Applications of Supervised Machine Learning in Autism Spectrum Disorder Research: a Review <s> Logistic Regression <s> We missed an important reference in Section 3.4. In page 309 we stated that ‘. . . which is based on the recently proposed algorithm LARS of Efron et al. (2004). They proved that, starting from zero, the lasso solution paths grow piecewise linearly in a predictable way. They proposed a new algorithm called LARS to solve the entire lasso solution path efficiently by using the same order of computations as a single OLS fit. . . .’ The following sentence should have been included. The piecewise linearity of the lasso solution path was first proved by Osborne et al. (2000), who also described an efficient algorithm for calculating the complete lasso solution path. Reference Osborne, M. R., Presnell, B. and Turlach, B. A. (2000) A new approach to variable selection in least squares problems. IMA J. Numer. Anal., 20, 389–403. <s> BIB001 </s> Applications of Supervised Machine Learning in Autism Spectrum Disorder Research: a Review <s> Logistic Regression <s> Previous studies are inconsistent regarding whether there are independent effects of maternal and paternal age on the risk of autism. Different biologic mechanisms are suggested by maternal and paternal age effects. The study population included all California singletons born in 1989–2002 (n ¼ 7,550,026). Children with autism (n ¼ 23,311) were identified through the California Department of Developmental Services and compared with the remainder of the study population, with parental ages and covariates obtained from birth certificates. Adjusted odds ratios and 95% confidence intervals were used to evaluate the risk of autism associated with increasing maternal and paternal age. In adjusted models that included age of the other parent and demographic covariates, a 10-year increase in maternal age was associated with a 38% increase in the odds ratio for autism (odds ratio ¼ 1.38, 95% confidence interval: 1.32, 1.44), and a 10-year increase in paternal age was associated with a 22% increase (odds ratio ¼ 1.22, 95% confidence interval: 1.18, 1.26). Maternal and paternal age effects were seen in subgroups defined by race/ethnicity and other covariates and were of greater magnitude among first-born compared with later-born children. Further studies are needed to help clarify the biologic mechanisms involved in the independent association of autism risk with increasing maternal and paternal age. autistic disorder; California; maternal age; paternal age <s> BIB002
Logistic regression is a generalized linear model used for binary classification, taking as input a set of independent variables. The independent variables can be discrete or continuous and are used to predict the probability or odds of the target result taking a particular binary value. To avoid overfitting the regression model, regularization techniques such as LASSO, ridge, and ENet can be deployed. LASSO, also known as L1 regularization, attempts to minimize the sum of the absolute value of the regression coefficients, which leads to automatic feature detection, removing input parameters that may provide little added value to the model. Ridge regression, or L2 regularization, constrains the sum of the squared differences of the regression coefficients, which minimizes an irrelevant feature's effect on the regression model, but unlike LASSO will not actually remove it  . The ENet regression combines the LASSO and ridge penalties BIB001 . Logistic regression model literature shows attempts to improve ASD screening practices, analyze neuroimaging data, and evaluate risk factors for developing ASD. Linear discriminant analysis is similar to logistic regression, as it uses a linear combination of continuous, independent variables to predict a categorical outcome; however, linear discriminant analysis assumes that the independent variables are normally distributed. BIB002 to evaluate the impact of parental age on the risk of developing ASD. The study sample included 7,550,026 individuals born in California between 1989 and 2002. Data from the California Department of Developmental Services were used to identify individuals with ASD (n = 23,311) while the remainder of the sample made up the control group. Using maternal and paternal ages obtained from birth certificates, the authors applied logistic regression to determine risk of developing ASD, with race/ethnicity, parental education level, and year of birth taken into account as covariates. Increased maternal age by 10 years was found to elevate the risk of ASD by 38% compared to 22% for increased paternal age by 10 years. These findings persisted through all subgroups based on covariates, although it was found that these risks greatly increased among first-born children. These findings demonstrate the potential of machine learning to evaluate risk factors for developing ASD in very large populations.