Journal of Biostatistics and Epidemiology 2017. 3(2):49-59.

Comparison between fractional polynomials, spline smoothing, and multiple logistic regression models in the study of associated hypertension risk factors
Maryam Ganji, Mir Saeed Yekaninejad, Mahdi Yaseri


Background & Aim: Previous studies about hypertension and risk factors have shown the linear relationship between them. However, we can improve the fit of models with some changes and have a better form for estimation of coefficients and interpret the effects of variables.
Methods & Materials: This survey was a cross-sectional study from 2010 to 2011 in Yazd, Iran. The participants were among the subjects aged from 40 to 80. Body mass index (BMI), sex, age, renal failure, history of diabetes (years of disease), type of diabetes (type 1 or type 2), the number of cigarettes per day and years of smoking were predictors and the binary response returned to hypertension (yes or no). The traditional logistic model was used for determining the relationship between covariates and the outcome. Then, the models were modified with multivariable fractional polynomials.
Results: Our findings displayed fitting the multivariable fractional polynomials (MFP) model in the parametric model which was the best fit for the modeling. The difference deviance in MFP was 21.952 (P < 0.001). The linear model in comparison with null model deviance differences was 22.170 (P < 0.001). The second-degree fractional polynomials model compared with first-degree fractional polynomials model, and the difference deviance was 21.850 (P < 0.001).
Conclusion: MFP model approach is an alternative procedure that can solve previous problems about the categorical approach, step function, and cut- off points.


Likelihood functions; Logistic regression model; Statistical models; Hypertension; Body mass index

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