It should be noted that the lengths of the confidence intervals between the four different BMI likelihoods were in line, which indicated that not only the estimated parameters 15. However, it is also driven by a flattening out of costs in the severe obesity group; the costs for this group plateau while they continue to increase for all other BMI categories over this age range. This is an open access article distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 15, PDF 248-2009: Learning When to Be Discrete: Continuous vs. Categorical Select "Compute BMI" and your BMI will appear below. However, the interpretation of For both boys and girls, we found that medical expenditures only increased substantially over the 99th percentile of BMI. Table 3 presents the same information as the distribution functions evaluated with the BMI categories (gray vertical lines in The intercept functions 1085). We estimated continuous BMI-related health care expenditures using data from the Medical Expenditure Panel Survey (MEPS) 20112016 for 175,726 respondents. Because of a potential impact of both smoking and sex of the individual on the entire distribution, we stratify this intercept function with respect to these two variables, We then used generalized additive models (GAMs) [23] to estimate the relationship between log BMI and the log of the standardized expenditures using the same two-part model described above. In addition, our estimates are based on the cross-sectional association between BMI and medical expenditures. As a library, NLM provides access to scientific literature. Like these discrete models, the continuous BMI logistic regression model does not require strong parametric assumptions for the conditional BMI distribution, yet it allows to model the . Our overall results are also similar to a meta-analysis of 12 studies which estimated that obesity-attributable medical costs were $1,901 (95% CI $1,239-$2,582) per person in 2014 $US, accounting for $150 billion at the national level [12]. 13. The approximation of the likelihood by the density was very accurate, as the estimated probabilities obtained from models estimated from numeric intervals taking rounding error into account (Int 2) and exact BMI values were very close. 29, smk:sex for each combination of smoking and sex were estimated as smooth and monotonically increasing functions of We found that health care expenditures are higher for people with excess weight across a wide range of ages and BMI levels, with especially high costs for people with severe obesity. Now, looking at the heading of the Table 3, it says Estimated b {18.5, 25, 30} obtained from model (4) are given in Efficient sieve maximum likelihood estimation of time-transformation models. The same problem occurs when the primary interest in a statistical analysis is the comparison of BMI distributions between different risk groups. Continuous BMI logistic regression, which avoided ad hoc categorization of BMI values, led to deeper insights into the impact of sex of the individuals and smoking status on the continuous BMI distribution. For current smokers, the odds ratio patterns that depended on BMI differed between males and females. broad scope, and wide readership a perfect fit for your research every time. : Association of cigarettes smoked daily with obesity in a general adult population. Modeling continuous response variables using ordinal regression. In this latter situation, we advocate post hoc categorization of model outputs instead of ad hoc categorization of BMI measurements to better combine measurement precision, ease of communication, comparability, and reproducibility. The model was fitted using the likelihood (Lik) defined by BMI measurements categorized according to the WHO and according to a different categorization with intervals of two BMI units (Int 1). All computations were performed using R version 3.4.2 odds ratios for a 10-year age difference and a single unit of drink (12g in Switzerland, although 10g is more internationally comparable). We compared models fitted to a cascade of increasingly precise BMI values, starting with the four WHO categories and ending with the exact BMI values. For the information you entered: Height: Weight: Your BMI is , indicating your weight is in the category for adults of your height.BMI is a screening measure and is not intended to diagnose disease or illness. Population for empirical evaluation. If there are earlier studies from Switzerland or neighboring countries, are the results more similar with these compared to studies conducted in other, geographically more distant populations (e.g. x)). Height Continuous Height in meter BMI Discrete BMI in Kg/m2 BMI_gr Ordinal BMI Group BP_diastolic Discrete Diastolic BP BP_systolic Discrete Systolic BP HTN Nominal Hypertension Duration_diabetes Discrete Duration of Diabetes Duration_diabetes_gr Ordinal Duration of Diabetes Group HbA1c Discrete HbA1c We therefore assumed that the covariate parameters would be the same in all binary or polytomous logistic regression models regardless of the ad hoc categorization applied. Associations between smoking and body weight in the US population: Analysis of NHANES II. To demonstrate the difference between traditional and this new logistic regression approach, I would like to see also estimated odds ratios for traditional logistic regression with ad hoc categorization for this cohort. hc.nimda.sfb@21bgs). As an alternative to multinomial regression following ad hoc categorization, we propose a continuous outcome logistic regression model for the estimation of a continuous BMI distribution. r( et