It depends upon the extent of the infestation. A single roach won't do it. You might be able to get out of the lease if the apartment is truly uninhabitable. Take a look at
You should request in writing that your landlord correct the problem, and describe for the landlord in that writing the health and livability concerns you have.
In the event the landlord still does nothing, you can pay to have a problem fixed, then deduct it from your rent payment. Landlords don't like this approach typically and it could result in an eviction dispute.
Or, if the apartment is truly unlivable, there is a legal doctrine of constructive eviction, which you could assert. If the premises are not fit for habitation then you probably have a basis to get out of a lease. You should consult an attorney, and provide the attorney with your lease agreement, before you do anything.