Question

STATS

A randomized trial was performed to evaluate the effectiveness of a new drug on controlling Type I diabetes in teenagers. A random sample of 150 patients were obtained from the pediatric diabetes clinic at Sick Kids in Toronto, Ontario; 75 were randomly assigned to the treatment group (new drug) and 75 were randomly assigned to the control group (existing drug). You may assume that basic factors such as validity of the inclusion criteria, blinding, etc. were performed appropriately.Baseline information such as age and gender were collected and key outcomes of A1C level and number of hypoglycemic events were measured after four weeks. A1C levels indicate what percentage of your hemoglobin is coated with sugar (glycated). Higher A1C levels indicate poorer blood sugar control and a higher risk for diabetes complications. A hypoglycemic event occurs when the plasma glucose levels become too low; this is a common and adverse effect of diabetes therapy which has been shown to negatively impact on quality of life.   The sample study data, which is comprised of 150 teenagers (75 treatment and 75 control). import the data too SPSS. (I will comment the data if someone can help)For reference, the dataset contains the following variables to be used in your analyses:

Variable	Units and Code
Age	Years
Gender	0 = Male; 1 = Female
Group	1 = Treatment; 0 = Control
A1C	%
Hypo	Hypoglycemic Events: 0=no events; 1=one event; 2=Two or more events

1. Based on the available data, your goal is to answer the following research questions:

1. Do the number of hypoglycemic events differ between the treatment and control groups? In other words, is there a statistically significant relationship between the number of hypoglycemic events and group (treatment and control)? Run the appropriate test at the 5% level of significance.
2. Is there a statistically significant difference in A1C levels between the treatment and control groups? Run the appropriate test at the 5% level of significance and decide on a 1-tail or 2-tail test.
3. Write appropriate Methods, Results and Conclusion sections for a peer-reviewed article based on the results of your analyses for questions 1a and 1b above.  

You are also encouraged to review peer-reviewed articles in medical journals (e.g. BMJ, Lancet, BMC-series journals, etc.) for examples of how to frame these sections and apply them to your report.

Data:

age	gender	group	A1C	hypo
14	1	1	8.7	0
17	1	1	7.4	1
15	0	1	6.3	1
14	1	1	8.6	2
14	1	1	7.6	2
15	0	1	7.5	1
14	0	1	6.9	1
17	1	1	11.7	0
13	1	1	4.4	0
14	1	1	8.2	2
16	1	1	9.1	1
13	1	1	7.3	1
16	1	1	7.0	1
18	0	1	4.1	2
17	1	1	9.0	0
14	0	1	9.1	1
15	0	1	9.7	0
18	0	1	10.2	0
13	0	1	8.1	0
17	0	1	7.1	0
16	0	1	8.5	2
17	0	1	5.6	2
17	1	1	10.1	1
18	1	1	4.5	0
17	1	1	7.0	0
14	1	1	7.5	0
17	0	1	8.6	0
13	0	1	8.2	0
13	0	1	6.0	0
18	1	1	10.2	0
14	1	1	7.9	2
18	0	1	6.5	0
16	1	1	8.4	1
18	0	1	9.3	0
15	1	1	6.2	1
13	0	1	9.6	1
17	0	1	8.0	0
17	1	1	6.8	2
16	1	1	8.4	0
18	0	1	4.6	0
14	1	1	8.8	1
15	0	1	8.0	1
14	0	1	10.9	0
14	1	1	7.9	1
15	1	1	7.6	0
13	0	1	6.3	0
18	0	1	10.9	1
14	1	1	7.3	0
16	1	1	7.8	0
16	1	1	5.2	2
16	1	1	4.6	0
18	0	1	9.9	2
16	0	1	5.3	0
14	0	1	7.5	1
18	1	1	6.6	1
13	0	1	7.7	0
18	0	1	7.1	2
17	0	1	8.2	2
17	1	1	8.0	1
18	0	1	8.2	0
16	0	1	7.0	0
13	0	1	4.7	0
13	1	1	8.0	1
13	0	1	4.9	1
16	0	1	6.2	1
16	0	1	7.9	1
13	0	1	8.8	2
16	0	1	8.0	0
16	1	1	4.1	1
13	1	1	11.4	1
16	1	1	11.2	0
15	0	1	5.8	1
14	1	1	6.1	0
16	1	1	6.7	0
17	1	1	4.8	0
15	0	0	8.1	2
13	1	0	8.1	1
17	0	0	11.0	1
18	1	0	6.4	0
13	0	0	8.0	1
17	1	0	9.6	2
15	0	0	6.9	0
13	1	0	10.0	2
13	1	0	6.7	0
15	0	0	8.3	0
17	0	0	6.7	0
16	1	0	9.5	0
14	1	0	8.9	0
15	0	0	7.6	0
15	1	0	5.7	0
18	0	0	7.9	2
17	0	0	9.5	0
14	1	0	6.7	0
16	1	0	10.5	2
18	1	0	6.7	0
15	1	0	8.8	0
18	1	0	8.4	1
14	0	0	7.3	0
13	1	0	7.9	0
18	0	0	4.7	0
14	1	0	7.3	1
16	0	0	3.0	0
15	1	0	8.0	0
17	0	0	5.9	2
16	1	0	6.1	1
13	1	0	5.6	1
17	0	0	9.4	0
13	1	0	7.6	2
14	0	0	7.6	2
14	1	0	5.1	1
16	1	0	9.0	0
13	1	0	5.4	0
17	1	0	11.5	2
15	0	0	5.5	0
14	0	0	7.0	1
13	0	0	9.8	0
14	1	0	7.1	0
15	0	0	7.7	2
13	0	0	10.4	2
14	1	0	7.8	0
14	0	0	7.3	0
18	0	0	8.5	0
13	1	0	6.5	0
14	1	0	4.7	1
16	0	0	6.7	1
15	0	0	7.9	2
13	1	0	8.4	0
15	0	0	6.7	2
15	1	0	9.7	0
16	0	0	9.9	1
15	1	0	8.0	1
13	0	0	7.1	0
18	1	0	5.3	0
15	0	0	8.8	0
14	1	0	7.1	1
16	1	0	7.3	1
14	1	0	10.5	0
13	0	0	9.3	1
14	1	0	6.3	0
13	0	0	8.2	1
18	0	0	4.1	0
15	1	0	5.4	0
18	1	0	8.0	2
15	0	0	11.7	0
13	0	0	7.5	0
18	1	0	8.5	2
18	1	0	8.1	1
17	0	0	8.0	2
18	1	0	9.7	0
13	0	0	8.8	2

