TYE was followed by significant visual improvement in the vast majority of cases, including CRAO, and was frequently associated with vitreous hemorrhage. Patients with poor visual acuity appear to benefit further and higher pulse energies may be detrimental. Lack of randomization and intrinsic biases prevent any definite conclusions regarding the benefits and further research is warranted.

Exposure assessment is often subject to measurement errors. We consider here the analysis of studies aimed at reducing exposure to potential health hazards, in which exposure is the outcome variable. In these studies, the intervention effect may be estimated using either biomarkers or self‐report data, but it is not common to combine these measures of exposure. Bias in the self‐reported measures of exposure is a well‐known fact; however, only few studies attempt to correct it. Recently, Keogh et al addressed this problem, presenting a model for measurement error in this setting and investigating how self‐report and biomarker data can be combined. Keogh et al find the maximum likelihood estimate for the intervention effect in their model via direct numerical maximization of the likelihood. Here, we exploit an alternative presentation of the model that leads us to a closed formula for the MLE and also for its variance, when the number of biomarker replicates is the same for all subjects in the substudy. The variance formula enables efficient design of such intervention studies. When the number of biomarker replicates is not constant, our approach can be used along with the EM‐algorithm to quickly compute the MLE. We compare the MLE to Buonaccorsi's method (Buonaccorsi, 1996) and find that they have similar efficiency when most subjects have biomarker data, but that the MLE has clear advantages when only a small fraction of subjects has biomarker data. This conclusion extends the findings of Keogh et al (2016) and has practical importance for efficiently designing studies.

BackgroundDevastation from the tobacco epidemic continues, with strong government tobacco control policy absent in most countries. Knowledge of the full scope of tobacco harm in populations may form the basis for healthier behavior, de-normalization of smoking, and a consensus about necessary public policy. However, many populations may be poorly-informed about the risks, and this ignorance may undermine both effective policy-making and implementation of tobacco control policies. We present knowledge and risk perceptions about smoking tobacco smoke exposure in Israel.MethodsA nationally-representative phone survey was conducted in Israel (n = 505; response rate = 61%). We assessed knowledge about active and passive smoking using four questions, three of which addressed knowledge about harm, and one of which addressed knowledge of tobacco-related harm relative to knowledge of harm due to traffic accidents. The three questions which addressed knowledge of harm were combined into a composite score. We also asked four risk perception questions concerning tobacco smoke exposure, which were measured on a 7-point Likert scale and then combined. Multivariable logistic regression and linear models were used to identify whether smoking status or socio-demographic variables were associated with knowledge of harm, comparative knowledge of harm, and risk perceptions.ResultsJust two in five respondents, and one in five respondents who were current smokers, accurately answered three simple questions about harms of smoking. Fewer than three in ten respondents, and fewer than one in five smokers, knew that smoking causes more damage than traffic accidents. Many (30.3%) were unaware that tobacco smoke exposure causes both lung cancer and heart disease, 27.7% did not know that smoking both shortens life and injures quality of life, and 31.1% did not know that smoking-attributable health problems will afflict all or most heavy smokers. Overall, risk perceptions regarding tobacco smoke exposure were high (mean = 24.5, SD:4.5, on a scale of 7–28, with 28 the indicating highest level). Smoking status was consistently associated with lower levels of knowledge, comparative knowledge, and risk perceptions, with current smokers having the lowest levels of knowledge and the lowest risk perceptions.ConclusionsLike many others, Israelis, and particularly Israeli smokers, do not fully grasp tobacco’s true dangers. Effective communication of the full range of tobacco risks to the public, with a focus on communication with smokers, is an essential component of comprehensive tobacco control policy.Electronic supplementary materialThe online version of this article (10.1186/s13584-018-0276-2) contains supplementary material, which is available to authorized users.

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