When people are organising a party they’re more than likely catering for a specific number of people so it’s not fair to just not turn up or to feign illness at the last moment. I would send a nice reply thanking them for the invitation and saying unfortunately I won’t be able to join you.
Illness is best, it can’t be disputed.
If you claim you had a prior engagement it’s easy for that to be pored over i.e. someone asking where it was or ‘I saw such and such the other day and she said you were not at that other event’ etc.
It’s mostly a female thing, men don’t quiz each other about such stuff.
I'd send a card, thank them for the invite but say you'd rather not attend. Who knows, you may be doing them a favour, maybe they were thinking, oh, sure we'll have to invite maydup and groan so, your 'I'd rather skip this invite, thank you', would be a welcome relief for them. I wouldn't create an excuse or illness though. The event will happen whether you attend or not