my $sql = {
     SELECT count(*)
     FROM patient_data
     WHERE name = ?
  };
  my $sth = $dbh->prepare($sql);
  $sth->execute($name);
  my ($count_rows) = $sth->fetchrow_array();
[download]

Note that this is not complete without a finish() call:

$sth->finish();
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You need to use finish if you don't repeat calling fetchrow_*, or equivalent, until it returns undef. So you need it in your second example, too.

If you omit it, you'll get a warning from DBI, or you should. (Maybe this depends on the database driver?)