Efficient study design to estimate population means with multiple measurement instruments

Michal Bitan*, Malka Gorfine, Laura Rosen, David M. Steinberg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Outcomes from studies assessing exposure often use multiple measurements. In previous work, using a model first proposed by Buonoccorsi (1991), we showed that combining direct (eg, biomarkers) and indirect (eg, self-report) measurements provides a more accurate picture of true exposure than estimates obtained when using a single type of measurement. In this article, we propose a tool for efficient design of studies that include both direct and indirect measurements of a relevant outcome. Based on data from a pilot or preliminary study, the tool, which is available online as a shiny app at https://michalbitan.shinyapps.io/shinyApp/, can be used to compute: (1) the sample size required for a statistical power analysis, while optimizing the percent of participants who should provide direct measures of exposure (biomarkers) in addition to the indirect (self-report) measures provided by all participants; (2) the ideal number of replicates; and (3) the allocation of resources to intervention and control arms. In addition we show how to examine the sensitivity of results to underlying assumptions. We illustrate our analysis using studies of tobacco smoke exposure and nutrition. In these examples, a near-optimal allocation of the resources can be found even if the assumptions are not precise.

Original languageEnglish
Pages (from-to)4327-4340
Number of pages14
JournalStatistics in Medicine
Issue number19
StatePublished - 30 Aug 2021


  • MLE
  • biomarker
  • intervention
  • measurement error model
  • randomized trials
  • self-report


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