Modelling menstrual cycle length in athletes using state-space models

The ability to predict an individual’s menstrual cycle length to a high degree of precision could help female athletes to track their period and tailor their training and nutrition correspondingly. Such individualisation is possible and necessary, given the known inter-individual variation in cycle length. To achieve this, a hybrid predictive model was built using data on 16,524 cycles collected from a sample of 2125 women (mean age 34.38 years, range 18.00–47.10, number of menstrual cycles ranging from 4 to 53). A mixed-effect state-space model was fitted to capture the within-subject temporal correlation, incorporating a Bayesian approach for process forecasting to predict the duration (in days) of the next menstrual cycle. The modelling procedure was split into three steps (1) a time trend component using a random walk with an overdispersion parameter, (2) an autocorrelation component using an autoregressive moving-average model, and (3) a linear predictor to account for covariates (e.g. injury, stomach cramps, training intensity). The inclusion of an overdispersion parameter suggested that $$26.36\%$$ 26.36 % $$[23.68\%,29.17\%]$$ [ 23.68 % , 29.17 % ] of cycles in the sample were overdispersed. The random walk standard deviation for a non-overdispersed cycle is $$27.41 \pm 1.05$$ 27.41 ± 1.05 [1.00, 1.09] days while under an overdispersed cycle, the menstrual cycle variance increase in 4.78 [4.57, 5.00] days. To assess the performance and prediction accuracy of the model, each woman’s last observation was used as test data. The root mean square error (RMSE), concordance correlation coefficient and Pearson correlation coefficient (r) between the observed and predicted values were calculated. The model had an RMSE of 1.6412 days, a precision of 0.7361 and overall accuracy of 0.9871. In conclusion, the hybrid model presented here is a helpful approach for predicting menstrual cycle length, which in turn can be used to support female athlete wellness.