The combination of total chemotherapy with oral methoxsalen (psoralen) and ultraviolet A radiation (called PUVA treatment) is an effective treatment for psoriasis. However, PUVA is mutagenic, increases the risk of squamous-cell skin cancer, and cause irregular, pigmented skin lesions. Stern et al. [8] performed a study to assess the incident of melanoma among patients treated with PUVA. The study identified 1380 patients with psoriasis who were first treated with PUVA in 1975 or 1976. Patients were subdivided according to the total number of treatments received (<250 or≥250 from 1975 to 1996). Within each group, the observed number of melanomas was determined from 1975 to 1996 and compared with the expected number of melanomas as determined by the published US age and sex specific melanoma incidence rates. The results were as in the table below.
Table 7.6 Relationship of PUVA treatment to incidence of melanoma (Rosner 2011)
OBSERVED EXPECTED
<250 5 3.7
≥250 6 1.1

problem: suppose we want to compare the observed and expected number of events among the group with <250 treatments. Perform inappropriate significant test and report two-tailed p - value.