial PREP-parentally reported exposure or protection RCT-randomized controlled trial RD-relative difference RR-relative risk SHS-secondhand smoke THS-thirdhand smoke TSE-tobacco smoke exposure Dr Rosen conceptualized and designed the study, oversaw all aspects of the research, performed the systematic review of the literature, extracted data from the original studies, contributed to the statistical analysis, wrote sections of the manuscript, and edited the entire manuscript; Ms Myers contributed to systematically reviewing the literature, extracted data from the original articles, contributed to the data analysis, and contributed to the writing of the manuscript; Dr Hovell contributed to the design of the meta-analysis and interpretation of the data and edited the manuscript for scientific content; Dr Zucker assisted with various statistical issues in the analysis of the manuscript and edited the manuscript; Ms Ben Noach contributed to the design of the study, the systematic review of the literature, data extraction, data analysis, data interpretation, and writing of the m...