An Implementation of Dimensionality Reduction
    via Regression using Kernel Ridge Regression.

Joint dimension reduction and spatial clustering is conducted for
    Single-cell RNA sequencing and spatial transcriptomics data, and more details can be referred to 
    Wei Liu, Xu Liao, Yi Yang, Huazhen Lin, Joe Yeong, Xiang Zhou, Xingjie Shi and Jin Liu. (2022) <doi:10.1093/nar/gkac219>. It is not only computationally efficient and scalable to the sample size increment, but also is capable of choosing the smoothness parameter and the number of clusters as well.

Cluster-randomized trials (CRTs) assign treatment to groups rather than individuals, so valid analyses must distinguish cluster-level and individual-level effects and define estimands within a potential-outcomes framework. This package supports right-censored survival outcomes for both single-state (binary) and multi-state settings. For single-state outcomes, it provides estimands based on stage-specific survival contrasts (SPCE) and restricted mean survival time (RMST). For multi-state outcomes, it provides SPCE as well as a generalized win-based restricted mean time-in-favor estimand (RMT-IF). The package implements doubly robust estimators that accommodate covariate-dependent censoring and remain consistent if either the outcome model or the censoring model is correctly specified. Users can choose marginal Cox or gamma-frailty Cox working models for nuisance estimation, and inference is supported via leave-one-cluster-out jackknife variance and confidence interval estimation. Methods are described in Fang et al. (2025) "Estimands and doubly robust estimation for cluster-randomized trials with survival outcomes" <doi:10.48550/arXiv.2510.08438>.

Targeted minimum loss-based estimators of counterfactual means and
    causal effects that are doubly-robust with respect both to consistency and
    asymptotic normality (Benkeser et al (2017), <doi:10.1093/biomet/asx053>; MJ
    van der Laan (2014), <doi:10.1515/ijb-2012-0038>).