  We develop and apply a novel method of analysis to study the X-ray spectral
properties of 908 QSOs in the Large Bright Quasar Survey (LBQS) that were
observed during the soft X-ray ROSAT All-Sky Survey (RASS). Due to the
relatively short (<600sec) RASS exposure times, only 10% of the QSOs are
detected in X-rays, so X-ray spectral model fits for individual QSOs are
precluded by poor photon statistics. Spectral stacking provides effectively
much more sensitive X-ray observations for an average QSO in bins of redshift,
and for several classes of QSOs. We model the stacked X-ray spectra in a way
that obviates both the distinction between detections and non-detections, and
the need to stack together only those objects observed through similar Galactic
column densities N_H. In application to the LBQS/RASS sample, we marginally
confirm a flattening of the X-ray spectral index of QSOs toward higher
redshifts. Radio-loud QSOs show flatter X-ray photon indices, in agreement with
previous work. We show that the apparent flattening of the photon index with
redshift is not due to an increasing fractional contribution from the
radio-loud class of QSOs.
