The phrase "a relatively minor cause" is correct and usable in written English.
It can be used when discussing factors or reasons that are not significant in the context of a larger issue or situation.
Example: "While there were several factors contributing to the problem, a relatively minor cause was the lack of communication between departments."
Alternatives: "a somewhat insignificant factor" or "a comparatively small reason".
We wuz robbed, say investors and employees of the Enrons -- but outright crookedness, highly publicized, is a relatively minor cause of the current furor.
There is, however, widespread agreement that drink inflation is a relatively minor cause of Ireland's spiral of rising prices, which at 5.2percentt is triple the average of other European Union members.
Even though currency issues are a relatively minor cause of global imbalances, they do make a serious problem worse.
The rapid decline in smallpox burials after 1800 coincided with the widespread adoption of Jenner's cowpox vaccination method, and despite incomplete coverage and low levels of re-vaccination, vaccination programmes succeeded in reducing smallpox to a relatively minor cause of death by the beginning of civil registration in 1837.
Manufacturing employment has dwindled (with NAFTA as one relatively minor cause among many); jobs in other industries have more than made up the losses.
Environmental factors (e.g. alcohol, retinoic acid) are relatively minor causes of birth defects [0.12 cases per 1000 births (Dolk et al., 2010)] and genetic factors are likely to be quantitatively more significant.
Superoxide anion poses a relatively minor threat for causing direct damage to DNA [55].
A decade ago, a relatively minor investment could yield huge competitive advantage.
Collectively these data indicated that RSV infection caused a relatively minor change in the global host-gene expression profile by 24 hpi.
Isoproterenol causes a relatively minor change in intermolecular FRET, with the only significant change occurring in the TM6/H8 FRET pair, but no change in FRET saturation.
Meanwhile, the bitcoin price has taken a tumble in the last few hours, with fears around the health of a relatively minor cryptocurrency exchange likely to be the cause of the sell-off.
