Biostats Final

The adjusted r^2 can be directly interpreted as the proportion of variability in the outcome explained by the predictors in a linear regression model T/F

False

The most common null hypothesis of interest for assessing correlation p between two variables is H0: p=1 T/F

False

How many degrees of freedom are required for a Chi-square Test of Independence when analyzing a 2x2 table?

1 Only 1 degree of freedom is required for a 2x2 table. For a row with R rows and C columns, (R-1)x(C-1) degrees of freedom are required, but when R=2 and C=2, (2-1)*(2-1)=1*1=1.

To calculate the association between flea bites and plague, a 2x2 table can be used to categorize people based on disease and exposure status. Let's say there are 100 people in a study, 50 with plague and 50 without. Of those with plague, 40 reported having a flea bite, leaving 10 who did not have a flea bite. Of those who did not have plague, 20 had a flea bite and 30 did not. Using this information, the boxes of the 2x2 table can be filled in as seen below. Plague Yes No Total Flea bite Yes 40 20 60 Flea bite No 10 30 40 50 50 100 Under the null hypothesis of no relationship between flea bite and plague, show how to calculate the expected number of people with flea bites who developed plague.

60*(50/100) We use the total number of people with flea bites (60) and multiply this by the total proportion of people developing plague (50/100). These numbers are found in the marginals (totals) of the rows and columns. If there is no relationship between the variables, the proportion developing plague will be the same for those with and without flea bites, so we can use the total row to calculate the expected value.

Use the table below to answer the following question. Disease + Disease - Total Test + 90 15 105 Test - 10 85 95 Total 100 100 200 Calculate the specificity in this example.

85/100 There are 85 true negatives and 15 false positives. Thus, the specificity is 85%

Use the table below to answer the following question. Disease + Disease - Total Test + 90 15 105 Test - 10 85 95 Total 100 100 200 Calculate the NPV in this example.

85/95 There are 85 true negatives and 10 false negatives. The negative predictive value is thus 89.5%.

Use the table below to answer the following question. Disease + Disease - Total Test + 90 15 105 Test - 10 85 95 Total 100 100 200 Calculate the sensitivity in this example.

90/100 There are 90 true positives and 10 false negatives, so the sensitivity is 90%.

Use the table below to answer the following question. Disease + Disease - Total Test + 90 15 105 Test - 10 85 95 Total 100 100 200

90/100 There are 90 true positives and 10 false negatives, so the sensitivity is 90%.

Use the table below to answer the following question. Disease + Disease - Total Test + 90 15 105 Test - 10 85 95 Total 100 100 200 Calculate the PPV in this example.

90/105 There are 90 true positives and 15 false positives. Thus, the PPV is 85.7%.

We enroll 100 firemen in a study. We measure their pulse rate. The firemen then undergo six weeks of physical training. At the end of this training period, we measure their pulse rate again. In this example, which test(s) could be used to test if physical training had any impact on the firemen's pulse rates (pre-training versus post-training)? Select ALL that apply. Sign test Wilcoxon signed rank test Paired t-test

ALL The data (pulse rates) are continuous. The sample size is reasonably large (100 pairs). Thus, any of the three tests listed would be appropriate, though we may tend to prefer the paired t-test or Wilcoxon signed rank test because they are more powerful (retain more information about the differences) whereas the sign test only retains the direction (improve or worsen).

When might we prefer to use a non-parametric test? Select ALL that apply. The sample size is small The underlying distribution of the observations is unknown The outcomes are ordered categories (e.g. rating scales)

ALL All of these are settings where we would prefer a non-parametric test

When might we prefer to use a non-parametric test? Select ALL that apply. The sample size is small The underlying distribution of the observations is unknown or is non-normal The outcomes are ordered categories (e.g. rating scales)

All of these are settings where we would prefer a non-parametric test.

Clinical Trial Phase 1

Assess safety and tolerability of vaccine. Requires the smallest sample size

Clinical Trial Phase 2

Assess safety of vaccine and whether vaccine generates a strong immune response. Identify best does and timing. Requires a medium sample size.

Clinical Trial Phase 3

Assess vaccine efficacy and safety. Compares the rate of infection in the vaccine and placebo groups. Requires the largest sample size.

