D a normal density for their CRP values within each day.

D a normal density for their CRP values within each day. At the second level of the hierarchical model, the individual within-day means followed a normal density, with the mean of this density allowed to vary by week. Similarly, a third level was added to accommodate monthly variations. At the fourth level of our model, variations between monthly means across individuals followed a normal density, with a Clavulanate (potassium) biological activity global mean per individual. At the top level of our hierarchical model, individual means were assumed to follow a normal density, with a global mean. While means can vary within individuals over time, our model ensures that any such changes will arise only from strong evidence in the data, otherwise the hierarchical structure will tend to pull meansback to their overall 23977191 averages. The variances estimated from these models were similarly ordered in a hierarchical fashion. In particular, the variance within days was nested into the variance within weeks, and then within months. Our global mean was given a very diffuse prior distribution, and similarly, all SDs from the above densities were given very wide uniform priors, covering the range of all plausible values with equal probability. Therefore, all inferences are essentially driven by the observed data. Models were fit for the study sample as a whole, and also within subgroups of subjects taking or not taking lipid-lowering medications. Finally, we fit another hierarchical model similar to the above, but now adding in potential covariates to attempt to explain between subject variability. Potential covariates, selected initially for potential effects from a clinical viewpoint, included aspirin, body mass index (BMI), sex, clinical group, left ventricular ejection fraction, use of lipid-lowering drugs and angiotensin-convertingenzyme inhibitors and adjudicated inflammation status. Final variable selection was by the BIC criterion. [25] All results are provided with 95 confidence intervals (CI) for frequentist results, and 95 credible intervals (CrI) for all Bayesian models. Models were fit using WinBUGS (Version 1.4.3, Cambridge, UK). The details of our approach with mathematical notation that describes exactly what is in each of the 5 levels of our hierarchical model is found in Appendix S1. Spontaneous variability in any marker over time combined with a fixed cutoff value for treatment decisions (such as initiating lipidlowering treatment with statins based on CRP levels) implies that decision errors can occur. For example, using a cutoff value ofCRP VariabilityFigure 3. Display of all CRP values of subjects with longstanding always stable coronary artery disease (CAD). doi:10.1371/journal.pone.0060759.g2 mg/L for CRP, someone with a true mean value below 2 mg/L and who the clinician may elect not to treat pharmacologically, may occasionally provide a value over 2 mg/L because of the random and generally unappreciated systematic variability inherent in any single measurement. We Vasopressin calculated the probability of such treatment errors (assuming that each individual does have a true mean value) by using an estimate of the individual betweenmonth SD of CRP.were not clinically or statistically different (Table 2). Not only was there considerable overlap of CIs but the group without CAD had the highest median CRP while this group might normally have been expected to have the lowest CRP value, making it likely that these differences are not clinically meaningful. Because the pattern of CRP var.D a normal density for their CRP values within each day. At the second level of the hierarchical model, the individual within-day means followed a normal density, with the mean of this density allowed to vary by week. Similarly, a third level was added to accommodate monthly variations. At the fourth level of our model, variations between monthly means across individuals followed a normal density, with a global mean per individual. At the top level of our hierarchical model, individual means were assumed to follow a normal density, with a global mean. While means can vary within individuals over time, our model ensures that any such changes will arise only from strong evidence in the data, otherwise the hierarchical structure will tend to pull meansback to their overall 23977191 averages. The variances estimated from these models were similarly ordered in a hierarchical fashion. In particular, the variance within days was nested into the variance within weeks, and then within months. Our global mean was given a very diffuse prior distribution, and similarly, all SDs from the above densities were given very wide uniform priors, covering the range of all plausible values with equal probability. Therefore, all inferences are essentially driven by the observed data. Models were fit for the study sample as a whole, and also within subgroups of subjects taking or not taking lipid-lowering medications. Finally, we fit another hierarchical model similar to the above, but now adding in potential covariates to attempt to explain between subject variability. Potential covariates, selected initially for potential effects from a clinical viewpoint, included aspirin, body mass index (BMI), sex, clinical group, left ventricular ejection fraction, use of lipid-lowering drugs and angiotensin-convertingenzyme inhibitors and adjudicated inflammation status. Final variable selection was by the BIC criterion. [25] All results are provided with 95 confidence intervals (CI) for frequentist results, and 95 credible intervals (CrI) for all Bayesian models. Models were fit using WinBUGS (Version 1.4.3, Cambridge, UK). The details of our approach with mathematical notation that describes exactly what is in each of the 5 levels of our hierarchical model is found in Appendix S1. Spontaneous variability in any marker over time combined with a fixed cutoff value for treatment decisions (such as initiating lipidlowering treatment with statins based on CRP levels) implies that decision errors can occur. For example, using a cutoff value ofCRP VariabilityFigure 3. Display of all CRP values of subjects with longstanding always stable coronary artery disease (CAD). doi:10.1371/journal.pone.0060759.g2 mg/L for CRP, someone with a true mean value below 2 mg/L and who the clinician may elect not to treat pharmacologically, may occasionally provide a value over 2 mg/L because of the random and generally unappreciated systematic variability inherent in any single measurement. We calculated the probability of such treatment errors (assuming that each individual does have a true mean value) by using an estimate of the individual betweenmonth SD of CRP.were not clinically or statistically different (Table 2). Not only was there considerable overlap of CIs but the group without CAD had the highest median CRP while this group might normally have been expected to have the lowest CRP value, making it likely that these differences are not clinically meaningful. Because the pattern of CRP var.