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Math Statistics Fundamentals of Biostatistics

To compare: The incidence density of breast cancer in current users vs. never users. Also, provide the p -value. The p-value is 0.005. Given: The table is: OC-Use group Number of cases Number of person-years Current users 13 4761 Past users 164 121091 Never users 113 98091 Calculation: To find the required values, consider the below table: OC-Use group Number of cases Number of person-years Current users 13 4761 Never users 113 98091 Total 126 102852 The incidence density of breast cancer in current users and never users could be calculated as: Incidence density Current users = Number of cases of current users Total number of current users × 10 5 = 13 4761 × 10 5 = 273.0519 Incidence density Never users = Number of cases of never users Total number of never users × 10 5 = 113 98091 × 10 5 = 115.1992 Thus, the incidence density for current users and never users are 273.0519 and 115.199 cases per 10 5 person-years respectively. The hypotheses are: H 0 : I D 1 = I D 2 There is no difference in true incidence densities of current and never users H a : I D 1 ≠ I D 2 There is a difference in true incidence densities of current and never users Now, consider the below table: OC-Use group Number of cases Number of person-years Current users (1) 13 a 1 4761 t 1 Never users (2) 113 a 2 98091 t 2 Total 126 a 1 + a 2 102852 t 1 + t 2 The values of mean and variance are: Mean E 1 = a 1 + a 2 t 1 t 1 + t 2 = 13 + 113 4761 4761 + 98091 = 5.8235 Variance V 1 = a 1 + a 2 t 1 t 2 t 1 + t 2 2 = 13 + 113 4761 98091 4761 + 98091 2 = 5.5625 If the obtained value of variance is higher than 5, it is plausible to apply the procedure. The calculation for the test statistic is done as: z = a 1 − E 1 − 0.5 V 1 = 13 − 5.8325 − 0.5 5.5625 = 6.6675 5.5625 ≈ 2.827 The p-value using excel is calculated as: The required p- value is 0.005. Decision rule: Reject H 0 if p − value > Level of significance . Here, p − value 0.005 < Assumed significance level 0.05 null hypothesis is decided to be rejected. Conclusion: Thus, there is enough proof to conclude that there is a significant difference between the incidence densities of current users and never users.

To compare: The incidence density of breast cancer in current users vs. never users. Also, provide the p -value. The p-value is 0.005. Given: The table is: OC-Use group Number of cases Number of person-years Current users 13 4761 Past users 164 121091 Never users 113 98091 Calculation: To find the required values, consider the below table: OC-Use group Number of cases Number of person-years Current users 13 4761 Never users 113 98091 Total 126 102852 The incidence density of breast cancer in current users and never users could be calculated as: Incidence density Current users = Number of cases of current users Total number of current users × 10 5 = 13 4761 × 10 5 = 273.0519 Incidence density Never users = Number of cases of never users Total number of never users × 10 5 = 113 98091 × 10 5 = 115.1992 Thus, the incidence density for current users and never users are 273.0519 and 115.199 cases per 10 5 person-years respectively. The hypotheses are: H 0 : I D 1 = I D 2 There is no difference in true incidence densities of current and never users H a : I D 1 ≠ I D 2 There is a difference in true incidence densities of current and never users Now, consider the below table: OC-Use group Number of cases Number of person-years Current users (1) 13 a 1 4761 t 1 Never users (2) 113 a 2 98091 t 2 Total 126 a 1 + a 2 102852 t 1 + t 2 The values of mean and variance are: Mean E 1 = a 1 + a 2 t 1 t 1 + t 2 = 13 + 113 4761 4761 + 98091 = 5.8235 Variance V 1 = a 1 + a 2 t 1 t 2 t 1 + t 2 2 = 13 + 113 4761 98091 4761 + 98091 2 = 5.5625 If the obtained value of variance is higher than 5, it is plausible to apply the procedure. The calculation for the test statistic is done as: z = a 1 − E 1 − 0.5 V 1 = 13 − 5.8325 − 0.5 5.5625 = 6.6675 5.5625 ≈ 2.827 The p-value using excel is calculated as: The required p- value is 0.005. Decision rule: Reject H 0 if p − value > Level of significance . Here, p − value 0.005 < Assumed significance level 0.05 null hypothesis is decided to be rejected. Conclusion: Thus, there is enough proof to conclude that there is a significant difference between the incidence densities of current users and never users.

Fundamentals of Biostatistics

Fundamentals of Biostatistics

8th Edition

ISBN: 9781305268920

Author: Bernard Rosner

Publisher: Cengage Learning

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