The US Preventive Services Task Force (USPSTF) recommends annual screening for lung cancer with low-dose computed tomography (LDCT) in adults aged 50 to 80 years who have a 20 pack-year smoking history and currently smoke or have quit within the past 15 years. This patient is 58 years old, has a 35-pack-year history, and quit 10 years ago, meeting all criteria for screening. Chest X-ray and sputum cytology have not been shown to reduce mortality and are not recommended for screening.

Major US guidelines (including the USPSTF and American Cancer Society) now recommend starting colorectal cancer screening for average-risk individuals at age 45. Colonoscopy every 10 years is a primary screening modality. While other options like annual FIT or flexible sigmoidoscopy are acceptable alternatives, initiating screening at age 45 is the current standard of care. Delaying screening until age 50 is based on outdated recommendations.

For men aged 55 to 69, the USPSTF recommends that the decision to undergo PSA-based screening for prostate cancer should be an individual one. This patient is at higher risk due to his age, African American race, and family history. The most appropriate approach is to engage in shared decision-making, discussing the potential benefits (small reduction in mortality) and harms (false positives, overdiagnosis, complications of biopsy and treatment) of screening before ordering a PSA test.

Current guidelines recommend cervical cancer screening with cytology (Pap test) alone every 3 years for women aged 21-29. Since this patient's last normal Pap test was 3 years ago at age 25, she is due for screening. HPV co-testing and primary HPV testing are not recommended as primary screening strategies for women under age 30.

For locally advanced rectal cancer (Stage II-III), the standard of care is neoadjuvant chemoradiation. This approach helps to downstage the tumor, increasing the likelihood of a complete surgical resection with negative margins (R0 resection) and improving the chance of sphincter preservation. It has also been shown to reduce local recurrence rates compared to postoperative radiation. Surgery first is incorrect for T3/N1 disease. Palliative therapy is not indicated for potentially curable disease.

This patient has hormone receptor (HR)-positive, HER2-negative breast cancer. For postmenopausal women, an aromatase inhibitor (e.g., anastrozole, letrozole, exemestane) is the preferred adjuvant endocrine therapy as it has shown superior efficacy compared to tamoxifen. Tamoxifen is typically used for premenopausal women. Trastuzumab is an anti-HER2 therapy and is not indicated. Doxorubicin is a chemotherapy agent, which may or may not be indicated depending on other risk factors (e.g., recurrence score), but endocrine therapy is standard for all HR-positive tumors.

The classic presentation of painless obstructive jaundice with a palpable, non-tender gallbladder (Courvoisier sign) and weight loss is highly suggestive of pancreatic adenocarcinoma at the head of the pancreas causing obstruction of the common bile duct. Acute cholangitis would present with fever and abdominal pain (Charcot's triad). Choledocholithiasis typically causes painful jaundice. Hepatocellular carcinoma is less likely to cause this specific constellation of symptoms unless very advanced.

For a newly diagnosed, potentially resectable non-small cell lung cancer, a PET/CT scan is the most important staging investigation. It is used to assess for mediastinal lymph node involvement and distant metastatic disease (e.g., in the bones, liver, adrenal glands), which are crucial for determining operability and treatment planning. Brain MRI is also part of standard staging but PET/CT provides comprehensive systemic staging. Bone scan and abdominal ultrasound have been largely replaced by the more sensitive whole-body PET/CT for initial staging.

A suspicious palpable mass with corresponding malignant-appearing mammographic findings requires tissue diagnosis. Core needle biopsy is the standard of care as it provides histologic architecture, which is necessary to differentiate in-situ from invasive carcinoma and allows for hormone receptor (ER, PR) and HER2 testing. Fine-needle aspiration only provides cytologic information and has a higher non-diagnostic rate. Excisional biopsy is a surgical procedure that is generally performed after a tissue diagnosis is established. Observation is inappropriate for a highly suspicious lesion.

For patients with early-stage invasive breast cancer and a clinically negative axilla (no palpable lymph nodes), sentinel lymph node biopsy (SLNB) is the standard procedure for staging. It accurately identifies whether the cancer has spread to the initial draining lymph nodes while avoiding the significant morbidity (e.g., lymphedema, nerve injury) associated with a full axillary lymph node dissection. Axillary dissection is reserved for patients with positive sentinel nodes (in some cases) or clinically positive nodes. FNA is used for suspicious nodes, not for staging a clinically negative axilla.