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Health economic models use a basecase that is generally representative of a subpopulation rather than the whole population. During sensitivity analysis, extrapolation of the model to other subpopulations or the whole population is estimated via sampling. Sampling is performed using summary statistics (e.g. mean and standard deviation) to inform generation of a distribution from which to draw values at random. Key population characteristics for healthcare include age, height, weight, and body mass index (BMI); all of which are commonly assumed to approximate to a normal distribution. Here the plausibility of this common assumption is tested.
Full data (N=451,075) were obtained from the 2010 Behavioral Risk Factor Surveillance System (BRFSS), a national, US, health-related, telephone survey. Data collected include age, gender, height and weight, with BMI being a calculated variable. Summary statistics and distributions were produced from the whole population. A sample of 2,500 records were extracted for in-depth analysis. Of these, 2,365 had complete data for age, gender, height, and weight. Analyses performed in R and Microsoft Excel® included subsampling, normality and Cullen-Frey tests.
None of the data assessed were normally distributed. Cullen-Frey plots indicate that the best distributions to approximate the data are Beta, Log-normal, Beta, Log-normal for age, weight, height and BMI, respectively. Taking 1,000 subsamples of 300 patients, 67% of samples had a mean age falling outside of the 99% confidence interval for the population. For BMI the percentage was 62%. The ability of progressively smaller subsamples to represent the population was progressively worse.
Many population characteristics of interest to healthcare do not follow a normal distribution. In the BRFSS dataset, the most descriptive distributions are the log-normal for BMI and the Beta distribution with negative skew for age. Age distribution skew may represent the aging population in the US setting.
Calculating the economic burden of disease requires data regarding disease prevalence. National estimates can be derived from surveys of the general population, which may also access individuals not actively participating in the healthcare system. The Behavioral Risk Factor Surveillance System (BRFSS) is the largest annual country-wide population sampling of health and risk factors. The fidelity of these data, however, may be questionable, relying on accurate self reporting. Cardiovascular disease (CVD) prevalence was examined by gender to assess the feasibility of predicting future trends.
BRFSS data were trimmed to complete cases for 9 CVD risk factors: gender, age, race, overweight, physical activity, diabetes, high blood pressure, smoking and alcohol consumption. Data from 2011 and 2013 were used to train Bayesian and tree-based algorithms to evaluate predictor performance on unseen data from subsequent years (2013 and 2015) by comparing predicted with reported prevalence.
For algorithms used, predictions of future prevalence were significantly better for males than females (p < 0.001, Šidák multiple testing correction). In the best performing algorithm (Naïve Bayes), the mean percent difference from the actual prevalence for males was 3.8±2.5% and females 151±62% (p < 0.05, two-tailed t-test). Data from 2013 yielded better 2-year predictions (2015) for women than the same time span with 2011 data (2011 to 2013, p < 0.05, two-tailed t-test), while for men, there was no significant difference (p = 0.54, two-tailed t-test). Models trained on the genders combined resulted in underestimates of prevalence (p<0.001, Z-test).
Patient-reported survey data can be used to predict cardiovascular disease prevalence. Accuracy of estimation is better in males versus females. Given that BRFSS data are retrospective, our findings may reflect more substantial lifestyle changes in females or suggest discussion on changes in how survey data from female respondents are collected.