al (2014 to the likelihood, which automatically takes the measurement error into account. Such results would be interpretable and universally comparable between studies using any type of category. The BMI distribution shifted towards larger BMI values from males who never smoked to male former smokers. Specific classical models, such as binary logistic regression or polytomous logistic regression, are implemented via a specific regression function Copyright: 2021 Ward et al. Department of Social and Behavioral Sciences, Harvard T. H. Chan School of Public Health, Boston, MA, United States of America. Simple maximum-likelihood estimation was performed for all model parameters simultaneously. b | smk, sex) = BMI-specific medical costs by age and sex are available in a public repository (https://doi.org/10.7910/DVN/872OW1). smoking, and ( The model was fitted using exact BMI values. x). Categorical variables come in nominal or ordinal flavours, whereas numerical variables can be discrete or continuous . This approach precludes comparisons with studies and models based on different categories. of the conditional continuous BMI distribution. b | smk, sex, Categorical, continuous, or dichotomous? the example of BMI Discrete vs. Continuous Data: What's the Difference? - G2 x, the results obtained from our continuous BMI logistic regression model and a Cox model stratified by sex and smoking would not be affected by this change, because for each combination of sex and smoking, a corresponding equivalent intercept function helps to understand the properties of specific models for BMI and connections between them. b, PLOS ONE promises fair, rigorous peer review, x) (BMI Body mass index (BMI) is a measure of body fat based on height and weight that applies to adult men and women. Introduction. ( The BMI data from this survey are encoded in various ways and the results show consistency of results (table 1 and 2). We find that among adults, obesity is associated with over $1,800 excess annual medical costs per person, accounting for over $170 billion of annual spending in the US. x then have an impact on the regression function Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data. In contrast, estimating continuous BMI-related costs provides a more accurate and flexible approach as it reflects the entire BMI distribution and does not rely on specific category thresholds. In models treating BMI as a continuous outcome, the exposure smoking status, sex, and covariates The odds ratios obtained with intervals of Int 1 differed more, but were still negligible. SNB and SLG were supported by the Centers for Disease Control and Prevention (CDC) (Grant No. It was obvious from the conditional BMI densities ( Accessibility 28. Continuous outcome logistic regression for analyzing body mass index Our precision in measuring these variables is often limited by our instruments. is confusing. The difference is explained in the following two sections. I have only minor comments on the manuscript. Slightly larger differences were observed between numeric intervals (Int 2) and intervals obtained by categorization Int 1. . 32, for numerical experiments with varying numbers of parameters]. Continuous, when the variable can take on any value in some range of values. Discuss your BMI category with your healthcare provider as BMI may relate to your overall health and well-being. Is it possible to perform chi-squared test on continuous data b | smk, sex, We also expected the results of the novel continuous outcome logistic model for BMI to be comparable to previously reported associations of smoking and BMI, and evaluated this hypothesis for the Swiss Health Survey 2012. b > 0. For example, despite doubts raised about the utility of the current cutpoints in Asian popoulations, WHO recommends to continue to use them for international comparisons. Additional methodological details and results. 2. Similar to Cox-Snell residuals, the residual Because we allow the entire BMI distribution to change with these two variables in more complex ways, there is no simple interaction term Background Estimates of health care costs associated with excess weight are needed to inform the development of cost-effective obesity prevention efforts. Table 1. If you look at the data on age and COVID-19 outcomes, you'll see it takes a . 1, 2017 Thus, continuous outcome logistic regression is applicable to studies that implement different BMI measurement scales or categorization schemes, or even a mixture of those. The estimated conditional BMI distribution for all combinations of smoking and sex were clearly non-symmetric, and the impacts of smoking and sex of the individual related to changes in the mean and higher moments (distribution functions in I understand that comparing these models was not the aim of this study, but still I think it would be interesting for the readers who are not familiar with this new approach to see this difference. sharing sensitive information, make sure youre on a federal I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. weights, is, Continuous outcome logistic regression, as a model for a continuous conditional distribution implemented in Likelihoods for BMI models. TL, SR and DF were supported by the Swiss Cancer Research foundation (grant no. The most important aspect here is a smooth and monotonically increasing intercept function Alcohol intake was included using the continuous variable grams per day. The BMI values of people of the German-speaking part of Switzerland were higher than those of the French- and Italian-speaking regions. In this way, the parameters and