Question

In: Statistics and Probability

Colorectal cancer (CRC) is the second most common cancer diagnosed in industrialized nations (Benson et al. 2008).

 

Colorectal cancer (CRC) is the second most common cancer diagnosed in industrialized nations (Benson et al. 2008). Worldwide, colon cancer is the fourth leading cause of cancer deaths, and it is the second leading cause of cancer deaths in the United States (Janout & Kollarova 2001). Risk of developing colon cancer increases with age; more than 90 percent of cases occur after age 50 (American Cancer Society 2005). A family history of colon cancer is another major risk factor. Individuals with one first-degree relative diagnosed after age 50 have a relative risk of 1.6. That increases to 2.6 if the relative was diagnosed before age 50. The presence of two first-degree relatives diagnosed with colon cancer increases risk further. Relative risk is 3.5 if both relatives were diagnosed after age 50, 5.6 if either or both were diagnosed before age 50 (Wilschut et al. 2011). You are a primary care provider and one of your patients, Mr. Jones, is a 50-year-old male with no history of colon cancer. He has heard about the recommendations for colon cancer screening and has some questions for you. How commonly is colon cancer diagnosed in the United States? Is Mr. Jones at increased risk? The latest statistics from the Centers for Disease Control and Prevention (CDC 2013) report that 136,717 cases of colon cancer are diagnosed annually. Mr. Jones is curious as to whether his gender places him at increased risk. Of those 136,717 cases of CRC, 70,223 were male and 66,494 were female. Of the US population, 148,640,424 are male and 152,711,352 are female. Mr. Jones is also curious about whether his older age places him at increased risk for CRC. Exhibit C.1 reports the cases and population size among males for various age categories (CDC 2013).

Questions

1. Assume a total US population of 301,351,776; calculate the overall incidence rate per 100,000 of colon cancer in the United States.

2. By calculating the ratio of incidence rates we can derive the relative risk of getting CRC (males compared to females), or the number of times more likely males are to get CRC than females. Calculate the incidence rate for males and females and the relative risk (males versus females)

Solutions

Expert Solution

(1)

Let , total US population = 301,351,776

From, CDC report of 2013, 136,717 cases of colon cancer are diagnosed annually out of total population of US.

Overall incidence rate (risk) is the total number of new cases divided by the total population.

  • Overall incidence rate = Number of cases diagnosed / total number of population

                                  = 136717 / 301351776

                                  = 0.000453679

To calculate the overall incidence rate per 100,000 of colon cancer in the US.

  • Overall incidence rate per 100000 = 0.000453679 *100000

                                                    = 45.367909164

So, we can conclude that overall Incidence rate per 100000 is approximately 45.

(2)

  • probability of Male diagnosed for CRC OR incidence rate for male

        = number of males diagnosed for CRC / total number of male in US population

Incidence Rate for Male = 70,223 / 148,640,424

                                    = 0.000472435

  • probability of Female diagnosed for CRC OR incidence rate for female is,

                  = number of females diagnosed for CRC / total number of female in US population

Incidence Rate for Female = 66494/ 152711352

                                        = 0.000435423

  • Relative risk(Male vs Female) = Incidence Rate for male / Incidence Rate for Female

                                           = 0.000472435 / 0.000435423

                                           = 1.0850024

So, Incidence rates for Male and Female are 0.000472435 and 0.000435423 Respectively. And Relative Risk for Male Vs Female is 1.0850024 .


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