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AbstractStatistics on the natural log scale, such as differences, regression coefficients, and standard deviations, frequently arise when analyzing log‐transformed data or modeling binary, count, or time‐to‐event data. The statistical properties of log‐transformed estimators (for example, log odds ratio estimators) frequently appear in statistical articles. Understanding the magnitude of these quantities can be useful. Remarkably, many can be readily interpreted, without exponentiation. In this note, we introduce four new interpretations. While a log‐scale standard deviation can be interpreted as an approximate coefficient of variation describing variation about an arithmetic mean, we argue it can be more useful to interpret it exactly as a "standard relative deviation" describing variation about a geometric mean. For positive‐valued estimators, we show how the standard error of a log‐transformed estimator can be interpreted as the "standard relative error" describing the precision of the untransformed estimator. We also show how the bias and root mean squared error of a the log‐transformed estimator can be interpreted as the "mean relative error" and "root mean squared relative error" of the untransformed estimator. We illustrate the usefulness of our interpretations for (i) the usual scale parameter of a lognormal distribution, (ii) statistical properties of a log odds ratio estimator, and (iii) a single measure of the precision of an odds ratio estimator which agrees with its usual, asymmetric 95% confidence interval.

ABSTRACTThis paper examines how the relationships between the factors (predisposing, enabling and illness) of the 1973 Andersen framework and service use are influenced by changes in the caring role in older women of the 1921–26 cohort of the Australian Longitudinal Study on Women's Health. Outcome variables were the use of three formal community support services: (a) nursing or community health services, (b) home-making services and (c) home maintenance services. Predictor variables were survey wave and the following carer characteristics: level of education, country of birth, age, area of residence, ability to manage on income, need for care, sleep difficulty and changes in caring role. Carer changes were a significant predictor of formal service use. Their inclusion did not attenuate the relationship between the Andersen framework factors and service use, but instead provided a more complete representation of carers' situations. Women were more likely to have used support services if they had changed into or out of co-resident caring or continued to provide co-resident care for a frail, ill or disabled person, needed care themselves, and reported sleep difficulties compared with women who did not provide care. These findings are important because they indicate that support services are particularly relevant to women who are changing their caring role and who are themselves in need of care.