Answer 1

Based on the available data, your goal is to answer the following research questions:

1. Do the number of hypoglycemic events differ between the treatment and control groups? In other words, is there a statistically significant relationship between the number of hypoglycemic events and group (treatment and control)? Run the appropriate test at the 5% level of significance.

Let us denote the treatment by subscript 1 and the 2 by the control or no treatment. We shall check the whether the mean number of events differ for the treatment group.

Null and alternate hypothesis

Null Hypothesis: The average number of hypoglycemic events are same in both the groups.

Alternate hypothesis: The average hypoglycemic events in control group is more since the treatment is expected to control the blood glucose levels.

Test statistic: We shall use a two sample t-test to test the hypothesis.

Level of significance:

Test statistic: , where s is the pooled sd of the samples and is given by

The summary statistics and the t-test results are summarized below:

t-Test: Two-Sample Assuming Equal Variances
	Trt	control
Mean	0.69333333	0.693333333
Variance	0.56684685	0.674954955
Observations	75	75
Pooled Variance	0.6209009
Hypothesized Mean Difference	0
df	148
t Stat	0
P(T<=t) one-tail	0.5
t Critical one-tail	1.65521451
P(T<=t) two-tail	1
t Critical two-tail	1.97612249

The t-test statistic is 0 since the mean of the treatment and control groups are same. The p-value for the one tailed test is 0.5. Since the p-value >0.05, we fail to reject the null hypothesis. Hence, we conclude that there is no evidence to claim that the treatment reduces number hypoglycemic events compared to control.

2. Is there a statistically significant difference in A1C levels between the treatment and control groups? Run the appropriate test at the 5% level of significance and decide on a 1-tail or 2-tail test.

Here, I shall choose a one tailed test as I shall be claiming that the A1C levels are less in treatment group.

Null Hypothesis: The average A1C levels are same in both the groups.

Alternate hypothesis: The average A1C in control group is more than the treatment group since the treatment is expected to control the blood glucose levels.

The test results.

t-Test: Two-Sample Assuming Equal Variances
	Trt	Control
Mean	7.590667	7.742667
Variance	3.271128	3.001939
Observations	75	75
Pooled Variance	3.136533
Hypothesized Mean Difference	0
df	148
t Stat	-0.52557
P(T<=t) one-tail	0.299985
t Critical one-tail	1.655215
P(T<=t) two-tail	0.59997
t Critical two-tail	1.976122

The mean A1C level for treatment group is 7.59% as compared to  7.74% in control group. Just an eye comparison says that the difference doesn't seem to vary much. Again, we can observe from the results that the difference is not statistically significant p-value=0.2995. Since p-value<0.05, we fail to reject the null hypothesis. Hence, we conclude that there is no sufficient evidence to claim that the treatment group reduces A1C levels in treated patiens.

3. Write appropriate Methods, Results and Conclusion sections for a peer-reviewed article based on the results of your analyses for questions 1a and 1b above.  

75 patients each are randomized to either receive a treatment or no treatment(control). At the end of the trail, the number of glycemic events and the A1C levels were analysed. The results had indicated that the treatment and the control group experienced on an average experienced 0.69 events which is not statistically significant.

The average A1C levels for treatment group is 7.59%(1.81) and the control group is 7.74%(1.73). (the figures in parenthesis is the SD).

From the foregone discussions, it can be inferred that the treatment did not exhibit the expected results.

(Note: This study should have done by comparing the difference between postbaseline and baseline comparisons in both the groups)