contrasts we are interested in are not directly parameterized in model (4) but nevertheless can be obtained from this model by relatively simple contrasts. The https:// ensures that you are connecting to the The regression coefficients This essentially removes the need to specify a strict parametric distribution, such as the normal, for BMI. x. The rightmost column contains the body mass index (BMI) computed using the height and weight measurements. Association of Body Shape Index (ABSI) with cardio - Home - PLOS Facebook - National Cancer Institute 1Department of Statistics, University of Innsbruck, Innsbruck, Austria. In an unconditional model for the marginal BMI distribution. Our study showed that it was possible to analyze and compare BMI distributions in terms of standard parameters without the need of ad hoc categorization. x) 1 Paper248-2009 Learning When to Be Discrete: Continuous vs. Categorical Predictors David J. x) corresponding to model (4) was evaluated for baseline covariates , (35, 37], > 37. We found a J-shaped curve of medical expenditures by BMI (Fig 1A), with higher costs in general for females and the lowest expenditures occurring at a BMI of 20.5 for females and 23.5 for males. smoking, insurance coverage, etc.). Is Date discrete or continuous? When you can represent the information you're gathering with numbers, you are collecting quantitative data. Numeric intervals taking rounding error into account (Int 2) and exact BMI values were used to estimate the model parameters. Adult BMI Calculator | Healthy Weight, Nutrition, and Physical Activity ( official website and that any information you provide is encrypted Calculate Your BMI - Standard BMI Calculator - NHLBI, NIH Severe obesity was associated with excess costs of $3,097 (95% CI $2,777-$3,413) per adult. Box plots of continuous variable values for each category of categorical variable; Side-by-side dot plots (means + measure of uncertainty, SE or confidence interval) . The characteristics such as age, sex, height, weight, body mass index (BMI), blood group, body temperature, blood glucose level, blood pressure, heart rate, number of teeth, severity of disease (mild, moderate, severe) etc. Treating BMI as a continuous variable is problematic in a small risk factor analysis, because by default, one is looking at a 1-unit increase in BMI as the predictor of COVID-19 outcomes. For each combination of smoking and sex, the conditional density of BMI corresponding to model (4) was evaluated for baseline covariates 32. 35). Estimated expenditures are controlled for potential confounding variables. It has been shown that former smoking is associated with being overweight as well as obesity, especially for males b | former smoker, female, e0247307. Of course, these constant regression coefficients might be incorrectly specified. Methods We estimated continuous BMI-related health care . Mead E, Batterham AM, Atkinson G, et al. Department of Health Policy and Management, Harvard T. H. Chan School of Public Health, Boston, MA, United States of America, Affiliation: BMI is typically coded in categories determined by the World Health Organization (WHO), but ad hoc categories may also be used, and other encodings of BMI are possible (e.g. r( are some of the examples for biological variables in research. 31 of order five. | smk, sex, Bethesda, MD 20894, Web Policies b | smk, sex, Similar to previous analyses [9, 11], we controlled for the following variables: BMI (continuous), year (continuous), geographical region (Northeast, Midwest, South, West), age (continuous), sex, race/ethnicity (White, Black, Hispanic, American Indian/Alaska Native, Asian/Native Hawaiian/Pacific Islander, multiple races), marital status (married, widowed, divorced, separated, never married), education (less than high school, some high school, GED or high school diploma, some college, college graduate, graduate school, unknown), smoking status (yes/no), poverty level (continuous), and insurance coverage (private, TRICARE, Medicare, Medicaid, other public A, other public B, none). . regression - BMI Continuous or categorical? - Cross Validated b | smk, sex)(4). We also estimated how categorical expenditures change with age by fitting smooth splines to the predicted costs within each BMI category by age. Our findings on the association between smoking and BMI are consistent with the results of previous studies. We used ridge regression [20, 21] to help guard against over-fitting to extreme values that can occur given the highly skewed nature of health expenditures [22]. A Body Shape Index (ABSI) is calculated by dividing waist circumference (WC) by its estimate obtained from allometric regression of weight and height [].ABSI was designed to be minimally associated with weight, height and body mass index (BMI) so that it can be used together with BMI to disentangle the independent contribution of WC and BMI to cardio-metabolic outcomes [1-3]. The narrower the interval representing the BMI value for a particular individual, the more information is contributed by this individual to the likelihood. Relationship between smoking and obesity: a cross-sectional study of 499,504 middle-aged adults in the UK general population. GUID:DEA52E7A-4C03-483D-9F4F-9B6FD411812F, An extension of ordered polytomous regression to continuous responses, treating the intercept function, An individual with a BMI value between 19 and 21 thus contributes. Department of Prevention and Community Health, Milken Institute School of Public Health, George Washington University, Washington, DC, United States of America, Affiliation: A Body Shape Index (ABSI) was specifically developed as a transformation of waist circumference (WC), statistically independent of BMI to better evaluate the relative contribution of WC to. We evaluated this hypothesis empirically by analyzing the association of smoking status and BMI using data from the Swiss Health Survey 2012 * In Table 2 there is a little typo, two commas "i.e.,,". Over 30 units of BMI, each one-unit BMI increase was associated with an additional cost of $253 (95% CI $167-$347) per person. Association of body mass index with health care expenditures in the ( The scatterplot shows how the body fat percentage tends to rise as BMI increases. Estimates of age/sex/BMI-specific annual medical costs are available at: https://doi.org/10.7910/DVN/872OW1. Treating smoking as the only exposure variable in the following, a generic logistic regression model for BMI, conditional on smoking status, sex, and covariates Types of biological variables - PMC - National Center for Biotechnology r is a smooth and monotonically increasing function of The cost of dichotomising continuous variables. This corresponds to the proportional odds assumption in polytomous logistic regression models. More precisely, the authors use recently developed conditional transformation models that directly model the distribution function of BMI outcomes and are therefore capable to estimate all moments of the response distribution simultaneously. Among children, obesity was associated with $116 (95% CI $14-$201) excess costs per person and $1.32 billion (95% CI $0.16-$2.29) of medical spending, with severe obesity associated with $310 (95% CI $124-$474) excess costs per child. This allowed an understanding of the impact of the measurement scale on the resulting models. x at all possible BMI values r( U48DP006376). Whether or not a high school graduate is accepted into a college. Using the fitted two-part model we then adjusted each respondents probability and level of total expenditure to be representative of a standardized individual. b; (2) the regression coefficients What did the authors do exactly, please clarify. Data is available for scientific research projects, and a data protection application form must be submitted. 4) The final paragraph of the discussion seems to imply that the WHO cutpoints will changes in the future as prevalence of overweight and obesity increases. Thus, our findings of little excess cost at younger ages is consistent with the epidemiological evidence that obesity-related disease mostly occurs later in life. r; details will be given in the next section. Prediction with confidence bands . b in model (4), the likelihood (2) can be evaluated for all types of intervals ( The number generated from this equation is then . Accurate estimates of excess weight-related health care costs are necessary to evaluate the cost-effectiveness of policies and programs aimed at helping to reverse the obesity epidemic and promote a healthy weight across a range of ages and BMI levels [14, 15]. sex (smoking and sex as factors), as well as It is calculated by taking a person's weight, in kilograms, divided by their height, in meters squared, or BMI = weight (in kg)/ height^2 (in m^2). Specifically, we propose that statistical analyses should be based on precise BMI measurements without ad hoc categorization, and then parameters and interesting contrasts thereof should then be categorized post hoc. b | smk, sex, Types of Quantitative Data: Continuous and Discrete. r(0 Because the regression function The basics Typically, a variable can describe either a quantitative or qualitative characteristic of an individual. Should I Specify a Model Predictor as Categorical or Continuous? - The The differences between these four ways of evaluating the likelihood with respect to the estimated probabilities were marginal. We distinguished between four different likelihood contributions corresponding to four different BMI measurement scales. Figure 1 and density functions in bmi (the numeric BMI values), 14, 4. Specifically, we used cubic splines to estimate the magnitude of self-report bias by BMI quantile and adjust the self-reported BMI in MEPS by age group. KFS-3048-08-2012). We calculated 95% confidence intervals (CIs) as the 2.5 and 97.5 percentiles of the bootstrapped results (see S1 File, Section 5 for details). After such an ad hoc categorization, only the conditional distribution of BMI at the corresponding cut-off points Quantitative variables are divided into two types: discrete and continuous. Binary or multinomial logistic regression models are commonly applied in this context, but are only applicable to BMI values categorized within a small set of defined ad hoc BMI categories. Language region reflecting cultural differences within Switzerland was categorized as German/Romansh, French, or Italian. Most often these variables indeed represent some kind of count such as the number of prescriptions an individual takes daily. i.e.,, using BMI measurements categorized according to the WHO and according to a different categorization with intervals of two BMI units (Int 2), numeric intervals taking rounding error into account (Int 2), and exact BMI values. 