The FP model for BMI produced a similar BMI-mortality curve compared to the model categorizing BMI into narrow bins for both genders. Learn how to carry out beta regression and fractional regression in Stata.The following code will come in handy for this tutorial:webuse sprogramsummarize pr. To prevent collinearity and model overfit, the best fitting first degree polynomial was chosen for age. 1997, 146 (4): 339-349. Second, your results indicate a highly skewed predictor x, which may mean outliers. We investigated the relationship between mortality and obesity through BMI using the logistic regression model, stratified by gender and adjusting for age and smoking history. JAMA. Int J Obes Relat Metab Disord. Connections between logistic regression, information value and Kullback-Leibler. N Engl J Med. 10.1038/oby.2008.237. Actually benefiting from logistic regression to estimate probability of default. CAS Am J Clin Nutr. Table 5.3 on page 143 using the whas500 data in a multivariate model.. stcox age hr sysbp diasbp bmi gender cvd afb chf miord mitype, nolog nohr failure _d: fstat analysis time _t: time Cox regression -- Breslow method for ties No. Int J Obes. 10 At each step of a 'back tting' algorithm MFP constructs a fractional polynomial The bottom panel of Figure 5 compares the MFP and categorical models for age 50 never smokers. Berrington de Gonzalez A, Hartge P, Cerhan JR, Flint AJ, Hannan L, MacInnis RJ, Moore SC, Tobias GS, Anton-Culver H, Freeman LB, et al: Body-mass index and mortality among 1.46 million white adults. In addition, the number of cutoff points and where to place cutoff points is arbitrary. At the optimal BMI, the MFP model produced lower mortality estimates compared to the linear-quadratic model, but higher mortality estimates compared to the categorical model for men. JAMA. Durazo et al. Shaded regions denote 95% confidence interval for the fractional polynomial model. of subjects = 500 Number of obs = 500 No. Diabetes Care. Fractional polynomials are an alternative to regular polynomials that provide flexible parameterization for continuous variables. Allison DB, Faith MS, Heo M, Kotler DP: Hypothesis concerning the U-shaped relation between body mass index and mortality. Death probabilities increased rapidly starting at BMI = 40. The data used in this study were from the NHIS, publicly available through the Centers for Disease Control and Prevention (CDC). Obesity (Silver Spring). 390 0 obj<>stream Dr. Wong was supported by the Department of Veterans Affairs, Health Services Research and Development Post-Doctoral Fellowship TPP 61-024. World Health Organization (WHO) BMI classifications [16] are typically used. You do not need the book to consider these questions: Here is the data and the R call to the MFP function. %%EOF 10.1056/NEJM199509143331101. 2010, 145 (1): 57-62. We then verified interactions found by the MFPI algorithm graphically using Lowess smoothed curves. 2010, 47 (1): 79-96. How important is p-value in a logistic regression based strategy? Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Int J Obes (Lond). Handling unprepared students as a Teaching Assistant, Consequences resulting from Yitang Zhang's latest claimed results on Landau-Siegel zeros, adding a fixed value to every observation so that there aren't any 'zeros'. Article 10.2105/AJPH.88.4.623. 2003, 57 (2): 130-133. We found important differences between the MFP model and other commonly used models with regard to the shape and nadir of the BMI-mortality curve and mortality estimates. Stack Exchange network consists of 182 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. (1998) [6] transformed BMI into a normally distributed variable using Tukey's "ladder of powers" method. The multivariable fractional polynomials (MFP) procedure was employed to determine the best fitting functional form for BMI and evaluated against the model that includes linear and quadratic terms for BMI and the model that groups BMI into standard weight status categories using a deviance difference test. J Am Geriatr Soc. Understanding the relation between obesity and BMI is important from a policy perspective, for addressing issues such as determining the efficacy of approaches designed to reduce obesity and in communicating with the public about the importance of obesity as a public health issue. 2010, 363 (23): 2211-2219. Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. A number of studies have used other approaches that maintain BMI as a continuous variable. Is this homebrew Nystul's Magic Mask spell balanced? 2009, 373 (9669): 1083-1096. - Regression using fractional polynomials of continuous covariates . Royston P, Ambler G, Sauerbrei W: The use of fractional polynomials to model continuous risk variables in epidemiology. Problem in the text of Kings and Chronicles, Covariant derivative vs Ordinary derivative. Smoothed Lowess regression lines illustrating the BMI-age (top panel) and age-smoking status (bottom panel) interactions in the female sample. 