Yang Han, Department of Mathematics (University of Manchester)

Confident and Logical Selection of a Biomarker Cut-point for Subgroup Targeting in Personalised Medicine

Confidently selecting a cut-point for a biomarker to target patients is challenging due to two levels of multiplicity: multiplicity arising from testing efficacy in the marker-positive and marker-negative subgroups at each potential cut-point, and the additional multiplicity induced by searching over infinitely many cut-points. Currently available methods do not strongly control the familywise type I error rate (FWER) across both levels of multiplicity. In this talk, I will present a method that achieves such control.

Adopting a confidence band approach, our method further establishes four principles that we believe any method for confident biomarker cut-point selection should strive to follow.  For diseases with continuous outcomes, such as type II diabetes and Alzheimer’s disease, our method provides exact simultaneous confidence intervals for efficacy in the marker-positive and marker-negative subgroups, simultaneously for all possible cut-point values. I will also demonstrate an interactive app implementing the proposed method.

Chen Huang, Department of Economics and Business Economics (Aarhus University)

Arellano-Bond LASSO Estimator for Dynamic Linear Panel Models (Victor Chernozhukov, Iván Fernández-Val, Chen Huang, Weining Wang)

The Arellano-Bond estimator is a fundamental method for dynamic panel data models, widely used in practice. However, the estimator is severely biased when the data's time series dimension T  is long due to the large degree of overidentification. We show that weak dependence along the panel's time series dimension naturally implies approximate sparsity of the most informative moment conditions, motivating the following approach to remove the bias: First, apply LASSO to the cross-section data at each time period to construct most informative (and cross-fitted) instruments, using lagged values of suitable covariates. This step relies on approximate sparsity to select the most informative instruments. Second, apply a linear instrumental variable estimator after first differencing the dynamic structural equation using the constructed instruments. Under weak time series dependence, we show the new estimator is consistent and asymptotically normal under much weaker conditions on  T's growth than the Arellano-Bond estimator. Our theory covers models with high dimensional covariates, including multiple lags of the dependent variable, common in modern applications. We illustrate our approach by applying it to weekly county-level panel data from the United States to study opening K-12 schools and other mitigation policies' short and long-term effects on COVID-19's spread.