Optimizing Fractional Polynomials by Using Variable Powers
Author(s)
Verhoek A1, Ouwens M2, Heeg B3
1Cytel, Rotterdam, Netherlands, 2AstraZeneca, Mölndal, O, Sweden, 3Cytel, Rotterdam, ZH, Netherlands
Presentation Documents
OBJECTIVES: Fractional Polynomials (FP) were introduced in 1994 by Royston and Altman, when computing time was limited. Therefore, limiting the powers to a fixed set of numbers that covers the desired range, p ∈ (-2;-1;-0:5; 0; 0:5; 1; 2; 3), was a natural choice. However, that restriction is lifted given the development in computational power. Therefore, we investigate whether making the powers into variables has benefits in both terms of fit and computational speed that outweigh the penalty for these additional variables.
METHODS: Using the network meta-analysis definition by Jansen (2011), there are 8 first-order FPs, 28 second-order FPs and 8 repeated-power FPs, totaling 44 FPs to run. This is reduced to four FPs when using powers as variable; a first-order, second-order, repeated-power and logarithmic FP, where the latter is normally used for p = 0. We use a network of 4 studies and 4 treatments in multiple myeloma to compare the effect of fixed versus variable powers on visual- and statistical fit (LOOIC), and computational time (CT). CT is calculated by summing the individual run times for the fixed and variable powers, respectively.
RESULTS: The results of all 48 models were first reviewed by visual and statistical fit. This resulted in 8 models with minimal differences in visual fit. Based upon statistical fit, the two best performing model were both second-order FPs, one with variable and one with flexible powers. The individual CT for a variable power model was only slightly longer than a fixed power model (28min versus 24min). When comparing the total CT for fixed powers and variable powers, we find 17.2hr versus 1.9hr, a reduction of 89.1%.
CONCLUSIONS: We demonstrated that the use of variable powers in FP leads to similar fitting model, while simultaneously yielding a huge reduction in computational time.
Conference/Value in Health Info
Value in Health, Volume 25, Issue 12S (December 2022)
Code
MSR134
Topic
Methodological & Statistical Research
Disease
No Additional Disease & Conditions/Specialized Treatment Areas