Preprocessing histograms of age at menopause using the fast Fourier transform

Abstract

Objective: In epidemiological and biological studies, the interpretation of frequency distributions (histograms) of the age at menopause (AAM) is hampered by the presence of background noise such as the last-digit-preference (LDP) of each woman. The objective of this study was to develop a standard method of preprocessing the AAM histogram such that noise can be effectively eliminated, thereby enabling a more thorough investigation of the underlying properties of the distribution. Methods: The Fast Fourier transform (FFT) is a technique which eliminates individual sources of noise based on their characteristic frequencies. Its effectiveness in eliminating noise from AAM data was explored using both simulated and published data, especially in regard to the elimination of cyclical LDP errors. Results: By preprocessing the histogram ‘signal’ using a low-pass filter of 0.15 cycles per year (cpy), common LDP noise is eliminated. Furthermore, this preprocessing also eliminates other forms of high-frequency noise, revealing a true AAM ‘signal’ which comprises three separate low-frequency components. The two major peaks correspond in the time domain to Gaussian functions with means at ∼51 and ∼43 years and peak-widths of ∼6 years; a smaller peak also exists at ∼35 years. Conclusions: The FFT is an effective tool in preprocessing AAM frequency distributions to reveal their underlying shape, which appears similar across several previously published studies and is characterized by three distinct peaks. These currently have no definitive interpretation, but call into question the analysis of epidemiological risk factors for AAM using statistical techniques which assume a single distribution.