You are conducting a case control study to determine if an association exists between melanoma and indoor tanning. From a statewide cancer registry, you identify 1,107 people who were diagnosed with melanoma in the last three years. You select 1,500 controls for your study. Through a follow-up survey, you find that 696 of those with melanoma had a history of indoor tanning. 48.2 percent of the control group reported no exposure to indoor tanning.
(a) Calculate the odds ratio.
(b) Interpret your results.

a. Odds ratio = 1.58

b.  Inasmuch the odds ratio is greater than 1, this means that higher odds of melanoma exist in people exposed to indoor tanning, than in those not exposed to indoor tanning

Explanation:

For case  study                                                  

Let 'a'  represent the total population of people with melanomia = 696                                                      

Let 'b' represent the total number of people with melanomia exposed to indoor tanning  =  1107 – 696 = 411 people

For  control study

Let 'c' represent the total population = 1500

Let 'd' represent the total number of people not exposed to indoor tanning = 1500 - (0.428 * 1500)

                                                          =  1500 - 723

Total number of people not exposed to indoor tanning   = 777 people

a. Odds ratio = (a/b) / (d/c) = (696/411) / (777/723)

                                                = 1.69 / 1.07 = 1.58

b. Inasmuch the odds ratio is greater than 1, this means that higher odds of melanoma exist in people exposed to indoor tanning, than in those not exposed to indoor tanning.