Power calculators for studies with designed missingness

缺失数据（Missingness）是任何数据驱动研究中的常见问题。当由于与研究相关或不相关的原因而导致待测量的单元格缺失时，数据集中会出现缺失。在任何数据驱动的研究中，缺失的数据都构成了一个真实的问题，因为它阻碍了进行研究的能力，最重要的是，当缺失的数据没有得到适当的处理时，它会严重地影响结果。对于样本量，重点始终是收集（完整的）“大”样本量，以检测具有研究意义的信号。然而，信号的检测（如果这样的信号存在于群体中）在某个样本大小处达到饱和点，超过该饱和点，任何更多的数据收集都是不必要的，并且是对资源的低效使用。此外，这些较大的样本量（超过所需）是以（例如）受试者参与负担、数据收集负担、数据存储等为代价的，这可能导致进一步（计划外）缺失数据。因此，研究设计可以减轻开展研究的负担，并提供足够/适当的样本量，从而节省和有效利用资源。本提案旨在确定研究设计的最佳样本量，其中数据单元格因设计而缺失（即在数据收集之前，数据中的随机单元格设计为缺失）。这种设计的好处有两个：（1）设计缺失的调查减少了完成调查和数据收集所需的时间;（2）设计未测量的单元可以节省资金，然后可以用于研究的其他方面或扩展研究范围。这种设计的第一个挑战是由于缺失单元而导致的信息丢失，从而影响统计推断。第二个挑战是确定样本量，以便在数据存在缺失的情况下，统计推断仍然可靠。有了这个建议，我将通过使用多重插补（MI）背景下的序贯分析（SA）方法来解决上述挑战。MI将有助于“恢复”由于设计缺失而丢失的信息，SA将有助于确定恢复所需的足够数量的插补（以及随后的样本量）。对于本建议中讨论的优化方面，没有现有的文献（在MI或SA），提出了这样一个新的和自然的应用方法，从SA在MI。例如，对于插补数量，MI的现有文献涉及基于模拟研究的结果。我提出的想法将提供一个插补大小（和样本大小）计算器，（与传统的截止值不同）保证良好的统计特性（通过SA的定理）。这项研究的结果将使加拿大和国际研究人员从任何学科受益，提供研究设计计算器，节省时间和金钱，而不影响统计推断。

Missing data (missingness) is a common issue in any data driven research. Missingness occurs in data sets when cells to be measured are missing due to reasons either related or unrelated to the study. In any data driven research, missing data poses a real problem since it hinders the ability to conduct research, and mostly importantly can severely bias the results when missing data are not handled appropriately. With sample size, the focus is always on collecting (complete) “large” sample sizes for the purpose of detecting signals that are of research interest. However, the detection of a signal (if such a signal exist in the population) reaches a saturation point at some sample size, beyond which any more data collection is unnecessary and is an inefficient use of resources. Additionally, these larger (than needed) sample sizes come at the cost of (for example) subject participation burden, data collection burden, data storage, etc, which can result in further (unplanned) missing data. So, a study design that lessens the burden of conducting the study with sufficient/adequate sample size will result in savings and efficient use of resources. This proposal aims at determining the optimum sample size for study designs where data cells are missing by design (i.e. prior to data collection, random cells in data are designed to be missing). The benefit of such a design is two folds: (1) surveys with designed missingness lessen the time needed to complete it, and data collection, (2) the cells not measured by design result in monetary savings, which can then be used in other aspects of the research or extend the study scope.The first challenge with such designs is the loss of information due to missing cells and consequently affecting statistical inference. The second challenge is determination of sample size such that statistical inference remains reliable given that the data has missingness. With this proposal, I will address these aforementioned challenges by using methods of Sequential Analysis (SA) in the context of Multiple Imputation (MI). MI will helps in “recovering” the information lost due to designed missingness, and SA will help determine to the adequate number of imputations (and later sample size) needed for the recovery. For the aspects of optimization discussed in this proposal, there is no existing literature (in MI or SA) that has proposed such a novel and natural application of methods from SA in MI. For example for number of imputations, existing literature in MI involves results based on simulation studies. My proposed ideas will provide an imputation size (and sample size) calculator that (unlike traditional cutoffs) guarantee good statistical properties (via theorems from SA). The findings from this research will benefit Canadian and international researchers from any discipline by providing study design calculators that save time and money without compromising statistical inference.