Evaluation of Drug to Lower Cholesterol

1. In terms of the practical use of this drug, what do you think the research question(s) should be? [5%]

Does the drug lower total cholesterol levels statistically significantly more than the placebo?

In patients with higher than normal cholesterol levels, does a new cholesterol lowering drug (Drug Name), statistically significantly lower cholesterol  levels compared to a placebo using a randomised control trial? 

To examine the efficacy of a new total cholesterol lowering drug (Name of new drug) to statistically significantly lower total cholesterol levels in blood more than a placebo in patients with higher than normal cholesterol levels using a randomised control trial.

 In Patients with higher than normal cholesterol levels, does a new cholesterol lowering drug statistically significantly change total cholesterol levels more than a placebo using a randomised control trial?

(Nyu Libraries 2019 and WHO, 2017)

2.What is your null hypothesis? [5%]

The new cholesterol lowering drug does not lower total cholesterol levels statistically significantly more than the placebo.

H0: u1 = u2

U1 = Proportion of population who gain benefit if given the drug. 

U2 = Proportion of population who gain benefit if given the placebo.

where population means from the two unrelated groups are equal.

3. What would be an appropriate statistical test(s) to answer these question [5%]

An Independent-Samples-t-test would be a suitable test. This tests for the difference between the same variable from different populations. The cholesterol levels in patients in the group given the new cholesterol lowering drug and the cholesterol levels in the group given the placebo are tested to provide an answer. The two groups comprise different people. The result of a test statistic (t-test) and the associated probability or p-value is given. (Turner, 2011) This test establishes if there is a statistically significant difference between the means in two separate groups.

4. What assumptions should be made about these test(s) and how did you check these assumptions [10%]

The data requirements for an Independent t-test include a random sample of data from a randomly selected portion of the total population. It is only accurate to interpret an independent t-test result, as valid if the data follows these assumptions:

A dependent variable that can be measured on a continuous scale.

An Independent variable which consists of two categorical independent groups and Independence of observations should take place.

Assumption of Independence applies as each person contributes to one cholesterol level test. This means the behaviour of one participant should not influence another. The observations between groups should be independent and the observation within each group should be independent. Violation of this assumption will yield a false p- value.  The key to avoiding violating the assumptions of independence is to make sure the data is independent while collecting it. If the study fails this assumption, another statistical test will have to be performed such as a paired-samples t-test.

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There should be no significant outliers in data. This can be checked using box-plots. A dependent variable should be normally distributed. The assumption of normality requires the populations from which he data were obtained to be normally distributed. Data should have an approximate normal distribution (or at least be symmetric) as the Independent t-test is generally robust to violations of this assumption. A graph of the data takes on the shape of a bell curve. Tests for Normality and Symmetry are useful for assessing whether data meets this assumption. The Shapiro-Wilks test of normality or a graphical method, such as a Q-Q Plot, are very common. You can run these tests using the SPSS statistical package.  Some tests (e.g. Regression) require that there be a linear correlation between the dependent and independent variables. Linearity can be shown graphically using histograms or scatter diagrams or by using techniques such as  Correlation, Regression and Multiple Regression. Data is shown to be linear when there is no correlation between them. A Kolmogerrov-smirnov test compares the scores in a sample with those of a normal distribution with the same mean and std deviation. If the test is not sig. (p<0.05) the distribution of the sample is not significantly different from a normal distribution. This can also be checked visually using a probability-probability plot. The data is ranked and sorted and the rank (expected z) and the data (actual z) are both converted to z values and plotted against each other. Normally distributed data will produce a straight line as the actual is equal to the expected. If the group's data is not approximately normally distributed and groups sizes differ, there are two options: (1) have the data transformed so that it becomes normally distributed. This can be performed in SPSS Statistics, or (2) perform the Mann-Whitney U test which is a non-parametric test that does not require the assumption of normality. (Ghasemi, 2012)

There needs to be Homogeneity of variances. This is tested using Levene's Test of Equality of Variances, which is produced in SPSS Statistics when running the Independent t-test procedure. This test for homogeneity of variance provides an F-statistic and a significance value (p-value). A significance value greater than 0.05 (i.e., p > .05) indicates our group variances can be treated as equal. However, if p < 0.05, it indicates unequal variances and the assumption of homogeneity of variances no longer applies. (Scale, 2019)

Statistical tests mostly obey some distribution function (such as the normal distribution). These are called parametric tests. When one of the key assumptions of a test is not obeyed, a non-parametric test can be used instead. Non-parametric tests don’t rely on a specific probability distribution function. However, they do result in a loss of power of a test. Other options when assumptions are not met include transforming the data. (Lund Research Ltd, 2018)

5. What is the dependent variable and independent variable? [5%]

Dependent variable: Cholesterol concentration levels in the blood of all participants in the study.  

