Question

This works for me but how do I do the same thing using html.dropdownlist?

Notice that the value passed is not the value that is shown to the user.

@model IEnumerable<MVR.Models.ViewIndividual>

<h2>Level1</h2>    
<select>
        @foreach (var item in Model) {
        <option value="@item.Case_Number">@item.Patient_Lastname , 
                                          @item.Patient_Firstname
        </option>
}
</select>

Answer 1

As always in an ASP.NET MVC application you start by defining a view model:

public class MyViewModel
{
    public string SelectedIndividual { get; set; }
    public SelectList Individuals { get; set; }
}

then you write a controller action that populates this view model from some data source or something:

public ActionResult Index()
{
    // TODO : fetch those from your repository
    var values = new[]
    {
        new { Value = "1", Text = "item 1" },
        new { Value = "2", Text = "item 2" },
        new { Value = "3", Text = "item 3" },
    };

    var model = new MyViewModel
    {
        Individuals = new SelectList(values, "Value", "Text")
    };
    return View(model);
}

and finally you have a strongly typed view using strongly typed helpers:

@model MyViewModel
@Html.DropDownListFor(
    x => x.SelectedIndividual,
    Model.Individuals
)

This being said, because I see that you are not using any view models in your application, you could always try the following ugliness (not recommended, do this at your own risk):

@model IEnumerable<MVR.Models.ViewIndividual>

<h2>Level1</h2>
@Html.DropDownList(
    "SelectedIndividual",
    new SelectList(
        Model.Select(
            x => new { 
                Value = x.Case_Number, 
                Text = string.Format(
                    "{0}, {1}", 
                    x.Patient_Lastname, 
                    x.Patient_Firstname
                ) 
            }
        ), 
        "Value", 
        "Text"
    )
)

Of course such pornography is not something that I would recommend to ever write in a view and I wouldn’t recommend even to my worst enemies.

Conclusion: In an ASP.NET MVC application you should always be using view models and strongly typed views with strongly typed helpers (see first part of my answer).