Declining PhD Interview

Dear XYZ,

thank you for considering me for this position. Unfortunately, for personal reasons I am no longer considering this option. Hence, I have to decline this invitation.

With best regards, clearseplex

In other words, like you would politely say no to any other opportunity - polite, short, and without going into details why exactly you changed your mind.

I thought I might give an alternate opinion here: is declining the interview in your best interests?

I am not an academic but I have recently been in the position of having multiple interviews / opportunities where I preferred some over others. What I didn't do was decline to speak with someone, knowing that the interview itself might actually convince me to join the company.

There are many benefits to speaking with them:

1. The way a person / company interviews a candidate should be part of your decision making process, perhaps there are parameters you are unaware of that might sway your decision.
2. You can get valuable experience in the exact setting you would be hoping to to do well in under the same or similar context even.
3. An offer from another university may actually improve your odds at landing the one you want. (stalking horse)

1. I don't think any apology is necessary.
2. Actually, I don't think "unfortunately" as suggested by @xLeitix is necessary. After all, who are you saying it is unfortunate for? You? No, you don't want the interview. Them? That seems presumptuous - you are implying they are unfortunate for missing out on your presence.

My suggestion

Thank you so much for your offer of an interview for blah, blah blah. After thinking about it seriously I have decided that the topic of this PhD is not for me at the present time. For that reason I shall withdraw my application at this point. I appreciate the time you have given me.

EDIT

See comment by @JBentley. I agree and would change "After thinking about it seriously" with "On considering my options" or similar.