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Table 1 Types of measurement error

From: Systematic review of statistical approaches to quantify, or correct for, measurement error in a continuous exposure in nutritional epidemiology

Within-person random error: This is the variation that is observed in exposure using a specific instrument when it is repeatedly measured in the same individual. A nutritional example would be the day-to-day variation in dietary intake reported using multiple 24-h recalls for an individual (assuming that it is possible to capture a single day’s dietary intake perfectly). The day-to-day variation may be random and thus results in an estimate of usual intake that is unbiased meaning that a person’s true usual intake is estimated accurately on average with several repeat measurements, although with some error.
Between-person random error: When error is random between individuals it results in an unbiased estimate of the mean usual exposure for the population of interest. Even with random measurement error within a person, it is possible to calculate an unbiased estimate for the population, by balancing out overestimation of some individuals with underestimation for others. With between-person random error the mean is estimated without bias, but the variance is inflated. In nutritional research this can be the result of using a single or a few repeat measurements of dietary intake per individual in the presence of within-person random error.
Within-person systematic error: Systematic errors are biases in the measurement of an exposure that consistently depart from the “true exposure” value in the same direction. Within-person systematic errors are systematic errors that are specific to an individual that are manifested as a positive or negative difference between an individual’s reported exposure. For example, some individuals may occasionally use dietary supplements which may lead to “systematic additive error,” indicating that a constant error is added to each person’s reported dietary intake. This could lead to over- or underestimation for all participants by the same amount. This directional difference (or intake-related bias) is usually constant within an individual and would remain regardless of how many repeat measurements are taken. Within-person systematic error may be related to individual characteristics, such as social/cultural desirability, that affects how a particular individual reports dietary intakes.
Between-person systematic error: Systematic errors in exposures can be additive or multiplicative. Additive between-person systematic error can occur when the dietary instrument of interest causes every measurement to be too large or too small by a constant amount from the truth. For example if the additive systematic error was negative each participants reported intake would be lower than their true intake using the dietary instrument of interest. Multiplicative between-person systematic error can occur when instead of reporting their true intake all participants report a fixed multiple of their true intake. This can be thought of as an intake-related bias where there is a systematic deviation from the truth due to a correlation between errors in the dietary instrument of interest and true intake. The attenuation (or flattened slope phenomenon) happens when both additive and multiplicative (intake-related bias) are present, which is typical in nutritional epidemiology. Person-specific bias is another type of between-person systematic error that may occur, if for example, a person that takes a dietary supplement every day – their average intake will be different from the predicted group-level flattened slope.