The 2x2 table below shows results from a study assessing the relationship between treatment (aspirin vs. placebo) and whether or not the subject died of cancer. [yes cancer death] [no cancer death] [total] placebo 347 11,188 11,535 aspirin 327 13,708 14,035 total 674 24,896 25,570 Which test(s) could be used here to evaluate the association between aspirin use and cancer death? (Select all that apply.) Chi-square Test of Independence Fisher's Exact Test Both tests can be used. The sample size is very large, so the expected cell counts will also be very large.

Both tests can be used. The sample size is very large, so the expected cell counts will also be very large.

There is a suspicion that zinc oxide, the white non-absorbent sunscreen traditionally worn by lifeguards is more effective at preventing sunburns that lead to skin cancer than absorbent sunscreen lotions. A study was conducted to investigate if exposure to zinc oxide is a more effective skin cancer prevention measure. The study involved comparing a group of former lifeguards that had developed cancer on their cheeks and noses to a group of lifeguards without this type of cancer and assess their prior exposure to zinc oxide or absorbent sunscreen lotions. What type of study was this? Case Control Study Cohort Study

Case-control This is a case control study because a set of cases are identified (former lifeguards with cancer) and a set of controls are identified (former lifeguards without cancer) and their exposure to zinc oxide was retrospectively assessed.

A study was designed to assess the impact of sun exposure on skin damage in beach volleyball players. During a weekend tournament, players from one team wore waterproof, SPF 35 sunscreen, while players from the other team did not wear any sunscreen. At the end of the volleyball tournament players' skin from both teams was analyzed for texture, sun damage, and burns. Comparisons of skin damage were then made based on the use of sunscreen. The analysis showed a significant difference between the cohorts in terms of the skin damage. What type of study was this? Case Control Study Cohort Study

Cohort This is a cohort study because the study began before the outcome (sun damage) developed.

A study was designed to assess the impact of sun exposure on skin damage in beach volleyball players. During a weekend tournament, players from one team wore waterproof, SPF 35 sunscreen, while players from the other team did not wear any sunscreen. At the end of the volleyball tournament players' skin from both teams was analyzed for texture, sun damage, and burns. Comparisons of skin damage were then made based on the use of sunscreen. The analysis showed a significant difference between the cohorts in terms of the skin damage. What type of study was this?

Cohort Study because the study began before the outcome (sun damage) developed.

Which description below best matches the procedure for the Wilcoxon rank sum test? (For simplicity, assume that the two groups have equal sample sizes.)

Combine the two groups and rank all observations. Calculate the sum of the ranks for each group separately. Compare the sums of the ranks across the two groups.

An alternative way to measure severity of diarrheal disease is to measure the total # of days for which the child experienced diarrheal illness. Which method should they use to test if these two measures of diarrheal illness (number of episodes of diarrhea and the total number of days for which the child experienced diarrhea) are significantly linearly related?

Correlation

The 2x2 table below shows results from a study assessing the relationship between gender (male vs. female) and whether or not the person is satisfied with his/her marriage. [satisfied] [unsatisfied] [total] male 5 3 8 female 2 4 6 total 7 7 14 Which test(s) could be used here to evaluate the association between gender and marital satisfaction? (Select all that apply.) Chi-square Test of Independence Fisher's Exact Test

Fisher's Exact Test The sample size is very small, so the expected cell counts will also be very small. In fact, all expected cell counts are below 5. The Chi-square Test is not recommended when one or more cell has an expected count less than 5.

To calculate Spearman's rank correlation coefficient, we replace the observed values with their ranks and then calculate Pearson's correlation coefficient. If the true population Spearman's rank correlation is \rho_s ρ s (rho_s), what is our null hypothesis of interest?

H0: rho_s = 0 When we learned about Pearson's correlation (population correlation \rho), we were interested in whether there was a correlation between the two variables. The null hypothesis was that there was no correlation -- H0: \rho=0. The same thing applies here with Spearman's rank -- we want to know if there is a correlation between the ranks of the two variables. As rank of one variable increases, does the other also increase? If there is no relationship, the Spearman's rank correlation will equal 0.

