Just use output buffering to put the output into the internal buffer and then capture it.
<?php
ob_start();
?>
<table id=patients>
<tr>
<th>Pt. username</th>
<th>Pt. number</th>
<th>Full Name</th>
<th>Added on</th>
</tr>
<?php $x=1;
foreach ($users as $patient) {
?> <tr <?php if ($x % 2 == 0) {echo "class='alt'"; } ?>>
<td> <a href="profile.php?username=<?php echo $patient['username'];?>"><?php echo $patient['username'];?></a></td>
<td> <?php echo $patient['id'];?></td>
<td> <?php echo $patient['name'];?></td>
<td> <?php echo $patient['joined'];?></td>
</tr>
<?php
$x++;
} ?>
</table>
<?php
$table = ob_get_clean();
?>