1. Consider the data in the following table. The objective of the study is to investigate...

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1. Consider the data in the following table. The objective of the study is to investigate associations between alcohol in take and incidence of oesophageal cancer, where age stratification is done to allow comparisons of cancer rate between individuals of similar age. No Cancer Cancer Age Group Alcohol Intake In Years 0-80g/day Alcohol Intake >80g/day Alcohol Intake 0-80g/day 25-34 35-44 Alcohol Intake >80g/day ITTTT 45-54 55-64 65-74 a. Chose the most appropriate generalized linear model (GLM) for the data, that will allow you to address/examine the objectives of the study. Specify all parameters of the model along with the necessary assumptions, and answer the following specific questions. i. Specify the formal null and alternative hypothesis corresponding to testing any associations between alcohol intake, age and incidence of oesophageal cancer. Provide the test statistic and its distribution. ii. Is there a statistically significant association among all the 3 factors? Provide the formal hypothesis and use R to calculate the observed test statistic along with the corresponding p-value. iii. Is there a pair-wise independence between alcohol intake and incidence of oesophageal cancer given age? How about age and oesophageal cancer given alcohol intake? Provide the formal hypotheses, use R to test the hypotheses and discuss your results. b. Calculate the odds of developing oesophageal cancer for an individual who is 46 years old and consumes 90g of alcohol per day. Use a final model that you think is the best fit for the data. c. Calculate the odds ratio (OR) for individuals who are age 65-74 years and consume 0-80g of alcohol per day compared to individuals within the same age category but consume >80g of alcohol per day. 1 1. Consider the data in the following table. The objective of the study is to investigate associations between alcohol in take and incidence of oesophageal cancer, where age stratification is done to allow comparisons of cancer rate between individuals of similar age. No Cancer Cancer Age Group Alcohol Intake In Years 0-80g/day Alcohol Intake >80g/day Alcohol Intake 0-80g/day 25-34 35-44 Alcohol Intake >80g/day ITTTT 45-54 55-64 65-74 a. Chose the most appropriate generalized linear model (GLM) for the data, that will allow you to address/examine the objectives of the study. Specify all parameters of the model along with the necessary assumptions, and answer the following specific questions. i. Specify the formal null and alternative hypothesis corresponding to testing any associations between alcohol intake, age and incidence of oesophageal cancer. Provide the test statistic and its distribution. ii. Is there a statistically significant association among all the 3 factors? Provide the formal hypothesis and use R to calculate the observed test statistic along with the corresponding p-value. iii. Is there a pair-wise independence between alcohol intake and incidence of oesophageal cancer given age? How about age and oesophageal cancer given alcohol intake? Provide the formal hypotheses, use R to test the hypotheses and discuss your results. b. Calculate the odds of developing oesophageal cancer for an individual who is 46 years old and consumes 90g of alcohol per day. Use a final model that you think is the best fit for the data. c. Calculate the odds ratio (OR) for individuals who are age 65-74 years and consume 0-80g of alcohol per day compared to individuals within the same age category but consume >80g of alcohol per day. 1