STT 200 Lab 14 | Complete Solution

Lab 14

In this lab, we will use some of the statistical methods discussed in Chapters 14 and 15 to analyze hypothetical clinical trial data using Minitab. While these data are not real, they have been generated to reflect what happened in a real clinical trial. For hypothesis testing throughout this lab, we will use 0.05 level of significance.
A. Suppose that 200 patients who undergo surgery were randomly assigned to one of two groups: group 1 received an experimental treatment following surgery, and group 2 received a conventional treatment following surgery. The duration of stay in the intensive care unit (ICU) following surgery is the outcome (response) variable of interest. The research question is whether the experimental treatment affects the duration of stay in the ICU following surgery.
Open the worksheet u:\msu\course\stt\201\s\icu_trial.mtw. The first column has a patient id, second column (ICU) has the duration of stay in the ICU in days, column c3 has the group variable (1=experimental, 2=conventional). Columns C4 and C5 contain patients’ sex and age (in years). Column C6 has patients’ body mass index (BMI). It is calculated as weight in kilograms divided by height in meters squared.
We begin the analyses by comparing the two groups to see if there is a difference between the groups with respect to the outcome variable, number of days spent in the ICU following surgery (variable name in the worksheet is ICU). We will test H0: 1 - 2 = 0 versus Ha: 1 - 2 ≠ 0. Subscript 1 refers to the population represented by a sample of patients who received experimental treatment. Subscript 2 refers to the population represented by a sample of patients who received conventional treatment.
Use Stat>Basic Statistics>2-sample t, choose the option “samples in one column”, select column ICU into samples field, and select column group into sample ids field. Click on options, keep the confidence level at 95%, test difference field should have value 0, and the alternative field should be set to “not equal”. Do not check “assume equal variances”. We are conducting a two-tailed test to see if there are differences between the groups with respect to the duration of stay in the ICU following surgery: H0: 1 - 2 = 0 versus Ha: 1 - 2 ≠ 0. Click OK and again OK. Use Minitab’s output to answer the following questions:
1. How many patients were randomized to the experimental group (group 1)?___________
2. How many patients were randomized to the conventional group (group 2)?_______
3. For the test of H0: 1 - 2 = 0 versus Ha: 1 - 2 ≠ 0, what is the value of the test statistic? t=_______
4. Based on the p-value and 0.05 level of significance, what decision is reached?
(a) The experimental and conventional treatments produce the same mean number of days in the ICU stay;
(b) The experimental and conventional treatments do not produce the same mean number of days in the ICU stay.
The data come from the randomized trial, meaning that the differences in ICU stays may be attributable to the experimental versus conventional treatment. The idea is that randomization creates two very similar groups, so that everything for the two groups is the same, except for the treatments they receive. Thus when differences in outcomes are found, they can be attributed to the treatment received as opposed to other factors such as age, sex, or BMI. In practice, when randomization is performed, the groups may or may not be the same at intake on every variable. To verify the success of randomization, we will compare the groups on other variables such as age, sex and BMI to see if the differences in outcome (ICU stay) may be attributable to other factors that were not equalized by the randomization.
Use Stat>Basic Statistics>2-sample t, choose the option “samples in one column”, select column age into samples field, and select column group into sample ids field. Click OK.
5. Based on the p-value and 0.05 level of significance, what decision is reached?
(a) The populations represented by samples that received experimental versus conventional treatments have the same mean age;
(b) The populations represented by samples that received experimental versus conventional treatments do not
have the same mean age.
Use Stat>Basic Statistics>2-sample t, choose the option “samples in one column”, select column BMI into
samples field, and select column group into subscripts field. Click OK.
6. Based on the p-value and 0.05 level of significance, what decision is reached?
(a) The populations represented by samples that received experimental versus conventional treatments have the
same mean BMI;
(b) The populations represented by samples that received experimental versus conventional treatments do not
have the same mean BMI;
For the categorical variable sex, we will conduct a test of H0: two populations have the same distribution of a
categorical variable versus Ha: not so. Use Stat>Tables>Cross Tabulation and Chi-Square. Select group as
categorical variable for rows, select sex as categorical variable for columns. Under display, check counts and
row percents. Click on Chi-square, and check the box to perform the chi-square test. Click OK and again OK.
7. Females make up what percent of group 1? ______ When submitting your answer to LON-CAPA, enter the
number between 0 and 100 without % symbol.
8. Females make up what percent of group 2? ______ When submitting your answer to LON-CAPA, enter the
number between 0 and 100 without % symbol.
9. For the chi-square test comparing the distribution of sex in two groups, what is the value of the chi-square
test statistic (found under Pearson chi-square on Minitab’s output)?__________
10. What is the p-value?___________
11. Is the distribution of sex the same in two populations, represented by the samples that received experimental
versus conventional treatment? ________
While randomization appears to be successful in this case, often the researchers choose to deliberately control
for important factors when designing randomization, so that not everything is left to chance. To choose these
important factors, the researchers need to know whether these factors affect the outcome, ICU stay in this case.
Let’s see if age, BMI and sex affect the duration of stay in the ICU.
Use Stat>Basic Statistics > 2-sample t, choose the option “samples in one column”, select ICU into samples
field, and select sex into subscripts field. Do not check “assume equal variances”. Click on options and check
that the alternative is “not equal”: we are conducting a two-tailed test to see if there are differences in the
duration of stay in the ICU between males and females: H0: female - male = 0 versus Ha: female - male ≠ 0.
The p-value for the test of H0: female - male = 0 versus Ha: female - male ≠ 0 is________.
12. Based on the p-value for the test of H0: female - male = 0 versus Ha: female - male ≠ 0, what decision do we
make at .05 level of significance, retain the null hypothesis or reject it?_______________.
To investigate the effect of age on the duration of stay in the ICU, construct a scatterplot of duration of stay in
the ICU versus age. Use Graph>Scatterplot to do this, choose option simple, and select ICU as Y variable, and
age as X variable. Click OK. Does the scatterplot suggest that there is an association between variables ICU and
age?_____
Use Stat>Regression>Regression>Fit Regression Model, use ICU as the response variable, and age as
continuous predictor. Use Minitab’s output for regression analysis to answer questions below.
13. What percent of variation in response is explained using the predictor? R-sq=_______(Enter the number
found under Model Summary without % symbol into LON-CAPA).
On the output, find the table called Coefficients that lists predictors, coefficients, and their standard errors
(between Model Summary and Regression Equation). Check Minitab’s calculations of T and p-value for the test
if the slope of the population regression equation E Y x 0 1 ( )    is zero. The hypotheses are
: 0 : 0 0 1 1     a H vs H . Output for the slope is in the second row of the table (for predictor age).
Use Minitab’s output to identify the sample slope (under Coef) ___________ 1 b  and its standard error (under
SE Coef) . .( )  1 s e b _________________.
14. Use the sample slope and its standard error to calculate the value of the test statistic
 
