Median (interquartile range) of percentage of characteristics of adult respondents and their households in 53 countries.

Median (interquartile range) of percentage of adult respondents with need for and access to care in 53 countries.

Comparison of the discriminatory power resulting from the gradient boosting approach when applying different values of the smoothing parameter . Numbers refer to to the median value and interquartile range (in parentheses) of the final on 100 simulation runs. The amount of pre-selected genes is denoted as , is the size of the training samples and cens. refers to the censoring rate. We recommend to use the value , which is also the default value of the new Cindex family for the R add-on package mboost.

An ideal performance evaluation metric would be predictive, objective, easy to administer, estimate the variance in performance, and provide a confidence interval for the level of uncertainty. Time series forecasting may provide objective metrics for predictive performance in mental arithmetic. Addition and summation (addition combined with subtraction) using the Japanese Soroban computation system was undertaken over 60 days. The median calculation time in seconds for adding 10 sequential six digit numbers [CTAdd) was 63 s (interquartile range (IQR) = 12, range 48–127 s], while that for summation (CTSum) was 70 s (IQR = 14, range 53–108 s), and the difference between these times was statistically significant p < 0.0001. Using the mean absolute percentage error (MAPE) to measure forecast accuracy, the autoregressive integrated moving average (ARIMA) model predicted a further reduction in both CTAdd to a mean of 51.51 ± 13.21 s (AIC = 5403.13) with an error of 6.32%, and CTSum to a mean of 54.57 ± 15.37 s (AIC = 3852.61) with an error of 8.02% over an additional 100 forecasted trials. When the testing was repeated, the actual mean performance differed by 1.35 and 4.41 s for each of the tasks, respectively, from the ARIMA point forecast value. There was no difference between the ARIMA model and actual performance values (p-value CTAdd = 1.0, CTSum=0.054). This is in contrast to both Wright's model and linear regression (p-value < 0.0001). By accounting for both variability in performance over time and task difficulty, forecasting mental arithmetic performance may be possible using an ARIMA model, with an accuracy exceeding that of both Wright's model and univariate linear regression.

Comparison of the discriminatory power resulting from boosting the -index and competing approaches. Numbers refer to the median value and interquartile range (in parentheses) of the final on 100 simulation runs. The true-index refers to the discriminatory power resulting from the true combination of predictors with known coefficients. The amount of pre-selected genes is denoted as , is the size of the training samples and cens. refers to the censoring rate.

*The time taken from deciding to leave home and arriving at the facility.†other modes of transport includes walking and borrowing a vehicle.