Martinez Josue G, Carroll Raymond J, Muller Samuel, Sampson Joshua N, Chatterjee Nilanjan
Texas A&M University, TX, USA.
Int J Biostat. 2010 Mar 29;6(1):Article 12. doi: 10.2202/1557-4679.1231.
We consider the problem of score testing for certain low dimensional parameters of interest in a model that could include finite but high dimensional secondary covariates and associated nuisance parameters. We investigate the possibility of the potential gain in power by reducing the dimensionality of the secondary variables via oracle estimators such as the Adaptive Lasso. As an application, we use a recently developed framework for score tests of association of a disease outcome with an exposure of interest in the presence of a possible interaction of the exposure with other co-factors of the model. We derive the local power of such tests and show that if the primary and secondary predictors are independent, then having an oracle estimator does not improve the local power of the score test. Conversely, if they are dependent, there is the potential for power gain. Simulations are used to validate the theoretical results and explore the extent of correlation needed between the primary and secondary covariates to observe an improvement of the power of the test by using the oracle estimator. Our conclusions are likely to hold more generally beyond the model of interactions considered here.
我们考虑在一个模型中对某些低维感兴趣参数进行得分检验的问题，该模型可能包含有限但高维的次要协变量及相关的干扰参数。我们研究通过诸如自适应套索等神谕估计器降低次要变量维度从而潜在提高检验功效的可能性。作为一个应用，我们使用最近开发的一个框架，用于在存在暴露与模型其他共同因素可能相互作用的情况下，对疾病结局与感兴趣暴露之间的关联进行得分检验。我们推导了此类检验的局部功效，并表明如果主要预测变量和次要预测变量是独立的，那么拥有一个神谕估计器并不会提高得分检验的局部功效。相反，如果它们是相关的，则存在提高功效的潜力。通过模拟来验证理论结果，并探索主要和次要协变量之间需要多大程度的相关性，才能通过使用神谕估计器观察到检验功效的提高。我们的结论可能比这里所考虑的相互作用模型更具普遍性。
