PHP class design with methods requiring database access

I've been a procedural PHP programmer for a long time but I'm getting to learn OOP and would like some advice. I'm designing a class which currently is composed mainly of simple getters/setters, but I'm not quite sure if I'm designing my class in the best way possible.

The getters require accessing a database to pull the requested information, so I'm checking if a property has been set first before running the query which seems like a good idea to me but I'm not sure.

I think I could make use of DI by type hinting the $connect parameter and using a DAL but this is not a public facing API and we're never going to use a different database engine so I'm not sure it's worth the trouble. I'm using a proprietary database engine which has a bug preventing me using PDO and parametrised queries. I'm also not sure if I should be try/catching/throwing exceptions inside class methods.

Here is a sample of the code below, there are more methods/properties but they all follow the same basic structure. I would very much appreciate any and all commentary.

class Patient {
  // Database connector
  private $connect;
  protected $_connection;

  public $dmg_ID;
  public $LNK_ID;
  public $dailyLNK_ID;

  public function __construct($connect, $lnkid, $dlkid = NULL) {
      $this->_connection = $connect;
      unset($connect);

      // Patient requires a LNK_ID but not always a daily link ID
      $this->LNK_ID = $lnkid;

      if (!is_null($dlkid) && is_numeric($dlkid)) {
        $this->dailyLNK_ID = $dlkid;
      }
  }

  public function getDmgID() {

      if ($this->dmg_ID) return $this->dmg_ID;

      $sql = "SELECT lnk_dmgID FROM LINK WHERE lnk_ID=".$this->LNK_ID;
      try { 
          $result = odbc_exec($this->_connection,$sql); 
          if($result) { 
              $dmgID = odbc_fetch_array($result);
          } 
          else { 
              throw new RuntimeException("Failed to connect."); 
          } 
      } 
      catch (RuntimeException $e) { 
          print("Exception caught: $e");
      }

      return $this->dmg_ID = $dmgID['LNK_DMGID'];
  }

  public function setDmgID() {

      if (!$this->dmg_ID) return false;

      $sql = "UPDATE LINK SET lnk_dmgID=".$this->dmg_ID." WHERE lnk_ID=".$this->LNK_ID;
      try { 
          $result = odbc_exec($this->_connection,$sql); 
          if(!$result) { 
              throw new RuntimeException("Failed to connect."); 
          } 
      } 
      catch (RuntimeException $e) { 
          print("Exception caught: $e");
      }

      return true;
  }
...