Question

Breast cancer specialists use BI-RADS scores (a whole number from 1 to 6) to classify mammogram findings. A score of 1 indicates a negative finding, while 6 indicates clear malignancy. The data set mammography.csv contains observations on 950 women who had mammograms and subsequent biopsies. Of interest is whether mean BIRADS score is, in fact, higher for women who have malignancies. For each woman, we have a BI-RADS score and the result of her biopsy (benign or malignant) respectively as below: "BI.RADS","Diagnosis" 5,"Malignant" 4,"Malignant" 5,"Malignant" 4,"Benign" 5,"Malignant" 4,"Benign" 4,"Benign" 5,"Benign" 5,"Malignant" 5,"Malignant" 5,"Malignant" 3,"Malignant" 4,"Benign" 4,"Benign" 4,"Benign" 4,"Benign" 3,"Benign" 4,"Malignant" 4,"Malignant" 4,"Benign" 5,"Malignant" 4,"Benign" 5,"Malignant" 4,"Malignant" 5,"Malignant" 2,"Benign" 5,"Benign" 5,"Malignant" 5,"Benign" 4,"Benign" 5,"Malignant" 5,"Malignant" 4,"Benign" 4,"Benign" 4,"Benign" 4,"Benign" 5,"Malignant" 4,"Malignant" 4,"Benign" 4,"Benign" 4,"Benign" 4,"Benign" 4,"Benign" 5,"Malignant" 5,"Malignant" 5,"Malignant" 4,"Benign" 2,"Benign" 5,"Malignant" 4,"Benign" 5,"Malignant" 4,"Benign" 4,"Benign" 4,"Malignant" 4,"Benign" 4,"Benign" 5,"Benign" 4,"Benign" 5,"Malignant" 5,"Malignant" 5,"Malignant" 4,"Benign" 3,"Benign" 5,"Malignant" 4,"Benign" 4,"Benign" 5,"Malignant" 4,"Benign" 4,"Benign" 4,"Benign" 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a. Which assumption is required to make inference about mean BI-RADS scores for women with and without malignancies?

b. What are the null and alternative hypotheses?

c. (1 mark) What is the value of the test statistic?

d. (1 mark) What is the approximate p-value?

e. Which assumption is required for the p-value in c) to be valid?

f. Using a significance level of alpha = 0.05, state your conclusions in the language of the problem.  

Answer 1

A, Assumption required to make inference about mean BI_RADS scores:

BI_RADS is a breast imaging reporting and data system and was established by the American College of Radiology..it was developed by radiologist for reporting mammogram results..it ranges from 0 to 5..0means mammogram study that is not yet complete..1means mammogram was negative it means no cancer..2means mammogram was probably normal need repeat mammogram after 6 months..the chance of cancer that is breast cancer..5means that mammogram results are highly suspicious with a 95% chance of breast cancer..6means that breast cancer been diagnosed..BI_RADS number helpful to follow-up after mammogram..it also include an assessment of your breast density.dense breast have less fatty tissues 6times more likely to develop cancer..it will be difficult to find out..

BI_RADS classifies breast density into four groups:

Mostly fatty: breast contain fat,fibrous and glandular tissue.. mammogram will show if anything Abnormal..

Scattered density: breast have little mre fat, with few areas of fibrous and glandular tissue..

Consistent density:many area of breast covered by fibrous and glandular tissue it is difficult to find out..

Extremely dense:large portion covered by fibrous and glandular tissue it will be hard to make out cancer tissue..

2, various hypothesis may be tested after the score..BI_RADS_US 3 lesions by and hypothesis that sonoelastography ultrasound identify a high_risk group and a low_risk group within these patients..in this cases we find false_negative and false_positive cases in population screening.high_risk group that receive immediate biopsy due to risk..more than 1million women newly diagnosed with breast cancer each year..cancer mortality reduced due to early detection..Despite technical advance than ultrasound in US BI_RADS introduced the standard..This technology used to make sure about benign and malignant masses our hypothesis,that elastography identify a high risk group and low risk group malignancy with a BI_RADS_US 3 lesion..we use Z_Test for high_risk group and low risk group..non palpable lesions were submitted for biopsy..

PPV calcification in the different BI_RADS categories equation below

True_positive(TP)/true_positive(TP)++false_positive(fp)

NPV calculation in the BI_RADS categories equation below

True_negative(TN)/true_negative(TN)++false_negative(FN)

Statitical analysis was performed with positive and negative predictive values,tje fishers exact test was employed for expected frequency of <5..the null hypothesis rejection level was set at 5 %(p<0•05)