Two methods for point and interval estimation of relative risk for log-linear exposure-response relations in meta-analyses of published ordinal categorical exposure-response data have been proposed. The authors compared the results of a meta-analysis of published data using each of the 2 methods with the results that would be obtained if the primary data were available and investigated the circumstances under which the approximations required for valid use of each meta-analytic method break down. They then extended the methods to handle nonlinear exposure-response relations. In the present article, methods are illustrated using studies of the relation between alcohol consumption and colorectal and lung cancer risks from the ongoing Pooling Project of Prospective Studies of Diet and Cancer. In these examples, the differences between the results of a meta-analysis of summarized published data and the pooled analysis of the individual original data were small. However, incorrectly assuming no correlation between relative risk estimates for exposure categories from the same study gave biased confidence intervals for the trend and biased P values for the tests for nonlinearity and between-study heterogeneity when there was strong confounding by other model covariates. The authors illustrate the use of 2 publicly available user-friendly programs (Stata and SAS) to implement meta-analysis for dose-response data.

In a systematic review and meta-analysis, Bahi Takkouche and colleagues examine the associations between exposure to tobacco smoke and allergic disorders in children and adults. Please see later in the article for the Editors' Summary

Summary Background Supplementation of vitamin A in children aged 6–59 months improves child survival and is implemented as global policy. Studies of the efficacy of supplementation of infants in the neonatal period have inconsistent results. We aimed to assess the efficacy of oral supplementation with vitamin A given to infants in the first 3 days of life to reduce mortality between supplementation and 180 days (6 months). Methods We did an individually randomised, double-blind, placebo-controlled trial of infants born in the Morogoro and Dar es Salaam regions of Tanzania. Women were identified during antenatal clinic visits or in the labour wards of public health facilities in Dar es Salaam. In Kilombero, Ulanga, and Kilosa districts, women were seen at home as part of the health and demographic surveillance system. Newborn infants were eligible for randomisation if they were able to feed orally and if the family intended to stay in the study area for at least 6 months. We randomly assigned infants to receive one dose of 50 000 IU of vitamin A or placebo in the first 3 days after birth. Infants were randomly assigned in blocks of 20, and investigators, participants’ families, and data analysis teams were masked to treatment assignment. We assessed infants on day 1 and day 3 after dosing, as well as at 1, 3, 6, and 12 months after birth. The primary endpoint was mortality at 6 months, assessed by field interviews. The primary analysis included only children who were not lost to follow-up. This trial is registered with the Australian New Zealand Clinical Trials Registry (ANZCTR), number ACTRN12610000636055. Findings Between Aug 26, 2010, and March 3, 2013, 31 999 newborn babies were randomly assigned to receive vitamin A (n=15 995) or placebo (n=16 004; 15 428 and 15 464 included in analysis of mortality at 6 months, respectively). We did not find any evidence for a beneficial effect of vitamin A supplementation on mortality in infants at 6 months (26 deaths per 1000 livebirths in vitamin A vs 24 deaths per 1000 livebirths in placebo group; risk ratio 1·10, 95% CI 0·95–1·26; p=0·193). There was no evidence of a differential effect for vitamin A supplementation on mortality by sex; risk ratio for mortality at 6 months for boys was 1·08 (0·90–1·29) and for girls was 1·12 (0·91–1·39). There was also no evidence of adverse effects of supplementation within 3 days of dosing. Interpretation Neonatal vitamin A supplementation did not result in any immediate adverse events, but had no beneficial effect on survival in infants in Tanzania. These results strengthen the evidence against a global policy recommendation for neonatal vitamin A supplementation.

BACKGROUND Vitamin D metabolites support innate immune responses to Mycobacterium tuberculosis. Data from phase 3, randomized, controlled trials of vitamin D supplementation to prevent tuberculosis infection are lacking. METHODS We randomly assigned children who had negative results for M. tuberculosis infection according to the QuantiFERON-TB Gold In-Tube assay (QFT) to receive a weekly oral dose of either 14,000 IU of vitamin D 3 or placebo for 3 years. The primary outcome was a positive QFT result at the 3-year follow-up, expressed as a proportion of children. Secondary outcomes included the serum 25-hydroxyvitamin D (25[OH]D) level at the end of the trial and the incidence of tuberculosis disease, acute respiratory infection, and adverse events. RESULTS A total of 8851 children underwent randomization: 4418 were assigned to the vitamin D group, and 4433 to the placebo group; 95.6% of children had a baseline serum 25(OH)D level of less than 20 ng per milliliter. Among children with a valid QFT result at the end of the trial, the percentage with a positive result was 3.6% (147 of 4074 children) in the vitamin D group and 3.3% (134 of 4043) in the placebo group (adjusted risk ratio, 1.10; 95% confidence interval [CI], 0.87 to 1.38; P = 0.42). The mean 25(OH)D level at the end of the trial was 31.0 ng per milliliter in the vitamin D group and 10.7 ng per milliliter in the placebo group (mean between-group difference, 20.3 ng per milliliter; 95% CI, 19.9 to 20.6). Tuberculosis disease was diagnosed in 21 children in the vitamin D group and in 25 children in the placebo group (adjusted risk ratio, 0.87; 95% CI, 0.49 to 1.55). A total of 29 children in the vitamin D group and 34 in the placebo group were hospitalized for treatment of acute respiratory infection (adjusted risk ratio, 0.86; 95% CI, 0.52 to 1.40). The incidence of adverse events did not differ significantly between the two groups. CONCLUSIONS Vitamin D supplementation did not result in a lower risk of tuberculosis infection, tuberculosis disease, or acute respiratory infection than placebo among vitamin Ddeficient schoolchildren in Mongolia. (Funded by the National Institutes of Health; ClinicalTrials.gov number, NCT02276755.

