Multivariable Fractional Polynomial Models

Sauerbrei, Willi; Royston, Patrick

doi:10.1002/9781118445112.stat07861

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…For each outcome, we estimated two specifications, the first assuming linear consequences of family and school affluence levels and the second allowing for nonlinear associations between these predictors and the outcomes (i.e., linear terms plus quadratic terms). We chose the quadratic polynomial after examining the functional form of unconditional associations using fractional polynomials—extensions of conventional polynomials that fit the optimal functional form to the data (Royston, Ambler, & Sauerbrei, ; Sauerbrei & Royston, ). These unconditional fractional polynomial estimates of relations between family and neighborhood income and the outcomes consistently took either linear or quadratic form.…”

Section: Methodsmentioning

confidence: 99%

Is Affluence a Risk for Adolescents in Norway?

Lund

Dearing

Zachrisson

2017

J of Research on Adolesc

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Studies suggest that affluence poses a risk for adolescents, but this has rarely been studied outside the United States. We examined the unique and additive roles of family and school affluence for adolescent outcomes among 10th-grade students (n = 7,203) in Oslo, Norway. Multilevel models were estimated separately by gender. For both boys and girls, school affluence was a risk for alcohol abuse and family affluence was a risk for conduct problems, although for conduct the risk was only at the very highest end of income distribution and adolescents in very poor families were also at risk. There was also a complex pattern of risk for early sexual debut; family affluence posed risk, but school affluence appeared protective.

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Section: Methodsmentioning

confidence: 99%

Is Affluence a Risk for Adolescents in Norway?

Lund

Dearing

Zachrisson

2017

J of Research on Adolesc

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“…By introducing power transformations of the predictor variables, this method can successfully model complex and nonlinear relationships and provide estimates that closely reflect the underlying data. (for more details, see Royston and Sauerbrei 2008; Sauerbrei and Royston 2016).…”

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confidence: 99%

Using Location Data From Mobile Phones to Study Participation in Mass Protests

Rotman

Shalev

2020

Sociological Methods & Research

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Automatically collected behavioral data on the location of users of mobile phones offer an unprecedented opportunity to measure mobilization in mass protests, while simultaneously expanding the range of researchable questions. Location data not only improve estimation of the number and composition of participants in large demonstrations. Thanks to high spatial and temporal resolution they also reveal when, where, and with whom different sociopolitical sectors join a protest campaign. This article compares the features and advantages of this type of data with other methods of measuring who participates in street protests. The steps in preparing a usable data set are explained with reference to a six-week campaign of mass mobilization in Israel in 2011. Findings based on the Israeli data set illustrate a wide range of potential applications, pertaining to both the determinants and consequences of protest participation. Limitations of mobile location data and the privacy issues it raises are also discussed.

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Multivariable fractional polynomial interaction to investigate continuous effect modifiers in a meta-analysis on higher versus lower PEEP for patients with ARDS

et al. 2016

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ObjectivesA recent individual patient data (IPD) meta-analysis suggested that patients with moderate or severe acute respiratory distress syndrome (ARDS) benefit from higher positive end-expiratory pressure (PEEP) ventilation strategies. However, thresholds for continuous variables (eg, hypoxaemia) are often arbitrary and linearity assumptions in regression approaches may not hold; the multivariable fractional polynomial interaction (MFPI) approach can address both problems. The objective of this study was to apply the MFPI approach to investigate interactions between four continuous patient baseline variables and higher versus lower PEEP on clinical outcomes.SettingPooled data from three randomised trials in intensive care identified by a systematic review.Participants2299 patients with acute lung injury requiring mechanical ventilation.InterventionsHigher (N=1136) versus lower PEEP (N=1163) ventilation strategy.Outcome measuresPrespecified outcomes included mortality, time to death and time-to-unassisted breathing. We examined the following continuous baseline characteristics as potential effect modifiers using MFPI: PaO2/FiO2 (arterial partial oxygen pressure/ fraction of inspired oxygen), oxygenation index, respiratory system compliance (tidal volume/(inspiratory plateau pressure−PEEP)) and body mass index (BMI).ResultsWe found that for patients with PaO2/FiO2 below 150 mm Hg, but above 100 mm Hg or an oxygenation index above 12 (moderate ARDS), higher PEEP reduces hospital mortality, but the beneficial effect appears to level off for patients with very severe ARDS. Patients with mild ARDS (PaO2/FiO2 above 200 mm Hg or an oxygenation index below 10) do not seem to benefit from higher PEEP and might even be harmed. For patients with a respiratory system compliance above 40 mL/cm H2O or patients with a BMI above 35 kg/m2, we found a trend towards reduced mortality with higher PEEP, but there is very weak statistical confidence in these findings.ConclusionsMFPI analyses suggest a nonlinear effect modification of higher PEEP ventilation by PaO2/FiO2 and oxygenation index with reduced mortality for some patients suffering from moderate ARDS.Study registration numberCRD42012003129.

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Multivariable Fractional Polynomial Models

Cited by 3 publications

References 29 publications

Is Affluence a Risk for Adolescents in Norway?

Is Affluence a Risk for Adolescents in Norway?

Using Location Data From Mobile Phones to Study Participation in Mass Protests

Multivariable fractional polynomial interaction to investigate continuous effect modifiers in a meta-analysis on higher versus lower PEEP for patients with ARDS

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