Docetaxel, Carboplatin, and Trastuzumab and/or Lapatinib in Treating Women With Stage I, Stage II, or Stage III Breast Cancer That Can Be Removed by Surgery

OBJECTIVES: Primary * To investigate the clinical efficacy of neoadjuvant docetaxel and carboplatin in combination with trastuzumab (Herceptin®) and/or lapatinib ditosylate by estimating the pathologic complete response (pCR) rate in the breast and axilla of women with HER2/neu-positive resectable stage I-III adenocarcinoma of the breast. Secondary * To estimate the molecular effects of lapatinib ditosylate and trastuzumab alone or in combination on tumor tissues of these patients by assessing changes in gene expression using serial gene microarray analysis. * To assess for gene expression and/or biomarker changes that may be correlated with or predict pCR and clinical response to lapatinib ditosylate and/or trastuzumab in these patients. * To evaluate the safety and tolerability of these regimens in these patients. * To evaluate the clinical efficacy of these regimens by estimating the clinical objective response rate (complete response and partial response) in these patients. * To estimate the rate of congestive heart failure or drop in LVEF (\> 10% points from baseline and below lower limits of normal) in each of the three treatment arms. OUTLINE: This is a multicenter study. Patients are stratified according to baseline tumor size (≤ 3 cm vs \> 3 cm) and hormone receptor status (estrogen receptor \[ER\]- and/or progesterone receptor \[PR\]-positive vs ER- and PR- negative). Patients are randomized to 1 of 3 treatment arms. * Arm I: Patients receive a trastuzumab IV over 90 minutes on day 1 in course 1. Patients receive docetaxel IV, carboplatin IV, and trastuzumab IV over 30 minutes on day 1 in courses 2-7. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity. * Arm II: Patients receive oral lapatinib ditosylate once daily on days 1-21 in course 1. Patients receive docetaxel IV, carboplatin IV as in arm I and oral lapatinib ditosylate once daily on days 1-21 in courses 2-7. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity. * Arm III: Patients receive trastuzumab IV as in arm I on day 1 and oral lapatinib ditosylate as in arm II on days 1-21 in course 1. Patients receive docetaxel IV, carboplatin IV, and trastuzumab IV as in arm I on day 1 and oral lapatinib ditosylate as in arm II on days 1-21 in courses 2-7. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity. Within 4-6 weeks after completion of chemotherapy, all patients under go definitive surgery and/or radiotherapy at the discretion of the treating physician. Tumor biopsy and blood samples are collected for biomarker analysis and molecular analysis at baseline, after course 1, and at the time of definitive breast surgery or completion of chemotherapy. Gene expression changes are analyzed by mRNA microarray analysis and molecular changes in protein expression profiles by IHC. Samples may also be analyzed by RT-PCR.