The TNM classification calculator for p16-negative oropharyngeal cancer evaluates the stage of cancer based on three key parameters provided by the user: tumor classification, lymph node classification, and metastasis classification. This classification system is designed to determine the extent of cancer progression, which aids in treatment planning and prognosis estimation.

The process begins by selecting the appropriate classification for the primary tumor (T), regional lymph nodes (N), and distant metastasis (M) from predefined options. Each selection corresponds to specific anatomical and pathological criteria:

Tumor Classification (T):
- Tx: Primary tumor cannot be assessed
- T0: No evidence of primary tumor
- Tis: Carcinoma in situ
- T1: Tumor <= 2 cm in greatest dimension
- T2: Tumor > 2 cm but <= 4 cm
- T3: Tumor > 4 cm or extension to lingual surface of epiglottis
- T4a: Tumor invading specific surrounding structures
- T4b: Tumor with further invasion into critical areas

Lymph Node Classification (N):
- Nx: Nodes cannot be assessed
- N0: No lymph node metastasis
- N1: Single ipsilateral node <= 3 cm without extranodal extension
- N2a: Single node <= 3 cm with extranodal extension; up to 6 cm without 
- N2b: Multiple ipsilateral nodes, none > 6 cm without extension
- N2c: Bilateral/contralateral nodes, none > 6 cm without extension
- N3a: Nodes > 6 cm, no extension
- N3b: Node(s) with overt extranodal extension

Metastasis Classification (M):
- M0: No distant metastasis
- M1: Distant metastasis present

Based on the selected classifications, the calculator follows a set of conditional checks to assign an overall cancer stage:

1. Stage 0 is assigned if carcinoma in situ (Tis), with no lymph node metastasis (N0), and no distant metastasis (M0) are present.
2. Stage I is determined by a tumor (T1) ≤ 2 cm, with no lymph node (N0) or distant metastasis (M0).
3. Stage II consists of a tumor (T2) > 2 cm but ≤ 4 cm, with no lymph node (N0) or distant metastasis (M0).
4. Stage III may result from a larger tumor (T3) with no lymph node involvement (N0) or such tumors (T1, T2, T3) where a single ipsilateral node <= 3 cm with no extranodal extension (N1) and no distant metastasis (M0) appears.
5. Stage IVA involves more invasive tumors (T4a) or any tumors (T1-T4a) with more extensive lymph node involvement (N2) but no distant spread (M0).
6. Stage IVB is applicable when there is extensive local tumor invasion (T4b) or any tumor with worse lymph node involvement (N3) but without distant metastasis (M0).
7. Stage IVC is assigned when any tumor shows presence of distant metastasis (M1).

If none of the conditions match, the result is inconclusive, indicating "Stage cannot be fully assessed".

The calculator in question is the TNM (Tumor, Node, Metastasis) classification for p16-negative oropharyngeal cancer. This classification system is used specifically for patients diagnosed with oropharyngeal cancer that is p16-negative. 

The TNM classification is a globally recognized standard for staging different types of cancer, including oropharyngeal cancer. It provides a systematic way to describe the extent of disease progression, which is crucial for determining the most appropriate treatment plan and predicting patient prognosis. 

In this specific context, the TNM classification is used to stage p16-negative oropharyngeal cancer. P16 is a protein that, when overexpressed, is often associated with human papillomavirus (HPV)-related oropharyngeal cancer. Therefore, p16-negative oropharyngeal cancer typically refers to non-HPV-related oropharyngeal cancer.

The TNM classification for p16-negative oropharyngeal cancer takes into account the size and extent of the primary tumor (T), the involvement of nearby lymph nodes (N), and the presence of distant metastasis (M). 

This calculator is not applicable to patients with p16-positive oropharyngeal cancer, other types