True Positive (TP)

Individual with a disease that tests positive for the disease

False Negative (FN)

Individual with a disease who tests negative for a disease

False Positive (FP)

Individual without a disease who test positive for a disease

True Negative (TN)

Individuals without a disease who test negative for a disease

ANOVA Non-Parametric Equivalent

KrusKal Wallis Test

What does it mean for a study to be double-blinded?

Neither the participants nor the study staff know which drug each participant is receiving

How many degrees of freedom are required for a Chi-square Test of Independence when analyzing a 2x2 table?

Only 1 degree of freedom is required for a 2x2 table. For a row with R rows and C columns, (R-1)x(C-1) degrees of freedom are required, but when R=2 and C=2, (2-1)*(2-1)=1*1=1.

To compare two independent group means, we generally use the two-sample t-test. When the two groups are paired (dependent), we generally use the paired t-test. 100 men are randomly sampled from the population. We administer a test of spatial reasoning. All men receive a caffeine pill and then complete the test of spatial reasoning a second time. We compare the mean score before and after receiving the caffeine pill. Which test would be most appropriate here?

Paired t-test for dependent samples The scores pre and post caffeine pill are dependent because the same men contribute to both sample. We expect there to be some dependence between the test scores because men who do well before the caffeine pill may also tend to perform well after the caffeine pill. Thus, we are interested in the mean difference in scores (e.g. post minus pre) and whether this mean difference is equal to zero.

Type II (beta) error and power are closely linked. If I design a study to have beta error of 20%, what is the power of my study?

Power is equal to 100% - beta error = 100% - 20% = 80%.

We enroll 100 firemen in a study. We measure their pulse rate. The firemen then undergo six weeks of physical training. At the end of this training period, we measure their pulse rate again. In this example, which test(s) could be used to test if physical training had any impact on the firemen's pulse rates (pre-training versus post-training)? Select ALL that apply. Sign test Wilcoxon signed rank test Paired t-test

Sign test Wilcoxon signed rank test Paired t-test The data (pulse rates) are continuous. The sample size is reasonably large (100 pairs). Thus, any of the three tests listed would be appropriate, though we may tend to prefer the paired t-test or Wilcoxon signed rank test because they are more powerful (retain more information about the differences) whereas the sign test only retains the direction (improve or worsen).

We enroll 100 pairs of twins in a study. For each pair of twins, one is randomized to a standard English course, and the other is randomized to an alternative education English course. At the end of the semester, all participants prepare a book report, and the letter grades are collected and analyzed. In this example, which test(s) could be used to compare academic performance after the standard English course with academic performance after the alternative education course? Select ALL that apply. Sign test Wilcoxon signed rank test Paired t-test

Sign test Wilcoxon signed rank test The data are clearly paired because academic performance is expected to be similar for twins (genetics, environment). The outcomes are ordered categories (letter grades). Thus, we can use the Wilcoxon signed rank test. We could also use the sign test, which just retains which twin performed better and analyzes whether more of the standard English course twins performed better, or whether more of the alternative ed twins performed better. We cannot use the paired t-test because the data (letter grades) are not quantitative (continuous or discrete).

We perform a study comparing two sunscreens - Sunscreen A and Sunscreen B. 100 individuals are enrolled. For each individual, Sunscreen A is applied to one arm, and Sunscreen B is applied to the other arm. After four hours in the sun, the arms are evaluated for evidence of sunburn. For each individual, there are two possible outcomes -- (1) the arm receiving Sunscreen A is less burned, or (2) the arm receiving Sunscreen B is less burned. In this example, which test(s) could be used to compare the performance of Sunscreen A and Sunscreen B in preventing sunburn? Select ALL that apply. Sign test Wilcoxon signed rank test Paired t-test

Sign test Here our outcome is just a direction indicating which sunscreen performed better in preventing sunburn. Thus, the only test we can use here is the sign test, which assesses whether we see roughly equal observations across both directions (null) or if we see more outcomes in one direction (alternative), indicating that one sunscreen is better than the other.

