Comparing and combining data across multiple sources via integration of paired‐sample data to correct for measurement error

In biomedical research such as the development of vaccines for infectious diseases or cancer, study outcomes measured by an assay or device are often collected from multiple sources or laboratories. Measurement error that may vary between laboratories needs to be adjusted for when combining samples across data sources. We incorporate such adjustment in the main study by comparing and combining independent samples from different laboratories via integration of external data, collected on paired samples from the same two laboratories. We propose the following: (i) normalization of individual-level data from two laboratories to the same scale via the expectation of true measurements conditioning on the observed; (ii) comparison of mean assay values between two independent samples in the main study accounting for inter-source measurement error; and (iii) sample size calculations of the paired-sample study so that hypothesis testing error rates are appropriately controlled in the main study comparison. Because the goal is not to estimate the true underlying measurements but to combine data on the same scale, our proposed methods do not require that the true values for the error-prone measurements are known in the external data. Simulation results under a variety of scenarios demonstrate satisfactory finite sample performance of our proposed methods when measurement errors vary. We illustrate our methods using real enzyme-linked immunosorbent spot assay data generated by two HIV vaccine laboratories.