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Register a new userPut the odds on your side: a new measure for epidemiological associations
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Added by
Olga Vsevolozhskaya
Publication date
2018
fields
Mathematical Statistics
and research's language is
English
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The odds ratio (OR) is a measure of effect size commonly used in observational research. OR reflects statistical association between a binary outcome, such as the presence of a health condition, and a binary predictor, such as an exposure to a pollutant. Statistical inference and interval estimation for OR are often performed on the logarithmic scale, due to asymptotic convergence of log(OR) to a normal distribution. Here, we propose a new normalized measure of effect size, $gamma$, and derive its asymptotic distribution. We show that the new statistic, based on the $gamma$ distribution, is more powerful than the traditional one for testing the hypothesis $H_0$: log(OR)=0. The new normalized effect size is termed `gamma prime in the spirit of $D$, a normalized measure of genetic linkage disequilibrium, which ranges from -1 to 1 for a pair of genetic loci. The normalization constant for $gamma$ is based on the maximum range of the standardized effect size, for which we establish a peculiar connection to the Laplace Limit Constant. Furthermore, while standardized effects are of little value on their own, we propose a powerful application, in which standardized effects are employed as an intermediate step in an approximate, yet accurate posterior inference for raw effect size measures, such as log(OR) and $gamma$.
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Analyses of population-based surveys are instrumental to research on prevention and treatment of mental and substance use disorders. Population-based data provides descriptive characteristics of multiple determinants of public health and are typically available to researchers as an annual data release. To provide trends in national estimates or to update the existing ones, a meta-analytical approach to year-by-year data is typically employed with ORs as effect sizes. However, if the estimated ORs exhibit different patterns over time, some normalization of ORs may be warranted. We propose a new normalized measure of effect size and derive an asymptotic distribution for the respective test statistic. The normalization constant is based on the maximum range of the standardized log(OR), for which we establish a connection to the Laplace Limit Constant. Furthermore, we propose to employ standardized log(OR) in a novel way to obtain accurate posterior inference. Through simulation studies, we show that our new statistic is more powerful than the traditional one for testing the hypothesis OR=1. We then applied it to the United States population estimates of co-occurrence of side effect problem-experiences (SEPE) among newly incident cannabis users, based on the the National Survey on Drug Use and Health (NSDUH), 2004-2014.
We present the first acoustic side-channel attack that recovers what users type on the virtual keyboard of their touch-screen smartphone or tablet. When a user taps the screen with a finger, the tap generates a sound wave that propagates on the screen surface and in the air. We found the devices microphone(s) can recover this wave and hear the fingers touch, and the waves distortions are characteristic of the taps location on the screen. Hence, by recording audio through the built-in microphone(s), a malicious app can infer text as the user enters it on their device. We evaluate the effectiveness of the attack with 45 participants in a real-world environment on an Android tablet and an Android smartphone. For the tablet, we recover 61% of 200 4-digit PIN-codes within 20 attempts, even if the model is not trained with the victims data. For the smartphone, we recover 9 words of size 7--13 letters with 50 attempts in a common side-channel attack benchmark. Our results suggest that it not always sufficient to rely on isolation mechanisms such as TrustZone to protect user input. We propose and discuss hardware, operating-system and application-level mechanisms to block this attack more effectively. Mobile devices may need a richer capability model, a more user-friendly notification system for sensor usage and a more thorough evaluation of the information leaked by the underlying hardware.
The odds ratio measure is used in health and social surveys where the odds of a certain event is to be compared between two populations. It is defined using logistic regression, and requires that data from surveys are accompanied by their weights. A nonparametric estimation method that incorporates survey weights and auxiliary information may improve the precision of the odds ratio estimator. It consists in $B$-spline calibration which can handle the nonlinear structure of the parameter. The variance is estimated through linearization. Implementation is possible through standard survey softwares. The gain in precision depends on the data as shown on two examples.
In this paper, we show that the likelihood-ratio measure (a) is invariant with respect to dominating sigma-finite measures, (b) satisfies logical consequences which are not satisfied by standard $p$-values, (c) respects frequentist properties, i.e., the type I error can be properly controlled, and, under mild regularity conditions, (d) can be used as an upper bound for posterior probabilities. We also discuss a generic application to test whether the genotype frequencies of a given population are under the Hardy-Weinberg equilibrium, under inbreeding restrictions or under outbreeding restrictions.
The odds ratio (OR) is a widely used measure of the effect size in observational research. ORs reflect statistical association between a binary outcome, such as the presence of a health condition, and a binary predictor, such as an exposure to a pollutant. Statistical significance and interval estimates are often computed for the logarithm of OR, ln(OR), and depend on the asymptotic standard error of ln(OR). For a sample of size N, the standard error can be written as a ratio of sigma over square root of N, where sigma is the population standard deviation of ln(OR). The ratio of ln(OR) over sigma is a standardized effect size. Unlike correlation, that is another familiar standardized statistic, the standardized ln(OR) cannot reach values of minus one or one. We find that its maximum possible value is given by the Laplace Limit Constant, (LLC=0.6627...), that appears as a condition in solutions to Kepler equation -- one of the central equations in celestial mechanics. The range of the standardized ln(OR) is bounded by minus LLC to LLC, reaching its maximum for ln(OR)~4.7987. This range has implications for analysis of epidemiological associations, affecting the behavior of the reasonable prior distribution for the standardized ln(OR).
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