Prospective Cohort Study

The following tables show the crude and sex-specific results from a Prospective Cohort Study that examines the association between a binary exposure (E) and the development of a disease (D) during 20 years of follow-up.

Use these data to solve the above problem, it will become easier
Full data
D+ D- Total
E+ 30 270 300
E- 20 180 200
Total 50 450 500

Male
D+ D- Total
E+ 12 108 120
E- 8 72 80
Total 20 180 200

Female
D+ D- Total
E+ 18 162 180
E- 12 108 120
Total 30 270 300

1. Assume that this cohort is a simple random sample from a broader population of interest. Model the number of disease positive individuals among all exposed individuals in the sample using the binomial distribution with probability of disease ; and model the number of disease positive individuals among the unexposed in the sample using a binomial distribution, with probability of disease . Estimate , the proportion of exposed individuals who are disease positive, and provide an exact 95% confidence interval.
Estimated Proportion: ????

Confidence Interval:
Lower Bound:????
Upper Bound:????

and
4. Now, we examine the risk difference between the exposed and unexposed populations. Estimate the risk
difference for the disease and construct a corresponding large-sample 95% confidence interval. Calculate the
risk difference as the proportion of diseased individuals in the exposed minus the proportion of diseased
individuals in the unexposed.
Risk Difference: ????
Confidence Interval:
Lower Bound: ????
Upper Bound: ????

Please help me count this two question, or explain.I need your help!

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You do realise that the questions are student specific? I've copied your table, for future reference.

Honour code...

Course does not study, its you who do it. Therefore course may be free or very expensive, but the gaining knowledge out of it is totally upto you.

please suggest the steps for solving this question. requesting you

To calculate the estimated proportion, confidence interval, risk difference, and corresponding confidence interval, we need to follow the steps below:

1. Estimate the proportion of exposed individuals who are disease positive:
- In the full data:
- Disease positive among exposed: D+E+ = 30
- Total exposed: E+ = 300
- Proportion of exposed individuals who are disease positive = D+E+ / E+
- Using the provided data, the estimated proportion of exposed individuals who are disease positive is 30/300 = 0.1 or 10%.

2. Calculate the exact 95% confidence interval for the proportion:
- To calculate the confidence interval, we can use the formula for the binomial distribution:
- Confidence interval = [p̂ - Z * sqrt((p̂*(1-p̂))/n), p̂ + Z * sqrt((p̂*(1-p̂))/n)]
- p̂ is the estimated proportion of exposed individuals who are disease positive (0.1)
- Z is the z-score corresponding to the desired confidence level (95% confidence level has Z = 1.96)
- n is the total number of exposed individuals (300)
- Plug in the values to calculate the confidence interval.

3. Estimate the risk difference:
- Risk difference = Proportion of diseased individuals in the exposed group - Proportion of diseased individuals in the unexposed group
- In the full data:
- Proportion of diseased individuals in the exposed group = D+E+ / (D+E+ + D-E+)
- Proportion of diseased individuals in the unexposed group = D+E- / (D+E- + D--E-)
- Risk difference = (D+E+ / (D+E+ + D-E+)) - (D+E-/ (D+E- + D--E-))
- Using the provided data, calculate the risk difference.

4. Calculate the large-sample 95% confidence interval for the risk difference:
- To calculate the confidence interval, we can use the formula:
- Confidence interval = [Risk difference - Z * sqrt((p1*(1-p1))/(n1) + (p2*(1-p2))/(n2)), Risk difference + Z * sqrt((p1*(1-p1))/(n1) + (p2*(1-p2))/(n2))]
- Risk difference is the estimated risk difference
- p1 and p2 are the proportions of diseased individuals in the exposed and unexposed groups, respectively
- n1 and n2 are the total numbers of exposed and unexposed individuals, respectively
- Z is the z-score corresponding to the desired confidence level (95% confidence level has Z = 1.96)
- Plug in the values to calculate the confidence interval.

Please provide the data for the male and female populations if you want the specific estimations and calculations for those populations.