Secondary Primary Tumor Prevention With EGFR, OSI-774, and Cyclooxygenase-2

Inclusion Criteria:

* Patients must have, or have previously had, stage I (T1NO) or stage II (T2NO) squamous cell carcinoma of the head and neck.
* Tumor sites include oral cavity (buccal mucosal, gingival, floor of mouth, dorsal/ventral tongue, pharyngeal wall), oropharynx, larynx (glottis, supraglottis, subglottis, epiglottis) hypopharynx, paranasal sinus and nasal cavity.
* May have oral pre-malignant lesions (i.e., hyperplasia, dysplasia, carcinoma in situ) provided their Stage I or II disease has been definitively treated.
* Must have been free of disease for a minimum period of 8 weeks up to maximum of 3 years following completion of surgery and/or radiotherapy.
* Must have an Eastern Cooperative Oncology Group (ECOG)/Zubrod performance status of 0-1.
* Patients must be 18 years of age or greater.
* Female patients of childbearing potential must practice adequate contraception and have a negative pregnancy test (β-HCG).
* Must be able to swallow the Erlotinib and Celecoxib pills.
* Final eligibility for a clinical trial is determined by the health professionals conducting the trial.

Exclusion Criteria:

* Acute intercurrent illness or those who had surgery within the preceding 4 weeks unless they have fully recovered.
* History of previous malignancies other than squamous cell carcinoma of the head and neck unless the cancer was non-melanoma skin cancer.
* Participants who are pregnant or breast feeding.
* Documented history of coagulopathy and/or those taking warfarin or warfarin-derivative anticoagulants within 6 months of entry into the study.
* Hypertension not adequately controlled by medication as shown by a systolic ≥180 @ screening.
* Documented history of interstitial lung disease.
* Known connective tissue disease.
* Participated in a clinical trial of an investigational drug within 12 months prior to enrollment.
* Any active cardiovascular events including angina, unstable angina, palpitation, tachycardia, arrhythmia, or participant has had a recent cerebrovascular accident (stroke) or Myocardial Infarction (\< 6 months).
* Any history of clinically significant ventricular arrythmias (such as ventricular tachycardia, ventricular fibrillation, or Torsades de Pointes).
* Final eligibility for a clinical trial is determined by the health professionals conducting the trial.