Power calculators for studies with designed missingness

在任何数据驱动的研究中，数据缺失是一个常见的问题。当要测量的细胞由于与研究相关或无关的原因而缺失时，数据集中就会出现缺失。在任何数据驱动的研究中，缺失的数据构成了一个真正的问题，因为它阻碍了进行研究的能力，最重要的是，当缺失的数据没有得到适当处理时，可能会严重影响结果。在样本量方面，重点始终是收集（完整的）“大”样本量，以检测有研究兴趣的信号。然而，信号的检测（如果在总体中存在这样的信号）在某个样本量上达到饱和点，超过这个饱和点就没有必要再收集任何数据，并且是对资源的低效利用。此外，这些更大的（比需要的）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，一个研究设计，减轻负担进行足够/足够的样本量的研究将导致节省和有效利用资源。本提案旨在确定设计中缺少数据单元的研究设计的最佳样本量（即，在数据收集之前，数据中的随机单元被设计为缺失）。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)设计未测量的单元节省了资金，然后可以将其用于研究的其他方面或扩大研究范围。

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.