. .( ) 1
1
s e b
b
t _____________________. Does it agree with the value reported under T-value in Minitab’s
output?
From Minitab’s output, the p-value for the test of : 0 : 0 0 1 1     a H vs H is ________________
15. Based on the p-value, what can we conclude about the significance of age as explanatory variable for the
duration of stay in the ICU, is it significant or not significant? _____________________
Is it important to control for age in trial design (e.g., during randomization)?________
Now we will calculate the 95% confidence interval for the slope of the population regression line using the
following steps:
Sample slope: _________ 1 b  Degrees of freedom=sample size minus 2=n-2= __________
To find the t* multiplier, use Calc>Probability Distributions>t, check inverse cumulative probability field,
enter the appropriate degrees of freedom (n - 2), and input constant 0.975. The non-centrality parameter should
remain 0. Click OK.
16. The multiplier t*=__________
From Minitab’s output for regression, the standard error of the sample slope, . .( )  1 s e b __________
Calculate the margin of error by multiplying* by the standard error.
17. Calculate the margin of error= * . .( )  1 t s e b ______________________________ Keep at least 3 decimals.
18. Does the confidence interval * . .( ) 1 1 b  t s e b contain 0?__________
To investigate the effect of BMI on the duration of stay in the ICU, use Stat>Regression>Regression> Fit
Regression Model, use ICU as the response variable, and BMI as predictor.
19. For the regression of ICU on BMI, the p-value for the test of : 0 : 0 0 1 1     a H vs H is ______________
20. Based on the p-value, what can we conclude about the significance of BMI as explanatory variable for the
duration of stay in the ICU, is it significant or not significant? _______________________
Is it important to control for BMI in trial design (e.g., during randomization)?________