Edit in JSFiddle

/*
 -------------------------------------------------------
 syntax 
 MAIN.createRelatedSelector(
    from   -> the filtering element           
    to     -> the element for filtered options
    obj    -> An object containing the options per
              option of the filtering (from) element
    [sort] -> optional sorting method for sorting
              of the complete or filtered options list
 --------------------------------------------------------
*/

//create the interdepent selectors
function initSelectors(){
 // next 2 statements should generate error message, see console
 MAIN.createRelatedSelector(); 
 MAIN.createRelatedSelector(document.querySelector('#continents') );
 
 //countries
 MAIN.createRelatedSelector
     ( document.querySelector('#continents')           // from select element
      ,document.querySelector('#selectcountries')      // to select element
      ,{                                               // values object 
        Asia: ['China','Japan','North Korea','South Korea','India','Malaysia','Uzbekistan'],
        Europe: ['France','Belgium','Spain','Netherlands','Sweden','Germany'],
        Africa: ['Mali','Namibia','Botswana','Zimbabwe','Burkina Faso','Burundi']
      }
      ,function(a,b){return a>b ? 1 : a<b ? -1 : 0;}   // sort method
 );

 //numbers
 MAIN.createRelatedSelector
   (   document.querySelector('#oddeven')
      ,document.querySelector('#numbers')
      ,{
        Odd: [1,3,5,7,9,11,13,15,17],
        Even: [14,2,4,6,8,10,12,16],
       }
      ,function(a,b){ return +a - +b; }
 );

 // persons
 MAIN.createRelatedSelector
  (    document.querySelector('#malefemale')
      ,document.querySelector('#names')
      ,{
        Female: ['Mary','Jeanette','Jo','Anne'],
        Male: ['John','Charles','Edward','Jim'],
       }
 );
}

//create MAIN namespace
(function(ns){ // don't pollute the global namespace
    
 function create(from, to, obj, srt){
  if (!from) {
         throw CreationError('create: parameter selector [from] missing');
  }
  if (!to) {
         throw CreationError('create: parameter related selector [to] missing');
  }
  if (!obj) {
         throw CreationError('create: related filter definition object [obj] missing');
  }
  
  //retrieve all options from obj and add it
  obj.all = (function(o){
     var a = [];
     for (var l in o) {
       a = /array/i.test (o[l].constructor) ? a.concat(o[l]) : a;
     }
     return a.sort(srt);
  }(obj));
 // initialize and populate to-selector with all
  populator.call( from
                  ,null
                  ,to
                  ,obj
                  ,srt
  );
    
  // assign handler    
  from.onchange = populator;

  function initStatics(fn,obj){
   for (var l in obj) {
       if (obj.hasOwnProperty(l)){
           fn[l] = obj[l];
       }
   }
   fn.initialized = true;
  }
     
 function populator(e, relatedto, obj, srt){
    // set pseudo statics
    var self = populator;
    if (!self.initialized) {
        initStatics(self,{optselects:obj,optselectsall:obj.all,relatedTo:relatedto,sorter:srt || false});
    }
     
    if (!self.relatedTo){
        throw 'not related to a selector';
    }
    // populate to-selector from filter/all
    var optsfilter = this.selectedIndex < 1
                   ? self.optselectsall 
                   : self.optselects[this.options[this.selectedIndex].firstChild.nodeValue]
       ,cselect = self.relatedTo
       ,opts = cselect.options;
    if (self.sorter) optsfilter.sort(self.sorter);
    opts.length = 0;
    for (var i=0;i<optsfilter.length;i+=1){
        opts[i] = new Option(optsfilter[i],i);
    }
  }
 }
    
 // custom Error
 function CreationError(mssg){
     return {name:'CreationError',message:mssg};
 }

 // return the create method with some error handling   
 window[ns] = { 
     createRelatedSelector: function(from,to,obj,srt) {
          try { 
              if (arguments.length<1) {
                 throw CreationError('no parameters');
              } 
              create.call(null,from,to,obj,srt); 
          } 
          catch(e) { console.log('createRelatedSelector ->',e.name,'\n'
                                   + e.message +
                                   '\ncheck parameters'); }
        }
 };    
}('MAIN'));
//initialize
initSelectors();

<div class="txt">Filter contintent (sorted)</div>
<select id="continents">
 <option value = 0>All</option>   
 <option value = 1>Asia</option>
 <option value = 2>Europe</option>
 <option value = 3>Africa</option>
</select> 
<select id="selectcountries"></select>

<br>

<div class="txt">Filter odd/even (sorted)</div>
<select id="oddeven">
 <option value = 0>All</option>   
 <option value = 1>Odd</option>
 <option value = 2>Even</option>
</select>
<select id="numbers"></select> 

<br>
    
<div class="txt">Filter Male/Female (unsorted)</div>
<select id="malefemale">
 <option value = 0>All</option>   
 <option value = 1>Male</option>
 <option value = 2>Female</option>
</select> 
<select id="names"></select>

body {font: normal 0.8em verdana,arial}
.txt {width: 200px; display:inline-block}