1. 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.
Full Data:
Sex-Specific Data:
Males
Females
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:
unanswered
Confidence Interval:
Lower Bound:
unanswered
Upper Bound:
unanswered
2. Would you expect the large-sample Wilson confidence interval to provide similar results to the exact confidence intervals in question 1?
Yes No
3. Consider the following hypothetical scenario. Suppose that the data generating mechanism was different, and the data were generated from a stratified random sample of the population, where the probability of disease varies by stratum and the sampling probabilities vary by stratum. For instance, suppose the sampling was stratified by gender, where males were oversampled. Would the binomial model described in question 1 still be appropriate for estimating the proportion of diseased positive individuals in the population within exposure groups? (Model the number of disease positive individuals among all exposed individuals in the sample using the binomial distribution; and model the number of disease positive individuals among the unexposed in the sample using a binomial distribution).
Yes No
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:
unanswered
Confidence Interval:
Lower Bound:
unanswered
Upper Bound:
unanswered
5. Conduct a two-sample proportion test that the risk difference is equal to zero (versus the alternative that the risk difference is not equal to zero) at the 0.05 level of significance.
What is the absolute value of the test statistic?
unanswered
What is the distribution of the test statistic under the null hypothesis?
Standard Normal t-distribution Binomial
What is the p-value?
unanswered
What is your conclusion? (enter the letter of your best answer from the options listed below)
(A) We have evidence that the risk difference is not equal to 0.
(B) We do not have evidence that the risk difference is different from zero.
(C) None of the above.
unanswered
6. Rather than testing that the risk difference is equal to 0 (as in question 5), could you have conducted a Pearson-chi square test to test for an association between disease and exposure?
Yes No
7. What is the value for the Crude Risk Ratio, comparing exposed subjects to non-exposed subjects?
unanswered
8. Using the Mantel-Haenszel formula, what is the value for the sex-adjusted Risk Ratio, comparing exposed subjects to non exposed subjects?
unanswered
9. Using the total data as a standard population, what is the value for the Standardized Risk Ratio?
unanswered
10. Is sex a confounder in this study? (enter the letter of your best answer from the options listed below)
(A) Yes, because the crude RR equals the sex-adjusted RR
(B) No, because the crude RR equals the sex-adjusted RR
(C) Yes, because the crude RR does not equal the sex-adjusted RR
(D) No, because the crude RR does not equal the sex-adjusted RR
(E) Yes, because the RR among the males equals the RR among the females
(F) No, because the RR among the males equals the RR among the females
unanswered
11. Using the Risk Ratio as a measure of association, is sex an effect modifier in this study?
Yes, because the crude RR equals the sex-adjusted RR No, because the crude RR equals the sex-adjusted RR Yes, because the crude RR does not equal the sex-adjusted RR No, because the crude RR does not equal the sex-adjusted RR Yes, because the RR among males equals the RR among females No, because the RR among males equals the RR among females
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
Also your data will not come through via copy and paste.
could u please at least suggest the steps to do it
1. To estimate the proportion of exposed individuals who are disease positive and provide an exact 95% confidence interval, we can use the binomial distribution.
The estimated proportion of exposed individuals who are disease positive can be calculated by dividing the number of disease positive individuals among the exposed by the total number of exposed individuals in the sample.
To calculate the exact 95% confidence interval, we can use the formula:
Lower Bound = estimated proportion of exposed individuals who are disease positive - (critical value * standard error)
Upper Bound = estimated proportion of exposed individuals who are disease positive + (critical value * standard error)
The critical value is determined based on the desired confidence level (95% in this case) and the normal distribution. The standard error can be calculated as the square root of (estimated proportion * (1 - estimated proportion) / sample size).
2. The large-sample Wilson confidence interval may provide similar results to the exact confidence intervals in question 1, especially when the sample size is large. However, for smaller sample sizes, the exact confidence intervals may be more accurate.
3. If the data were generated from a stratified random sample where the probability of disease varies by stratum and the sampling probabilities vary by stratum, the binomial model described in question 1 may still be appropriate. The binomial distribution can be used to model the number of disease positive individuals among all exposed individuals and among the unexposed individuals in each stratum.
4. The risk difference for the disease can be calculated as the proportion of diseased individuals in the exposed minus the proportion of diseased individuals in the unexposed. To construct a corresponding large-sample 95% confidence interval, we can use the formula:
Lower Bound = risk difference - (critical value * standard error)
Upper Bound = risk difference + (critical value * standard error)
The critical value is determined based on the desired confidence level (95% in this case) and the normal distribution. The standard error can be calculated as the square root of ((proportion of exposed * (1 - proportion of exposed)) / sample size of exposed + (proportion of unexposed * (1 - proportion of unexposed)) / sample size of unexposed).
5. To conduct a two-sample proportion test on the risk difference, we can calculate the test statistic. The test statistic can be calculated as the absolute difference between the sample risk difference and the hypothesized risk difference (in this case, zero), divided by the standard error of the risk difference.
The distribution of the test statistic under the null hypothesis is the standard normal distribution.
The p-value can be calculated by comparing the test statistic to the appropriate critical value in the standard normal distribution.
The conclusion can be based on the p-value. If the p-value is less than the chosen level of significance (in this case, 0.05), we can reject the null hypothesis and conclude that there is evidence that the risk difference is not equal to zero.
6. Yes, a Pearson-chi square test could be conducted to test for an association between disease and exposure. However, this test is typically used when both the exposure and outcome variables are categorical, rather than when comparing proportions.
7. The value for the Crude Risk Ratio, comparing exposed subjects to non-exposed subjects, can be calculated as the ratio of the proportion of diseased individuals in the exposed group to the proportion of diseased individuals in the non-exposed group.
8. Using the Mantel-Haenszel formula, the sex-adjusted Risk Ratio, comparing exposed subjects to non-exposed subjects, can be calculated by stratifying the data by sex and calculating the risk ratio within each stratum. The Mantel-Haenszel risk ratio weights the stratum-specific risk ratios by the inverse of the variance of each stratum-specific risk ratio.
9. Using the total data as a standard population, the Standardized Risk Ratio can be calculated by comparing the proportion of diseased individuals in the exposed group to the proportion of diseased individuals in the non-exposed group in the total population.
10. To determine if sex is a confounder in this study, we can compare the crude risk ratio to the sex-adjusted risk ratio.
If the crude risk ratio equals the sex-adjusted risk ratio, then sex is not a confounder (option B). If the crude risk ratio does not equal the sex-adjusted risk ratio, then sex is a confounder (option C).
11. To determine if sex is an effect modifier in this study, we can compare the crude risk ratio to the sex-adjusted risk ratio.
If the crude risk ratio equals the sex-adjusted risk ratio, then sex is not an effect modifier (option No, because the crude RR equals the sex-adjusted RR). If the crude risk ratio does not equal the sex-adjusted risk ratio, then sex is an effect modifier (option Yes, because the crude RR does not equal the sex-adjusted RR).