Background: Epidemiologic studies examining associations between carotenoid intakes and risk of breast cancer by estrogen receptor (ER) and progesterone receptor (PR) status are limited. Objective: We investigated these associations in a pooled analysis of 18 cohort studies. Design: Of 1,028,438 participants followed for a maximum followup of 26 y across studies, 33,380 incident invasive breast cancers were identified. Study-specific RRs and 95% CIs were estimated by using Cox proportional hazards regression and then pooled by using a random-effects model. Results: a-Carotene, b-carotene, and lutein/zeaxanthin intakes were inversely associated with the risk of ER-negative (ER2) breast cancer (pooled multivariable RRs of the comparison between the highest and lowest quintiles): a-carotene (0.87; 95% CI: 0.78, 0.97), b-carotene (0.84; 95% CI: 0.77, 0.93), and lutein/zeaxanthin (0.87; 95% CI: 0.79, 0.95). These variables were not inversely associated with the risk of ER-positive (ER+) breast cancer (pooled multivariable RRs for the same comparison): a-carotene (1.04; 95% CI: 0.99, 1.09), b-carotene (1.04; 95% CI: 0.98, 1.10), and lutein/zeaxanthin (1.00; 95% CI: 0.93, 1.07). Although the pooled RRs for quintile 5 for b-cryptoxanthin were not significant, inverse trends were observed for ER2 and ER+ breast cancer (P-trend 0.05). Nonsignificant associations were observed for lycopene intake. The associations were largely not appreciably modified by several breast cancer risk factors. Nonsignificant associations were observed for PR-positive and PR-negative breast cancer. Conclusions: Intakes of a-carotene, b-carotene, and lutein/zeaxanthin were inversely associated with risk of ER2, but not ER+, breast cancer. However, the results need to be interpreted with caution because it is unclear whether the observed association is real or due to other constituents in the same food sources.Am J Clin Nutr 2012;95:713-25.

Two methods of quantifying heterogeneity between studies in meta-analysis were studied. One method quantified the proportion of the total variance of the effect estimate due to variation between studies (RI), and the other calibrated the variance between studies to the size of the effect itself through a between-study coefficient of variation (CVB). Bootstrap and asymptotic confidence intervals for RI and CVB were derived and evaluated in an extensive simulation study that covered a wide range of scenarios likely to be encountered in practice. The best performance was given by asymptotic Wald confidence intervals developed for RI and CVB. The use of these heterogeneity measures together with their confidence intervals was illustrated in 5 typical meta-analyses. A new user-friendly SAS macro (SAS Institute, Inc., Cary, North Carolina) is provided to implement these methods for routine use and can be downloaded at the last author's website.

Assessing the magnitude of heterogeneity in a meta-analysis is important for determining the appropriateness of combining results. The most popular measure of heterogeneity, I(2) , was derived under an assumption of homogeneity of the within-study variances, which is almost never true, and the alternative estimator, R^I, uses the harmonic mean to estimate the average of the within-study variances, which may also lead to bias. This paper thus presents a new measure for quantifying the extent to which the variance of the pooled random-effects estimator is due to between-studies variation, R^b, that overcomes the limitations of the previous approach. We show that this measure estimates the expected value of the proportion of total variance due to between-studies variation and we present its point and interval estimators. The performance of all three heterogeneity measures is evaluated in an extensive simulation study. A negative bias for R^b was observed when the number of studies was very small and became negligible as the number of studies increased, while R^I and I(2) showed a tendency to overestimate the impact of heterogeneity. The coverage of confidence intervals based upon R^b was good across different simulation scenarios but was substantially lower for R^I and I(2) , especially for high values of heterogeneity and when a large number of studies were included in the meta-analysis. The proposed measure is implemented in a user-friendly function available for routine use in r and sas. R^b will be useful in quantifying the magnitude of heterogeneity in meta-analysis and should supplement the p-value for the test of heterogeneity obtained from the Q test. Copyright © 2016 John Wiley & Sons, Ltd.

In the development of risk prediction models, predictors are often measured with error. In this paper, we investigate the impact of covariate measurement error on risk prediction. We compare the prediction performance using a costly variable measured without error, along with error-free covariates, to that of a model based on an inexpensive surrogate along with the error-free covariates. We consider continuous error-prone covariates with homoscedastic and heteroscedastic errors, and also a discrete misclassified covariate. Prediction performance is evaluated by the area under the receiver operating characteristic curve (AUC), the Brier score (BS), and the ratio of the observed to the expected number of events (calibration). In an extensive numerical study, we show that (i) the prediction model with the error-prone covariate is very well calibrated, even when it is mis-specified; (ii) using the error-prone covariate instead of the true covariate can reduce the AUC and increase the BS dramatically; (iii) adding an auxiliary variable, which is correlated with the error-prone covariate but conditionally independent of the outcome given all covariates in the true model, can improve the AUC and BS substantially. We conclude that reducing measurement error in covariates will improve the ensuing risk prediction, unless the association between the error-free and error-prone covariates is very high. Finally, we demonstrate how a validation study can be used to assess the effect of mismeasured covariates on risk prediction. These concepts are illustrated in a breast cancer risk prediction model developed in the Nurses’ Health Study.