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while (my $row = $sth->fetchrow_hashref) {
      $$patients{$row->{'pat_id'}} ||= {
...
      }
      $x++;
}

my %sorted =
sort { $patients->{$a}{old_file} cmp $patients->{$b}{old_file} }
   (keys %{$patients});
my $patients = \%sorted;
# or put { } around the sort expression to do it one line.

sort { $$patients{$a}->{old_file} cmp $$patients{$b}->{old_file} }