Case-control studies help determine whether certain exposures are associated with outcomes such as developing cancer. The built-in dataset esoph contains data from a case-control study in France comparing people with esophageal cancer (cases, counted in ncases) to people without esophageal cancer (controls, counted in ncontrols) that are carefully matched on a variety of demographic and medical characteristics. The study compares alcohol intake in grams per day (alcgp) and tobacco intake in grams per day (tobgp) across cases and controls grouped by age range (agegp).

The dataset is available in base R and can be called with the variable name esoph:

head(esoph)

You will be using this dataset to answer the following four multi-part questions (Questions 3-6).

You may wish to use the tidyverse package:

library(tidyverse)

The following threeparts have you explore some basic characteristics of the dataset.

Each row contains one group of the experiment. Each group has a different combination of age, alcohol consumption, and tobacco consumption. The number of cancer cases and number of controls (individuals without cancer)are reported for each group.

Question 3a

0.0/1.0 point (graded)

How many groups are in the study?

Question 3b

0.0/1.0 point (graded)

How many cases are there?

Save this value as all_cases for later problems.

Question 3c

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How many controls are there?

Save this value as all_controls for later problems.

The following fourparts ask you to explore some probabilities within this dataset related to alcohol and tobacco consumption.

Question 4a

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What is the probability that a subject in the highest alcohol consumption group is a cancer case?

Report your answer to 3 significant figures.

Question 4b

0.0/1.0 point (graded)

What is the probability that a subject in the lowest alcohol consumption group is a cancer case?

Report your answer to 3 significant figures.

Question 4c

0.0/1.0 point (graded)

Given that a person is a case, what is the probability that they smoke 10g or more a day?

Question 4d

0.0/1.0 point (graded)

Given that a person is a control, what is the probability that they smoke 10g or more a day?

Report your answer to 3 significant figures.