Pass service to view model or leave thin controller as is
I would suggest having a separate class for doing this processing and mapping.
It will be a service or mapper class takes your Service object in the constructor and has a method which return WelcomeAnalyzeViewModel object.

Also you can do it all through the method, by passing your Service object to this method and return the WelcomeAnalyzeViewModel, this will make your controller very thin something like that:

public PartialViewResult Analyze()
{
        var viewModel = Mapper.GetWelcomeAnalyzeViewModel(Service);
        return PartialView("Analyze", viewModel);
}

public class Mapper
{
  public WelcomeAnalyzeViewModel(ServiceType service)
  {
      return new WelcomeAnalyzeViewModel
        {
            IsDrugsPanelVisible = !Service.IsMDStandalone(),
            IsDevicesPanelVisible = Service.IsSubscribedToMedTech(),
            IsCompaniesPanelVisible = !Service.IsCTStandalone(),
            IsCountriesPanelVisible = !Service.IsCTStandalone() || (Service.IsCTStandalone() &amp;&amp; Service.HasImsAddOn()),
            IsFinancePanelVisible = !Service.IsCTStandalone()
        };
  }
}


And i will put this mapper class in the ViewModels project if you have a separate project for them.