while (my $row = $sth->fetchrow_hashref) {
      $$patients{$row->{'pat_id'}} ||= {
          first_name => "$row->{'first_name'}",
          last_name => "$row->{'last_name'}",
          dme_num => "$row->{'dme_num'}",
          dme_pid => "$row->{'dme_pid'}",
          phone => "$row->{'phone'}",
          pid => "$row->{'pat_id'}"
      };
      my $hash = {
        file_name => "$row->{'file_name'}",
        file_type => "$row->{'file_type'}",
        date_uploaded => "$row->{'date_uploaded'}",
        date_faxed => "$row->{'date_faxed'}"
      };
      push(@{$$patients{$row->{'pat_id'}}->{files}}, $hash);
      if (($row->{'date_uploaded'} < $$patients{$row->{'pat_id'}}->{'old_file'}) or (!$$patients{$row->{'pat_id'}}->{'old_file'}))  {
         $$patients{$row->{'pat_id'}}->{'old_file'} = $row->{'date_uploaded'};
      }
      $x++;
}

##</code><code>##

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.

##</code><code>##

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