Applied
researchers, our noses deep in the data sources we rely on, are keenly aware of
errors and inconsistencies we encounter.
Though aware of the potential problems (e.g., attenuation bias) that can
result from measurement error, we often plow on with conventional estimation
strategies, explicitly or implicitly making convenient assumptions about the nature
of the measurement error and hoping for the best. The staffing allocation methods we study
represent a different degree of measurement error because the available
staffing data (outside of California OSHPD data) are at the hospital level and
ad hoc rules are used to allocate staff to the inpatient setting. In this paper, we use data from California where in-patient acute care staffing is
recorded directly and estimate the measurement error from applying various
staffing allocation methods. We find
that the measurement error in allocated staffing levels is large enough to
induce significant bias. For example, in
our benchmark simple regression model the adjusted patient days
method has measurement error large enough to cause the expected coefficient
estimate for the effect of nurse staffing on quality of care to be 30-32% too
small (and this attenuation bias becomes worse in a multiple regression
model). Fortunately, there are easy to
implement alternate estimation methods that can be applied to overcome this
bias. Instrumental variable estimation
may be applied, using the revenue proportion staffing measure as an instrument
for staffing measured by adjusted patient days or administrative hours (but
some caution is warranted in using administrative hours as an instrument for
adjusted patient days or vice-versa).
Alternatively, the California OSHDP data may be treated as validation
data to obtain predicted staffing levels which may be used as the measure of staffing
without the resulting estimates suffering from attenuation bias.