1 Durazo-arvizu R, McGee D, Li Z, Cooper R: Establishing the nadir of the body mass index-mortality relationship: a case study. The multivariable fractional polynomial interaction (MFPI) algorithm [26] was used to assess interactions, which first determined the best fitting polynomial functions for BMI and age using MFP and then tested for significant interactions between fractionally transformed variables and smoking history using a deviance difference test. To allow for flexibility in fitting a curve with a single turning point, we considered second degree polynomial transformations for BMI. 0000002652 00000 n Pharmaceutical Outcomes Research and Policy Program, University of Washington, Seattle, WA, USA, Edwin S Wong,Bruce CM Wang,Louis P Garrison,Rafael Alfonso-Cristancho&Sean D Sullivan, Northwest Center for Outcomes Research in Older Adults, VA Puget Sound Health Care System, Seattle, WA, USA, Surgical Outcomes Research Center, University of Washington, Seattle, WA, USA, Group Health Research Institute, Seattle, WA, You can also search for this author in By using this website, you agree to our Regression models using fractional polynomials of the covariates have appeared in the literature in an ad hoc fashion over a long period; we provide a unified description and a degree of formalization for them. Consequences resulting from Yitang Zhang's latest claimed results on Landau-Siegel zeros. If the first test was statistically significant, a second deviance difference test with three degrees of freedom was applied to compare the best fitting second degree FP against the linear model. Categorizing BMI using finer intervals can alleviate some of these difficulties, but the decision of which categories to add is generally an arbitrary choice. Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling (with discussion). 1994. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Part of (2006) [25] treated BMI non-parametrically without categorization. In contrast, the BMI associated with minimum mortality for women increased with age. Bioz Stars score: 86/100, based on 1 PubMed citations. Use MathJax to format equations. Menu fp Statistics >Linear models and related >Fractional polynomials >Fractional polynomial regression fp . We addressed this difficulty by allowing the data from across the entire BMI distribution to predict mortality risk at extreme obesity levels, where fewer observations exist. For each unit sampled, a randomly selected adult and child (if present) were used to collect core health information. 10.1056/NEJMoa054017. The mortality risk of individuals in different BMI groups is computed relative to a reference BMI category. M CAS Improvements in model fit were found relative to other commonly used models including the linear-quadratic BMI model, which imposes symmetry on the BMI-mortality curve. 0000005032 00000 n 1995, 48 (7): 903-916. Will Nondetection prevent an Alarm spell from triggering? 0000002252 00000 n and c) Another Fractional Polynomial degree 1 covariate exponentiated as ^-2. a) two coefficients of the same variable (the deviance test indicated that a fractional polynomial exponentiated to powers -2 and -2 was better than a reduced model with a linear tern) signed negatively. s.d. Third, if the tight turn on the left-hand side of your graph is a real feature it's a tough call for a fractional polynomial to mimic it. Stack Overflow for Teams is moving to its own domain! For women, the MFP model produced lower mortality estimates compared to both the linear-quadratic and categorical models. Connect and share knowledge within a single location that is structured and easy to search. The class of fractional polynomial (FP) functions is an extension of power transformations of a covariate. Logistic regression results for the FP model, including significant interactions are in Table 2. Why are standard frequentist hypotheses so uninteresting? Assessing the risk of a BMI category relative to the normal category is a convenient method to account for the nonlinear form, but assumes mortality is uniform across a BMI category, which is problematic when a category is heterogenous. 1989, 13 (2): 123-136. 374 0 obj <> endobj On page 141 in the book BMI is not significant so it is not included in cycle 2. Wong, E.S., Wang, B.C., Garrison, L.P. et al. The most significant drawback is the loss of information and power through what is equivalent to rounding. Similar improvements in model fit were found in the female sample for the FP model relative to the untransformed model (Deviance Difference = 173.04, p-value < 0.001), the linear-quadratic model (Deviance Difference = 131.93, p-value < 0.001) and the categorical model (Deviance Difference = 82.11, p-value < 0.001). Journal Of The Royal Statistical Society Series A. 2000, Hyattsville, MD: National Center for Health Statistics. First, as it appears that you have just one predictor then a graph of (average) y versus x should indicate (a) what