Demographic factors in hip fracture incidence and mortality rates in California, 2000-2011.

BACKGROUND: Hip fractures result in both health and cost burdens from a public health perspective and have a major impact on the health care system in the USA. The purpose was to examine whether there were systematic differences in hip fracture incidence and 30-, 90-, and 365-day mortality after hip fracture in the California population as a function of age, gender, and race/ethnicity from 2000-2011. METHODS: This was a population-based study from 2000 to 2011 using data from the California Office of Statewide Health and Planning and Development (OSHPD, N = 317,677), California State Death Statistical Master File records (N = 224,899), and the US Census 2000 and 2010. There were a total of 317,677 hospital admissions for hip fractures over the 12-year span and 24,899 deaths following hip fractures. All participants without linkage (substituted for social security) numbers were excluded from mortality rate calculations. Variation in incidence and mortality rates across time, gender, race/ethnicity, and age were assessed using Poisson regression models. Odds ratio and 95 % confidence intervals are provided. RESULTS: The incidence rate of hip fractures decreased between 2000 and 2011 (odds ratio (OR) = 0.98, 95 % confidence interval (CI) 0.98, 0.98). Mortality rates also decreased over time. There were gender, race/ethnicity, and age group differences in both incidence and mortality rates. CONCLUSIONS: Males were half as likely to sustain a hip fracture, but their mortality within a year of the procedure is almost twice the rate than women. As age increased, the prevalence of hip fracture increased dramatically, but mortality did not increase as steeply. Caucasians were more likely to sustain a hip fracture and to die within 1 year after a hip fracture. The disparities in subpopulations will allow for targeted population interventions and opportunities for further research.

An introduction to modeling longitudinal data with generalized additive models: applications to single-case designs.

Single-case designs (SCDs) are short time series that assess intervention effects by measuring units repeatedly over time in both the presence and absence of treatment. This article introduces a statistical technique for analyzing SCD data that has not been much used in psychological and educational research: generalized additive models (GAMs). In parametric regression, the researcher must choose a functional form to impose on the data, for example, that trend over time is linear. GAMs reverse this process by letting the data inform the choice of functional form. In this article we review the problem that trend poses in SCDs, discuss how current SCD analytic methods approach trend, describe GAMs as a possible solution, suggest a GAM model testing procedure for examining the presence of trend in SCDs, present a small simulation to show the statistical properties of GAMs, and illustrate the procedure on 3 examples of different lengths. Results suggest that GAMs may be very useful both as a form of sensitivity analysis for checking the plausibility of assumptions about trend and as a primary data analysis strategy for testing treatment effects. We conclude with a discussion of some problems with GAMs and some future directions for research on the application of GAMs to SCDs.

Using generalized additive (mixed) models to analyze single case designs.

This article shows how to apply generalized additive models and generalized additive mixed models to single-case design data. These models excel at detecting the functional form between two variables (often called trend), that is, whether trend exists, and if it does, what its shape is (e.g., linear and nonlinear). In many respects, however, these models are also an ideal vehicle for analyzing single-case designs because they can consider level, trend, variability, overlap, immediacy of effect, and phase consistency that single-case design researchers examine when interpreting a functional relation. We show how these models can be implemented in a wide variety of ways to test whether treatment is effective, whether cases differ from each other, whether treatment effects vary over cases, and whether trend varies over cases. We illustrate diagnostic statistics and graphs, and we discuss overdispersion of data in detail, with examples of quasibinomial models for overdispersed data, including how to compute dispersion and quasi-AIC fit indices in generalized additive models. We show how generalized additive mixed models can be used to estimate autoregressive models and random effects and discuss the limitations of the mixed models compared to generalized additive models. We provide extensive annotated syntax for doing all these analyses in the free computer program R.

A d-statistic for single-case designs that is equivalent to the usual between-groups d-statistic.

We describe a standardised mean difference statistic (d) for single-case designs that is equivalent to the usual d in between-groups experiments. We show how it can be used to summarise treatment effects over cases within a study, to do power analyses in planning new studies and grant proposals, and to meta-analyse effects across studies of the same question. We discuss limitations of this d-statistic, and possible remedies to them. Even so, this d-statistic is better founded statistically than other effect size measures for single-case design, and unlike many general linear model approaches such as multilevel modelling or generalised additive models, it produces a standardised effect size that can be integrated over studies with different outcome measures. SPSS macros for both effect size computation and power analysis are available.

Bayesian estimates of autocorrelations in single-case designs.

Researchers in the single-case design tradition have debated the size and importance of the observed autocorrelations in those designs. All of the past estimates of the autocorrelation in that literature have taken the observed autocorrelation estimates as the data to be used in the debate. However, estimates of the autocorrelation are subject to great sampling error when the design has a small number of time points, as is typically the situation in single-case designs. Thus, a given observed autocorrelation may greatly over- or underestimate the corresponding population parameter. This article presents Bayesian estimates of the autocorrelation that greatly reduce the role of sampling error, as compared to past estimators. Simpler empirical Bayes estimates are presented first, in order to illustrate the fundamental notions of autocorrelation sampling error and shrinkage, followed by fully Bayesian estimates, and the difference between the two is explained. Scripts to do the analyses are available as supplemental materials. The analyses are illustrated using two examples from the single-case design literature. Bayesian estimation warrants wider use, not only in debates about the size of autocorrelations, but also in statistical methods that require an independent estimate of the autocorrelation to analyze the data.

Characteristics of single-case designs used to assess intervention effects in 2008.

This article reports the results of a study that located, digitized, and coded all 809 single-case designs appearing in 113 studies in the year 2008 in 21 journals in a variety of fields in psychology and education. Coded variables included the specific kind of design, number of cases per study, number of outcomes, data points and phases per case, and autocorrelations for each case. Although studies of the effects of interventions are a minority in these journals, within that category, single-case designs are used more frequently than randomized or nonrandomized experiments. The modal study uses a multiple-baseline design with 20 data points for each of three or four cases, where the aim of the intervention is to increase the frequency of a desired behavior; but these characteristics vary widely over studies. The average autocorrelation is near to but significantly different from zero; but autocorrelations are significantly heterogeneous. The results have implications for the contributions of single-case designs to evidence-based practice and suggest a number of future research directions.