Power calculators for studies with designed missingness

数据缺失(Missing)是任何数据驱动型研究中的常见问题。当要测量的单元格由于与研究相关或无关的原因而丢失时，数据集中就会发生丢失。在任何数据驱动的研究中，丢失数据都是一个真正的问题，因为它阻碍了进行研究的能力，最重要的是，当丢失数据得不到适当处理时，可能会严重偏离结果。对于样本量，重点总是收集(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总体中)在某个样本大小处达到饱和点，超过该饱和点就没有必要进行更多的数据收集，并且是对资源的低效使用。此外，这些较大的(超出所需的)样本量是以(例如)受试者参与负担、数据收集负担、数据存储等为代价的，这可能导致进一步的(计划外的)数据丢失。因此，以足够的样本量/足够的样本量减轻进行研究的负担的研究设计将导致节省和有效地使用资源。该建议旨在确定研究设计的最佳样本量，其中数据单元因设计而丢失(即，在数据收集之前，数据中的随机单元被设计为丢失)。这种设计的好处有两个方面：(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)未按设计衡量的单元格节省了金钱，然后可以用于研究的其他方面或扩大研究范围。*这种设计的第一个挑战是由于丢失单元格而造成的信息损失，从而影响统计推断。第二个挑战是确定样本大小，以便在数据有缺失的情况下，统计推断仍然可靠。在这项提议中，我将在多重归因(MI)的背景下使用序贯分析(SA)的方法来解决上述挑战。MI将帮助“恢复”由于设计缺失而丢失的信息，SA将帮助确定恢复所需的足够数量的推算(以及后来的样本量)。对于本提案中讨论的优化方面，还没有现有的文献(在MI或SA中)提出从SA到MI的方法的如此新颖和自然的应用。例如，对于归因数，现有的MI文献涉及基于模拟研究的结果。我提出的想法将提供一个补偿大小(和样本大小)计算器，它(不同于传统的截止)保证良好的统计特性(通过SA的定理)。这项研究的发现将通过提供研究设计计算器，在不影响统计推断的情况下节省时间和金钱，从而使任何学科的加拿大和国际研究人员受益。

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.**