Advanced Methods Library

• Clinical Trial Simulations — The link describes Novel Methods for 21^st Century Clinical trials
• DAGitty — This is a browser-based environment for creating, editing, and analyzing causal models (also known as directed acyclic graphs or causal Bayesian networks). The focus is on the use of causal diagrams for minimizing bias in empirical studies in epidemiology and other disciplines
• Deep Learning & Big Data Platform with R — A very nice workshop with introduction to Deep Learning, hands on examples, and big data platform with Spark through R sparklyr package. 
• Mixed Effect Model — Also known as multilevel hierarchical or random coefficient model. Mixed effect model is used for analyzing outcome data that are correlated.
• Multiple Imputation for Missing Data — A method that hands missing data in multivariate analysis using sequential. The application of multiple imputation will assure that statistical inferences are approximately unbiased so long as the mechanism of missingness follows a missing at random [MAR] structure.

Joint Modeling

This framework that takes into account the dependency and association between outcome variables with different data types. It has been demonstrated that use of joint modeling framework will lead to correction of biases in estimation and the potential for enhanced efficiency by borrowing statistical strength across multiple outcomes.

• Joint modeling: survival observations and longitudinal observations
• Joint modeling: survival observations and count data

Regularization Methods (ex. LASSO, Ridge, Elastic Net)

Regularization methods, particularly Least Absolute Shrinkage and Selection Operator (LASSO) and elastic net, are commonly used in the situation where the number of predictors exceeds the number of observations. LASSO uses an L1-norm penalty to shrink coefficients toward zero, performing model selection; ridge regression uses an L2-norm penalty, which performs some shrinkage but all coefficients are maintained in the model; and elastic net implements a mixture of the two penalties. Lasso enables model selection in high dimensional data sets, selecting a minimal set of uncorrelated predictors. Ridge regression may be useful if there is collinearity among the predictors, and it is desirable to retain all predictors in the model. Elastic net is useful if one wishes to strike a balance between lasso and ridge, performing some model selection but also allowing correlation among predictors. The primary package used in R is glmnet, and here is a link to the glmnet vignette: https://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html.

Here is a link to another tutorial on regularization methods in R: https://www.datacamp.com/community/tutorials/tutorial-ridge-lasso-elastic-net

One down side to glmnet’s implementation is that levels of categorical variables, for example the variable “colors” (with levels: red, orange, yellow, green, blue) are coded as separate dummy variables, and the selection process may keep some of the levels and exclude others. In general, we would like the selection process to exclude or keep all levels of the colors variable.  An alternative approach that enables grouping of levels of categorical variables is to use group lasso, which has now been implemented in several R packages: gglasso, grplasso, and grpreg.

Lasso/elastic net/group lasso are typically used for prediction modeling, not for explanatory modeling.  R packages implementing regularization typically do not provide inference that investigators are looking for in the case of explanatory modeling (95% confidence intervals and p-values). The reason provided by the authors of the penalized package is that the coefficients are strongly biased – the penalization method reduces the variance of the coefficients by introducing bias. While bootstrapping could provide estimates of the variance of the coefficients, it does not provide a reliable estimate of the bias.  That said, the authors of the glmnet package have created a package called SelectiveInference that provides confidence intervals and p-values for both lasso and step-wise regression methods, where the confidence intervals “properly account for the inherent selection carried out by the procedure”.