Category:
Mathematics

This is the final project:

In this final assignment, we will revisit datasets that we have utilized in previous assignments, but with new objectives.

- In the Week One assignment, you looked at mortality in your particular state, with two different metrics: the first was numbers of deaths, and the second was years of life lost. For this question, return to the original dataset, but this time first pool all
*cancer*causes of death together, so that cancer constitutes the only category for cause of death. Then, repeat your analyses from Week One. How do your conclusions change?

- In the Week Two assignment, you looked at sex ratios for births in your state.

- In the Week Three assignment, you were given levels of tumor-associated antigens in a sample of 90 normal (non-cancer) individuals, and 160 hepatocellular carcinoma (HCC) patients. Here is a proposed diagnostic test for HCC:
- For each individual, calculate a numerical score:
- score = -3.95 + 10.7 * HCC1 – 4.14 * P16 + 13.95 * P53 + 28.92 * P90 + 6.48 * survivin
- (This equation was derived from logistic regression.)

- If this score is positive (i.e., > 0), diagnose this individual as an HCC patient; if this score is negative (i.e., <0), diagnose this individual as normal (i.e., non-cancer).
- Apply this rule to the entire cohort of 250 individuals. Report the sensitivity of this rule, the specificity, the false positive rate, the false negative rate, and the overall accuracy. Do you think the score function provides a good diagnostic test for HCC? Explain.

- For each individual, calculate a numerical score:

- In the Week Four assignment, we considered a simple two-by-two crossover trial of a new experimental treatment for interstitial cystitis. We calculated t tests for carryover and treatment effects, but we have not yet considered period effects. It is unlikely that there are any period effects in this trial, but we may want to test this formally. If there were a period effect, then patient responses under either treatment would likely be systematically higher in one period than the other. (Here’s an analogy: Think of taking the same test twice. You would likely perform better on the test the second time, since you have learned from your experience of taking the first test.) Explain how you would devise a t test for assessing a period effect in this trial. (Hint: look at the explanation of the t test for treatment effects given in the Week Four assignment. There, we based the test on the random variable X – Y. Suppose we look instead at X + Y?)

- In the Week Five assignment, you investigated measures of brain size and intelligence in a sample of 20 youths. A potential shortcoming of your prior analyses is that you did not take into account all available information in the dataset, in particular, gender. Answer the following questions and explain your answers:
- Do any of the physiologic variables CCSA, HC, TOTSA, TOTVOL, and WEIGHT differ significantly between males and females?
- Do IQs differ significantly by gender?
- Undertake a paired analysis of IQs, in order to assess whether firstborns have higher IQs than non-firstborns. In this regard, there are 10 pairs of related youths, as denoted by the variable PAIR.

**Completing the Final Project**

The Final Project:

- Must include a title page with the following:
- Title of paper
- Student’s name
- Course name and number
- Instructor’s name
- Date submitted

- Must begin with an introductory paragraph that has a succinct thesis statement.
- Must address the topic of the paper with critical thought.
- Must end with a conclusion that reaffirms your thesis.
- Must use at least three scholarly, peer-reviewed sources published within the last five years (not including the course text) or those applicable to the data sets.
- Must document all sources in APA style, as outlined in the Ashford Writing Center.
- Must include a separate reference page, formatted according to APA style as outlined in the Ashford Writing Center. The number of pages must be applicable to the specific data sets outlined in the Final Project assignment.In this final assignment, we will revisit datasets that we have utilized in previous assignments, but with new objectives.
- In the Week One assignment, you looked at mortality in your particular state, with two different metrics: the first was numbers of deaths, and the second was years of life lost. For this question, return to the original dataset, but this time first pool all
*cancer*causes of death together, so that cancer constitutes the only category for cause of death. Then, repeat your analyses from Week One. How do your conclusions change?

- In the Week Two assignment, you looked at sex ratios for births in your state.

- In the Week Three assignment, you were given levels of tumor-associated antigens in a sample of 90 normal (non-cancer) individuals, and 160 hepatocellular carcinoma (HCC) patients. Here is a proposed diagnostic test for HCC:
- For each individual, calculate a numerical score:
- score = -3.95 + 10.7 * HCC1 – 4.14 * P16 + 13.95 * P53 + 28.92 * P90 + 6.48 * survivin
- (This equation was derived from logistic regression.)

- If this score is positive (i.e., > 0), diagnose this individual as an HCC patient; if this score is negative (i.e., <0), diagnose this individual as normal (i.e., non-cancer).
- Apply this rule to the entire cohort of 250 individuals. Report the sensitivity of this rule, the specificity, the false positive rate, the false negative rate, and the overall accuracy. Do you think the score function provides a good diagnostic test for HCC? Explain.

- For each individual, calculate a numerical score:

- In the Week Four assignment, we considered a simple two-by-two crossover trial of a new experimental treatment for interstitial cystitis. We calculated t tests for carryover and treatment effects, but we have not yet considered period effects. It is unlikely that there are any period effects in this trial, but we may want to test this formally. If there were a period effect, then patient responses under either treatment would likely be systematically higher in one period than the other. (Here’s an analogy: Think of taking the same test twice. You would likely perform better on the test the second time, since you have learned from your experience of taking the first test.) Explain how you would devise a t test for assessing a period effect in this trial. (Hint: look at the explanation of the t test for treatment effects given in the Week Four assignment. There, we based the test on the random variable X – Y. Suppose we look instead at X + Y?)

- In the Week Five assignment, you investigated measures of brain size and intelligence in a sample of 20 youths. A potential shortcoming of your prior analyses is that you did not take into account all available information in the dataset, in particular, gender. Answer the following questions and explain your answers:
- Do any of the physiologic variables CCSA, HC, TOTSA, TOTVOL, and WEIGHT differ significantly between males and females?
- Do IQs differ significantly by gender?
- Undertake a paired analysis of IQs, in order to assess whether firstborns have higher IQs than non-firstborns. In this regard, there are 10 pairs of related youths, as denoted by the variable PAIR.

**Completing the Final Project**

The Final Project:

- Must include a title page with the following:
- Title of paper
- Student’s name
- Course name and number
- Instructor’s name
- Date submitted

- Must begin with an introductory paragraph that has a succinct thesis statement.
- Must address the topic of the paper with critical thought.
- Must end with a conclusion that reaffirms your thesis.
- Must use at least three scholarly, peer-reviewed sources published within the last five years (not including the course text) or those applicable to the data sets.
- Must document all sources in APA style.
- Must include a separate reference page, formatted according to APA style. The number of pages must be applicable to the specific data sets outlined in the Final Project assignment.