Multivariable regression model building by using fractional polynomials: Description of SAS, STATA and R programs

Sauerbrei, Willi; Meier‐Hirmer, Carolina; Benner, A.; Royston, Patrick

doi:10.1016/j.csda.2005.07.015

Cited by 310 publications

(223 citation statements)

References 22 publications

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“…We recommend fractional polynomial regression as a relatively straightforward and robust method for transforming age that offers significant advantage over conventional methods such as categorization of continuous variables using quantiles, personal preference, groupings from previous studies, or establishment via a systematic search for "optimal" cutpoints. 36,37 Our study reports other important findings. We found that men of younger age (18 to 47 years) have a lower probability of survival to hospital discharge from OHCA than similarly aged women.…”

Section: Discussionsupporting

confidence: 70%

“…We used fractional polynomial regression to determine the optimal transformation for age as a continuous variable for a linear relationship with survival in the logit scale, independently assessing age for males and females. 35,36 Fractional polynomial regression revealed that no transformation for age as a continuous variable for female OHCA victims significantly improved model fit, so age was left as an untransformed continuous variable for females. However, for males, a fractional polynomial transformation for age (0 3, ln(age) + age 3 ) significantly improved model fit and provided a linear relationship between age and survival in the logit scale, a key assumption for continuous covariates.…”

Section: Study Protocolmentioning

confidence: 99%

See 1 more Smart Citation

Differential Survival for Men and Women from Out-of-hospital Cardiac Arrest Varies by Age: Results from the OPALS Study

et al. 2014

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Section: Discussionsupporting

confidence: 70%

Section: Study Protocolmentioning

confidence: 99%

Differential Survival for Men and Women from Out-of-hospital Cardiac Arrest Varies by Age: Results from the OPALS Study

et al. 2014

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“…If the PH hypothesis is rejected, the time-dependent effect of the prognostic factor can be estimated with flexible survival models, using either fractional polynomials (Sauerbrei et al, 2007) or splines (Gray, 1992;Hess, 1994;Kooperberg et al, 1995;Abrahamowicz et al, 1996;Abrahamowicz and MacKenzie, 2007), including the method incorporated in the R package (Grambsh and Therneau, 1994). To test the linearity hypothesis and estimate non-linear effects of continuous predictors on the hazard, one can use splines (Gray, 1992;Kooperberg et al, 1995;Abrahamowicz and MacKenzie, 2007;Remontet et al, 2007), or fractional polynomials (Royston and Altman, 1994;Sauerbrei et al, 2007;Royston and Sauerbrei, 2008), incorporated in STATA (StataCorp LP, College Station, TX, USA), R (R Foundation for Statistical Computing, Vienna, Austria) package mfp (Sauerbrei et al, 2006), and a SAS (SAS Institute Inc.) macro (Sauerbrei et al, 2006).…”

Section: Discussionmentioning

confidence: 99%

Flexible modeling improves assessment of prognostic value of C-reactive protein in advanced non-small cell lung cancer

et al. 2010

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BACKGROUND: C-reactive protein (CRP) is gaining credibility as a prognostic factor in different cancers. Cox's proportional hazard (PH) model is usually used to assess prognostic factors. However, this model imposes a priori assumptions, which are rarely tested, that (1) the hazard ratio associated with each prognostic factor remains constant across the follow-up (PH assumption) and (2) the relationship between a continuous predictor and the logarithm of the mortality hazard is linear (linearity assumption). METHODS: We tested these two assumptions of the Cox's PH model for CRP, using a flexible statistical model, while adjusting for other known prognostic factors, in a cohort of 269 patients newly diagnosed with non-small cell lung cancer (NSCLC). RESULTS: In the Cox's PH model, high CRP increased the risk of death (HR ¼ 1.11 per each doubling of CRP value, 95% CI: 1.03 -1.20, P ¼ 0.008). However, both the PH assumption (P ¼ 0.033) and the linearity assumption (P ¼ 0.015) were rejected for CRP, measured at the initiation of chemotherapy, which kept its prognostic value for approximately 18 months. CONCLUSION: Our analysis shows that flexible modeling provides new insights regarding the value of CRP as a prognostic factor in NSCLC and that Cox's PH model underestimates early risks associated with high CRP.

