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Abstract
Introduction/Objective: Forty-three case-series describing fifty-three emergency medical services systems were included in our meta-analysis evaluating the effectiveness of different EMS systems for survival after out-of-hospital cardiac arrests. These systems were classified according to level of care: basic life support (BLS), BLS with defibrillation (BLS-D), advanced life support (ALS), BLS+ALS and BLS-D+ALS. The system response time (RT) and the likelihood of bystander cardiopulmonary resuscitation (CPR) were deemed to be important exposed factors. Reasonable models of survival were necessary for inferences on both EMS levels and exposure effects. Apparently, logistic regression models that assumed a linear relationship between RT, CPR and survival produced clinically untenable results. We explored the functional form for the contributions of RT, CPR toward survival to select a suitable model.
Methods: Functional forms of RT and CPR were examined through smoothing-functions in generalized additive models (Hastie 1990). We categorized RT into levels suggested by the shape of its empirical contribution. A family of logistic regression models allowing for different shapes and interactions of RT, CPR and EMS were considered. We plotted the AIC statistic, partitioned it into under- and over-fitting components, against the number of model parameters. This plot, the test of nested models and the stability of model coefficients were considered for selecting the best model. For model diagnostics, we used residual plots and Cook's distance. Odds-ratios and fitted values for EMS levels and RT, CPR effects were derived from the fitted model.
Results: A total of 15 models were considered by plotting their AIC statistic versus the number of model parameters. One model attained a reasonable balance between under- and over-fitting and produced clinically interpretable coefficients. Influential studies detected by the Cook's distance plot coincided exactly with a single large sample size case-series. Survival was constant if the response time was less than 6 minutes, decreased as the interval increased from 6 to 11 minutes, and leveled off after 11 minutes (p<0.01). Compared to BLS-D, odds ratio (95% confidence interval) of survival were: ALS 1.71 (1.09, 2.70; p=0.01), BLS+ALS 1.47 (0.89, 2.42; p=0.07) and BLS-D+ALS 2.31 (1.47, 3.62; p<0.01). Odds of survival were 1.06 (1.03, 1.10; p<0.01) per 5% increase in bystander CPR.
Discussion: The selection of an appropriate model is essential for proper inference in a meta-analysis of case-series. Graphical methods may be used to balance over versus under fitting, so as to select an appropriate model.
Methods: Functional forms of RT and CPR were examined through smoothing-functions in generalized additive models (Hastie 1990). We categorized RT into levels suggested by the shape of its empirical contribution. A family of logistic regression models allowing for different shapes and interactions of RT, CPR and EMS were considered. We plotted the AIC statistic, partitioned it into under- and over-fitting components, against the number of model parameters. This plot, the test of nested models and the stability of model coefficients were considered for selecting the best model. For model diagnostics, we used residual plots and Cook's distance. Odds-ratios and fitted values for EMS levels and RT, CPR effects were derived from the fitted model.
Results: A total of 15 models were considered by plotting their AIC statistic versus the number of model parameters. One model attained a reasonable balance between under- and over-fitting and produced clinically interpretable coefficients. Influential studies detected by the Cook's distance plot coincided exactly with a single large sample size case-series. Survival was constant if the response time was less than 6 minutes, decreased as the interval increased from 6 to 11 minutes, and leveled off after 11 minutes (p<0.01). Compared to BLS-D, odds ratio (95% confidence interval) of survival were: ALS 1.71 (1.09, 2.70; p=0.01), BLS+ALS 1.47 (0.89, 2.42; p=0.07) and BLS-D+ALS 2.31 (1.47, 3.62; p<0.01). Odds of survival were 1.06 (1.03, 1.10; p<0.01) per 5% increase in bystander CPR.
Discussion: The selection of an appropriate model is essential for proper inference in a meta-analysis of case-series. Graphical methods may be used to balance over versus under fitting, so as to select an appropriate model.