model(s) is/are plausible (b) what pathologies in your data might be inhibiting or prohibiting convergence. Here is a running line smoother of the data if that helps. PubMed Central All analyses were stratified by sex. JAMA. In particular, the normal category consists of a mix of healthy and sick lean. All statistical models were fit using the STATA Statistical Software (Version 11; College Station, TX). We maintained BMI as a continuous variable in our analysis. Mathematics. Google Scholar. You can browse but not post. - The MFP method also scaled and centered variables in model selection process to improve numerical stability and to provide a model intercept that was easier to interpret. If a Cox PH model is required then the outcome should be specified using the Surv () notation used by coxph. Fitted curves showing the relationship between the 5-year probability of death and the associated 95% confidence interval as a function of BMI are in Figure 3. Stack Overflow for Teams is moving to its own domain! He recommends using robust standard errors (otherwise the standard errors are too large; you can A deviance difference test showed a statistically significant improvement in model fit compared to other BMI functions. As we increase the value for h, the model is able to fit nonlinear relationships better . 2006, 355 (8): 779-787. As an example, the optimal BMI for the model with linear and quadratic BMI terms without interactions is In both samples, the best fitting model included a squared term for age. dormitories, boarding houses) were randomly sampled. Demography. Login or. The fractional polynomial regression model is an emerging tool in applied research. The data is as shown below: Using Stata to fit a regression line in the data, the output is as shown below: The Stata output has three tables and we will explain them one after the other. 2 Asking for help, clarification, or responding to other answers. Chaturvedi N, Fuller JH: Mortality risk by body weight and weight change in people with NIDDM. Is it enough to verify the hash to ensure file is virus free? 10.1056/NEJM199801013380101. where N Engl J Med. For example, studies of excess mortality using WHO BMI classification implicitly assume all individuals that are in the normal category (BMI = 18.5-25) exhibit the same mortality risk. 10.2337/diacare.18.6.766. Many studies have measured the detrimental effect of obesity on life expectancy by estimating the relationship between mortality and body mass index (BMI) [weight (kg)/height2 (m2)]. Multivariable fractional polynomial (MFP) method is such a method that it allows software to determine whether an explanatory variable is important for the model, and its functional form ( 2, 3 ). of Stata. The final sample contained 117,961 respondents. If I set trace on then Stata is 'stuck' at. The downward slope at the low end of the BMI distribution for men stemmed from the fact that the normal BMI category consists of a mix of healthy lean and chronically ill, which confounded the relationship between mortality and obesity. To evaluate the validity of the FP model for BMI, we graphically compared three models with the main FP model defined by (1). What is the rationale of climate activists pouring soup on Van Gogh paintings of sunflowers? 0 10.1038/sj.ijo.0801925. startxref Studies employing the categorical approach also typically take the mortality risk of obese individuals beyond a given threshold as constant. We hypothesized that this method would provide the ability to capture the relationship between mortality and BMI in a compact, parsimonious model. PubMedGoogle Scholar. However, for black men and women, the BMI of minimum mortality was 27.1 and 26.8, respectively. BCMW, LPG, RAC and DEA participated in the design of the study and helped to draft the manuscript. Hozawa A, Okamura T, Oki I, Murakami Y, Kadowaki T, Nakamura K, Miyamatsu N, Hayakawa T, Kita Y, Nakamura Y, et al: Relationship between BMI and all-cause mortality in Japan: NIPPON DATA80. Here, I've done a block-bootstrap by the variable year. This in conjunction with low variation in mortality among those in the 21-30 BMI range and high mortality among those with BMI over 40 resulted in an overly flat curve in the center. Further differences were identified within the female sample through interactions. 2 Ever smokers made up 54.93% of the male sample and 40.47% of the female sample. 10.1002/sim.2331. Lancet. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. was the 5-year death probability for individual i, p1 and p2 were the fractional powers for BMI, and q1 was the fractional power for age. i Applied Statistics. We compared the BMI-mortality curves derived using the MFP method with the continuous BMI model containing linear and quadratic BMI terms and the categorical model based on WHO BMI classifications. Our study also employed methods that differentiate the effect of BMI across gender and age.
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