33. All analyses were performed in R (version 3.6.1). In contrast to the partial likelihood of Cox models that treat the intercept functions as nuisance parameters, the likelihood for continuous outcome logistic regression is evaluated for fully parameterized intercept functions and all model parameters are estimated by maximum likelihood [similar to Basterra-Gortari FJ, Forga L, Bes-Rastrollo M, et al. Individuals who never smoked stated that they did not currently smoke and never regularly smoked for longer than a six-month period; former smokers had quit smoking but had smoked for more than 6 months during their life. Study with Quizlet and memorize flashcards containing terms like Classify the following data. 27, This is an open access peer review report distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. It would be also interesting to compare the magnitude of the association between smoking and BMI in their study and in the previous studies. Discrete variables (also called categorical variables) are divided into 2 subtypes: (unordered) and (ordered). However, this point is not too critical, since it is possible to obtain the data on request. The model was fitted to BMI observations categorized according to the WHO and to a different categorization with intervals of two BMI units (Int 1). Thus, it is widely used for describing underweight, overweight, and obesity r is defined for all possible BMI values 11, The site is secure. 9. U = (BMI Waist circumference as a vital sign in clinical practice: a Consensus 18. PLOS is a nonprofit 501(c)(3) corporation, #C2354500, based in San Francisco, California, US. b] is simply the probability, in light of some specific regression function For males, this association was reversed and had an inverted U-shaped pattern. Total and excess annual medical expenditures by BMI category ($US 2019). Why? The monotonicity constrained on the intercept functions renders the addition of smoothing penalty terms to the likelihood unnecessary, because the effective number of parameters is less than the order of the Bernstein polynomial [see b | smk, sex, Models to estimate the cost-effectiveness of obesity interventions among adults thus need to take into account effects on mortality as well [14]. See S1 File, Section 2 for details. To estimate confidence intervals for all results we bootstrapped the MEPS dataset 1,000 times, taking into account the complex survey structure, and re-estimated all models described above. For each of the ten strata given by the five smoking categories and two categories of sex, an intercept function was defined by six increasing parameters of a Bernstein polynomial Numerical Summaries for Discrete Variables - Boston University School b. Discrete, when the variable takes on a countable number of values. With these predicted expenditures we also estimated costs by binary obesity status: non-obesity vs obesity, and by BMI category: underweight, normal weight, overweight, moderate obesity, severe obesity (see S1 File, Section 4.2 for category definitions). * In section "Discussion" the authors say that a conditional normal distribution with covariate specific variance would describe the BMI distributions less accurately. For this study, we restricted the sample from the 2012 survey to 16,427 individuals aged between 18 and 74 years. b | smk, sex, x)) = Association of Body Shape Index (ABSI) with cardio-metabolic risk Pasta, ICON Clinical Research, San Francisco, CA ABSTRACT Some predictors, such as age or height, are measured as continuous variables but could be put into categories ("discretized"). x, the probabilities obtained from model (4) for BMI 18.5, BMI 25, and BMI 30 are given for each combination of smoking and sex of the individual. Dia BP: diastolic blood pressure (Continuous) BMI: Body Mass Index (Continuous) Heart Rate: heart rate (Continuous In medical research, variables such as heart rate though in fact discrete, yet are considered continuous because of large number of possible values.) This is partly due to increasing costs among those with normal weight as a result of ageing. The interpretation of the sex- and smoking-specific intercept functions, and thus the associations of smoking and sex with BMI, however, is fundamentally different from the interpretation of the regression coefficients In general, the association of smoking and BMI was less pronounced for females than for males. smk:sex (the sex- and smoking-specific log-cumulative hazard in the stratified Cox model) can be found on both the logit and cloglog scales. For predictions by BMI and age (Fig 1C) we found a similar J-shaped relationship of expenditures by BMI at all ages, with increasing expenditures by age. Using discrete categories likely underestimates the health care cost impact of changes in population BMI, as only changes in weight that cross specific category thresholds are accounted for, therefore ignoring changes within categories at all other parts of the BMI distribution. Even more troublesome is the problem of comparability of studies and findings over time because the WHO categories can be expected to be updated to better reflect contemporary BMI distributions. The most prominent standard BMI categories, underweight, normal weight, overweight, and obesity as defined by the World Health Organization [WHO, former smoker:female Download the BMI calculator app today (available for iPhone and Android ). This also applied to the marginally less accurate odds ratios obtained from models fitted to BMI values categorized according to WHO criteria. The interpretation of the parameters During this case each year, quarter, month, day, hour, etc. The IQ scores of students at the local college., ____occurs if a researcher intentionally chooses a favorable sample., Collecting . Distribution regression, transformation model, conditional distribution, odds ratio, smoking, ### set-up increasing Bernstein polynomial, ### plot conditional BMI distribution for, ### 18 year-old never-smoking non-drinking.
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