Paired t-test Non Parametric Equivalent

Signed test or Wilcoxon Signed Rank Test

Pearson's correlation Non-Parametric Equivalent

Spearmens Rank correlation

Which of the following are binary (yes/no) outcomes? Select all that apply. Systolic blood pressure greater than 140 mmHg Diastolic blood pressure in mmHg Decrease in systolic blood pressure exceeding 10mmHg one week after starting an anti-hypertensive Continuous variables, like systolic blood pressure and decrease in systolic blood pressure, can be transformed into binary (yes/no) variables. Here, if systolic blood pressure exceeds a certain value, or if drop in blood pressure exceeds a certain value, a participant is given a YES. Otherwise, they are given a NO.

Systolic blood pressure greater than 140 mmHg Decrease in systolic blood pressure exceeding 10mmHg one week after starting an anti-hypertensive Continuous variables, like systolic blood pressure and decrease in systolic blood pressure, can be transformed into binary (yes/no) variables. Here, if systolic blood pressure exceeds a certain value, or if drop in blood pressure exceeds a certain value, a participant is given a YES. Otherwise, they are given a NO.

When two predictor variables that are highly collinear are entered into the same linear regression model, the standard errors of the slopes may become very large T/F

True

For a 2x2 table, if the null hypothesis is true and there is no relationship between the two categorical variables, which of the following will be true? (Select all that apply.) The odds ratio in the population will equal 1 The risk difference in the population will equal 1 The odds ratio in the population will equal 0 The risk difference in the population will equal 0

The odds ratio in the population will equal 1 The risk difference in the population will equal 0 When there is no association between two variables, the odds ratio will equal 1 (same odds in both groups, so their ratio is equal to 1) and the risk difference will equal 0 (same risk in both groups, so their difference is equal to 0).

If the two-sample t-test is appropriate (underlying assumptions are met), either the two-sample t-test or the Wilcoxon rank sum test can be used to test that the groups are equal. Which test is more powerful, meaning it is more likely to detect a significant effect (p<0.05) when an effect truly exists?

The two sample t-test is slightly more powerful, with the Wilcoxon rank sum test having 95% as much power as the two sample t-test when analyzing the same data when the assumptions for a two-sample t-test are met.

Disease + Disease - Total Test + 90 15 105 Test - 10 85 95 Total 100 100 200 Calculate the specificity in this example.

There are 85 true negatives and 15 false positives. Thus, the specificity is 85%. 85/100

When conducting a Chi-square Test of Independence or a Fisher's Exact Test on a table summarizing two categorical variables, what is the null hypothesis?

There is no relationship between the two categorical variables

If the slope is significantly different from 0 in a simple linear regression between two variables, the correlation between these two variables is also statistically significantly different from 0 T/F

True

The Pearson correlation coefficient, r can only be between -1 and +1 T/F

True

The height-for-age Z score for a child can be calculated by taking the child's height, subtracting the population mean height for other children of the same age, and dividing by the population standard deviation of heights for other children of the same age. T/F

True

To compare two independent group means, we generally use the two-sample t-test. When the two groups are paired (dependent), we generally use the paired t-test. 100 men and 100 women are randomly sampled from the population. We administer a test of spatial reasoning. We compare the mean score for women with the mean score for men. Which test would be most appropriate here?

Two-sample t-test for independent samples The 100 men and 100 women are sampled randomly and are thus independent. If the men and women were part of a married couple, they would be dependent, but no indication is given that this is the case.

To compare two independent group means, we generally use the two-sample t-test. When the two groups are paired (dependent), we generally use the paired t-test. 100 men and 100 women are randomly sampled from the population. We administer a test of spatial reasoning. We compare the mean score for women with the mean score for men. Which test would be most appropriate here? Two-sample t-test for independent samples Paired t-test for dependent samples

Two-sample t-test for independent samples The 100 men and 100 women are sampled randomly and are thus independent. If the men and women were part of a married couple, they would be dependent, but no indication is given that this is the case.

When are the odds of an outcome and the probability of an outcome similar?

When the event is rare (occurs less than 10% of the time)

Two sample t-test (independent samples) Non Parametric Equivalent

Wilcoxon rank-sum or Mann-Whitney U test

As you change the cutoff of a test to increase sensitivity, specificity generally...

decreases There is an inverse relationship between sensitivity and specificity, so as one increases, the other typically decreases.