When you receive an invite to an event, whether it is a birthday, wedding, party or shower, it is appropriate to send a response, even if you cannot attend. It is appropriate not only to inform the parties that you will not be attending over the phone, but in writing as well. It also appears more genuine and shows that you are genuinely sorry that you cannot be in attendance and send your regards. Writing an "I cannot attend" letter is not the same as writing any other letter in daily correspondence.
Start your letter by thanking the inviting party for inviting you to the event and letting them know how much you appreciate receiving the invitation.
Inform the reader that you, unfortunately, will not be attending the event. Mention why you cannot attend, if appropriate. When multiple people in your household are invited on one invitation, mention whether anyone else in the household will be able to attend.
Include a gift card or other present if appropriate, such as for a birthday party or shower, to compensate for your absence.
Wish the parties well and tell them you hope they enjoy themselves.
Send your letter through the mail in a timely manner. Do not type the letter or email it, since that is very impersonal and has a tendency to feel forced. Write your letter on stationary, not a piece of ripped-out notebook paper. A letter needs to have a personal touch to it.