The appropriate test statistic?

[AyazM]

Hello there, I am a medical student and I would like to discuss a slightly confusing question that I got in a certain examination. Here it is:

A researcher wanted to study the association between breast cancer and oral contraceptive use. She selected 50 women diagnosed with breast cancer and 50 women not having breast cancer, and determined the use of oral contraceptives among those women. Forty women reported having used contraceptives, 25 of them were women diagnosed with breast cancer.

The researcher further wants to test if this association is statistically significant or not at alpha = 0.05

1. State the null and alternative hypothesis
2. Calculate the appropriate test statistic
3. What is your decision and conclusion based on the calculated value of test statistic if the critical value of test statistic is 3.841 at alpha = 0.05?

Other parts of this question merely revolved around calculating and interpreting odds ratio but this particular bit was confusing. We have no calculators or t/z score tables in the examination. And till now, I still haven't been able to decide on what test statistic exactly did it prompt because it doesn't seem right trying a guess at using t/z or chi square tests here.

I'm sorry if I'm overlooking the "obvious" here because I'm not very well versed in mathematics.

 

[SW VandeCarr]

It seems simple enough. Just construct a 2x2 table. The columns will be, from left to right, the number of women with and without disease. The rows will be, from top (cells a,b) to bottom (cells c,d), women taking and not taking oral contraceptives. Arranged this way, ad/bc will be the odds ratio (relative risk estimate) for disease with and without oral contraceptives. The odds ratio(OR) does not have a normal distribution, but its log transform does. The Robins-Breslow-Greenland estimator (second link) for the variance of the ln(OR) is (1/a+1/b+1/c+1/d).

http://www.ispub.com/journal/the_internet_journal_of_epidemiology/volume_6_number_2_26/article/bias_adjusted_exposure_odds_ratio_for_misclassified_data_1.html

http://www.epi-perspectives.com/content/2/1/9

 

[AyazM]

Thankyou for the answer! I'm sure we have never been taught about Robins-Breslow-Greenland estimator neither is it found anywhere in our medical textbooks. Seems like an over-efficient effort on part of my examiner!

Still thanks for your answer :)

 

[zli034]

I can think about, test of compare 2 proportion, or Pearson good fit test. If I have my old test book where the details are.