I love how at least one person on these threads always predicts a horrible accident happening to the parent - because it would obviously be better for a 7 year old to witness their parent being run over/ die with them in a car crash than to be safe at home in bed 
I'd say people focus on the wrong things.
What matters is:
Is the child nauseous or have they been vomiting - if so don't leave her alone.
Is the child feverish - if so don't leave her alone (my eldest is secondary age and more than capable of being home alone but she gets paranoid and tearful and a bit panicky with a fever, so definitely wouldn't leave her if feverish and not at the right interval between meds to know the fever isn't on the way back up).
Has the child been left home alone before a few times - personally I wouldn't be very happy leaving a child for the first time while ill, which is a pretty good reason to do some practice runs before its actually necessary.
Are there other people the child can phone if she can't reach you? If you do get struck by lightening do you have several separate adults - dad, grandparents, good long term friends, trusted neighbours... nearby who can get to her within a relatively short time and would be willing to do so? (Several because one or more might not be available)
Is she able to easily phone her other contact people - numbers saved in phone and very easily able to use the speeddial to call the right person?
Do you do fire drills and know that she would automatically get out of the house if the alarm went off, and is she well enough to do so?
Is she absolutely familiar with your rules on opening the door and answering the phone and what she may and may not do while you are out, and do you trust her as far as any human trusts another to stick to those rules?
What people school would think is so utterly irrelevant unless you really think you will have your children taken away for making a rational decision to leave a 7 year old in their own warm, safe, cosy house instead of dragging them on a half hour walk in the cold, when they are off colour.
I've left my older kids from age 6 for that length of time, but we live in Germany where I am more than happy for school and their younger sibling's Kindergarten to know that is what I've done, and indeed do end conversations with staff by saying I have to go because DC2 aged 8, who they know well, is home alone, and not an eyebrow has ever been raised.