The Sorbinil Retinopathy Trial was conducted among 497 type...

The Sorbinil Retinopathy Trial was conducted among 497 type I (insulin-dependent) diabetic patients who had little or no evidence of retinopathy at baseline [31]. Retinopathies are abnormalities of the retina that sometimes occur among diabetic patients and can result in substantial losses of vision in advanced stages. Patients were randomized to either Sorbinil, an aldose-reductase inhibitor, or placebo and were seen at 1 year and then every 9 months up to 48 months after randomization. In addition, all subjects had a final visit at the end of the trial (max $=56$ months). Sixteen of the patients provided no follow-up. The primary endpoint of the trial was based on change in retinopathy severity level from baseline to maximum follow-up (i.e., severity level at maximum follow-up - severity level at baseline). An ordinal grading scale was used to evaluate change: $2+$ levels better, 1 level better, no change, 1 level worse, ..., 5+ levels worse. The outcome data by treatment group are given in Table 10.49. The primary outcome for the study was worsening by 2 or more levels. Implement the test in Problem 10.147 , and provide a $p$ -value (two-tailed). A more efficient method of analysis would leave the change in retinopathy level in its raw form without grouping the data

The Sorbinil Retinopathy Trial was conducted among 497 type I (insulin-dependent) diabetic patients who had little or no evidence of retinopathy at baseline [31]. Retinopathies are abnormalities of the retina that sometimes occur among diabetic patients and can result in substantial losses of vision in advanced stages. Patients were randomized to either Sorbinil, an aldose-reductase inhibitor, or placebo and were seen at 1 year and then every 9 months up to 48 months after randomization. In addition, all subjects had a final visit at the end of the trial (max $=56$ months). Sixteen of the patients provided no follow-up. The primary endpoint of the trial was based on change in retinopathy severity level from baseline to maximum follow-up (i.e., severity level at maximum follow-up - severity level at baseline). An ordinal grading scale was used to evaluate change: $2+$ levels better, 1 level better, no change, 1 level worse, ..., 5+ levels worse. The outcome data by treatment group are given in Table 10.49.
The primary outcome for the study was worsening by 2 or more levels.
Implement the test in Problem 10.147 , and provide
a $p$ -value (two-tailed).
A more efficient method of analysis would leave the change in retinopathy level in its raw form without grouping the data

Key Concepts

Randomized Controlled Trial

A randomized controlled trial (RCT) is an experimental design used to evaluate the effect of an intervention by randomly allocating participants into different groups. This helps to eliminate selection bias and confounding factors, ensuring that differences in outcomes can be attributed to the treatment rather than external factors.

Ordinal Data Analysis

Ordinal data are measurements that reflect an order or ranking among categories, though the exact differences between consecutive categories are not necessarily equal. Analyzing ordinal data involves using methods that respect this inherent order, such as nonparametric tests or models that can handle data without assuming equal intervals.

Primary Endpoint in Clinical Trials

The primary endpoint is the main outcome measure used to determine the effect of an intervention in a clinical trial. It is defined prior to the study and serves as the key metric around which the hypothesis test is structured, guiding the interpretation of the trial's success or failure.

Hypothesis Testing and p-value

Hypothesis testing is a statistical method used to make inferences about a population based on sample data. The p-value is a probability measure that quantifies the evidence against the null hypothesis, indicating the chance of obtaining the observed results if the null hypothesis were true. In a two-tailed test, the p-value accounts for extreme outcomes in both directions, making it suitable when deviations from the null hypothesis can occur on either side.

Transcript

00:01 So in this problem, we're going to be looking at how outliers impact the scatter plot.

00:06 I'm going to be doing this in excel.

00:08 However, if you need to do this in a graphing calculator, i will include the steps for that at the end.

00:15 So first, we're going to be making a scatter plot of the data.

00:19 I'm going to do free because later on in the problem, we're going to need to separate the data into these three sections.

00:30 Right so here's the data set in excel i just highlight two columns go to insert and then over here are the scatter plots so this is going to be the one of all of them the next one we want is without number 15 so to do that i'm going to highlight all of them and hold control on mac it might be different maybe command and then click on the two i want to get rid of so then same thing again, insert a new scatter plot, and i'll retitle this one without 15.

01:14 So now i'm going to make one without 18, and i'll title this one accordingly.

01:36 Okay, next, we need to find the correlation for all three categories, and then i'm going to do the first part of part c at the same time.

01:46 We're going to make the regression line for all three categories.

01:51 Now, doing this in excel, we can just click on the graph.

01:55 Hit this plus button, check the trendline box, and go to more options.

02:01 And from there, we'll put display equation on charts and display r squared on charts.

02:08 And i'll move those up here.

02:11 So i'm just going to go and do that with the other two now.

02:16 Add trendline equation and r2.

02:20 Squared value if these are too small to see i'll write them down at the end again so don't worry if you can't see them trend align more options equation and r squared now don't just copy these down this is r squared we don't want r squared we want r the reason why r squared is called r squared is because it's literally just r squared so to get r all we have to do is take the square root of r squared so i'm going to go back into a problem and i'll write down what we have so far so our first equation i'll put these in order r is equal to 0 .482 and y is equal to 10 .408x plus 66 .429.

03:32 So about 15, we get r is equal to 0 .568 and y is equal to 8 .9 and y is equal to 8 .9204x.

03:47 Plus 69 .487.

03:51 And then about 18, we get r is equal to 0 .533, and y is equal to 12 .194x plus 53 .913...

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