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“…The constants a, b, c and d are determined by fitting the Cox model to the data in the usual way. Software to run the MFP algorithm is available in the packages Stata, SAS and R (see Sauerbrei et al, 2006 for details).…”

Section: Fractional Polynomialsmentioning

confidence: 99%

An approach to estimating prognosis using fractional polynomials in metastatic renal carcinoma

Royston

Reitz²,

Atzpodien

2006

Br J Cancer

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We present a prognostic model for metastatic renal cell carcinoma based on fractional polynomials. We retrospectively analysed 425 metastatic renal cell carcinoma patients treated with subcutaneous recombinant cytokine-based home therapies in consecutive trials. In our approach, we categorised a continuous prognostic index produced by the multivariable fractional polynomial (MFP) algorithm, using a strategy in which continuous predictors are kept continuous. The MFP algorithm selected five prognostic factors as significant at the 5% level in a multivariable model: lymph node metastases, liver metastases, bone metastases, age, C-reactive protein and neutrophils. The MFP model allowed us to divide patients into four risk groups achieving median overall survivals of 38 months (low risk), 23 months (low intermediate risk), 15 months (high intermediate risk) and 5.6 months (high risk). Our approach, based on categorising a continuous prognostic index produced by the MFP algorithm, allowed more flexibility in the determination of risk groups than traditional approaches. British Journal of Cancer (2006) For renal cell carcinoma, certain prognostic staging factors, notably, performance status, disease-free interval, erythrocyte sedimentation rate (ESR), lactate dehydrogenase (LDH), neutrophils, haemoglobin, extrapulmonary and bone metastases, and number of metastatic sites were identified as prognostic factors for survival (Elson et al, 1988;Palmer et al, 1992;Lopez-Hänninen et al, 1996;Gelb, 1997;Culine et al, 1998;Hoffmann et al, 1999;Motzer et al, 1999Motzer et al, , 2002Atzpodien et al, 2003).However, the importance of each predictor varies from study to study and is, therefore, controversial. Besides heterogeneity in patient populations and treatments between different studies, a substantial reason for the observed variation might be attributable to an inadequate use of statistical methods (Simon and Altman, 1994).Most researchers who develop and publish prognostic models in cancer seem to assume that to introduce continuous predictors, such as age and haemoglobin, into a multivariable statistical model, it is necessary first to 'categorise' the predictors into two groups. However, the choice of an appropriate cutpoint is not usually obvious a priori. To avert the worry that an arbitrary choice may be sub-optimal, there have been strategies searching for the 'optimal' cutpoint for each continuous predictor, thus, yielding the smallest P-value when testing the effect of the categorised predictor in a univariate Cox model or log-rank analysis. Once such a set of cutpoints has been found, the final multivariable model is often determined by applying a standard algorithm, such as stepwise selection of variables, to the candidate predictors. Sometimes, only those individually significant at the 5% level are considered as candidates for inclusion in the multivariable model.The disadvantages of such a modelling strategy have been rehearsed quite often in the statistical literature. Here, we will illustrate an alternative...

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Multivariable regression model building by using fractional polynomials: Description of SAS, STATA and R programs

Cited by 310 publications

References 22 publications

Differential Survival for Men and Women from Out-of-hospital Cardiac Arrest Varies by Age: Results from the OPALS Study

Differential Survival for Men and Women from Out-of-hospital Cardiac Arrest Varies by Age: Results from the OPALS Study

Flexible modeling improves assessment of prognostic value of C-reactive protein in advanced non-small cell lung cancer

An approach to estimating prognosis using fractional polynomials in metastatic renal carcinoma

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