Independent Variable: Treatment groups 1=group given the placebo and 2=group given the new cholesterol lowering drug.

6. If this study used more than one treatment group as well as the placebo, (e.g. more than one dose of the drug was tested) what would be an appropriate test(s) to assess differences between these groups?[5%]

A paired Samples t-test is used to compare the mean scores for the same group of people on two occasions. This could be used to determine if there is a difference in Cholesterol levels within the treatment group across two dose levels.

However, a one- way ANOVA test, is required in this case to compare more than two means from treatment groups and the placebo. ANOVA testing allows detection of a significant difference between treatments as a unit. Testing using several t-tests would only increase the error rate.

ANOVA compares variability between sample means with the variability within the samples using a ratio called F.  Where the variation between sample means is large compared to the variation within samples it is concluded that at least one of the means is different to the others. The Kruskal-wallis H test is a rank based nonparametric test that can be used as an alternative to the one-way ANOVA, if the data from the new group is not normally distributed. It will determine if there are statistically significant differences between two or more Independent groups. (Lund Research, 2018)

Input the raw data (found on page 2) into SPSS and use your chosen test(s) to answer your research question.

7. If it was found that the assumptions could not be met, alternative strategies can usually be used – Pick one assumption and describe the alternative strategy one could follow if this assumption was not met.[10%]

The sampling distribution is normal.

The data when plotted results in a normal distribution as shown by a bell-shaped distribution curve. This can also be checked visually with a probability – probability plot. The data is ranked and sorted and the rank (expected z) and the data (actual z) are both converted to z values and plotted against each other. If the data is normal you get a straight line. The Shapiro-Wilks test, Kolmogorov-Smirnov test or a graphical method such as the Q-Q plot can be run using the SPSS statistics. The t -test is generally robust with respect to deviation from normality but not if the ratio of the smallest to the largest group size is greater than 1.5. The data should not deviate too seriously from normality. If the p<0.05 using the Kolmogorov-Smirnov test, this indicates a lack of normality.

When you violate the normality assumption you can: 

Transform the data so that the data becomes normally distributed. This can be performed using SPSS statistics. Also see what you can do with possible outliers to see if they can be dropped from analysis. A box-plot is very useful for identifying outliers. The parametric test can then be performed on the transformed data.

Use a non-parametric Mann-Whitney U Test which can be run in SPSS statistics as it does not require the assumption of normality. (Lund Research Ltd, 2018) It compares two populations based upon the ranks of values to determine if they are the same or different. Ranking procedures are commonly used in non-parametric tests as these evens out the effect of any outliers. The null hypothesis is the medians are equal. The alternative hypothesis is the medians are not equal. Given the nonparametric nature of this statistical analysis, there are fewer assumptions to assess. The data must come from random samples of the population, the data are independent, meaning that scores from one participant are not dependent on scores of the others, and the measure of the two samples have a dependent variable that is either ordinal or continuous. (Statistics Solutions, 2019) (Lund research Ltd, 2018)

8. Looking at the SPSS output, do you accept or reject the Null hypothesis?  What aspect(s) of the SPSS output led you to this conclusion about the Null hypothesis, explain.       [15%]

The SPSS output:

Figure 1: Histogram of data showing Normal Distribution. The frequency of the groups levels of total cholesterol is plotted against total cholesterol concentration levels.

Table 2: SPSS output of Independent Samples t-test comparing means and reporting the probability and significance values of this test.

Independent Samples Test
​

Independent Samples Test  

The null hypothesis Ho is rejected as there is a significant difference in the levels of Cholesterol in the treatment group compared to the placebo group.

The results of the SPSS output for the independent t-test, includes the t-statistic value, the degrees of freedom (df) and the significance value of the test (p-value). t (9.482) = df 77.828, p = 0.000.

It was found after the two interventions the cholesterol levels in the group given the cholesterol lowering drug (mean=4.94mmol/L +/- 0.75) were significantly lower than in the group given the placebo (mean=6.57 mmol/L +/-0.79), t (78) = 9.48 p=0.000.

The data shows normal distribution in the Histogram (Fig 1) plotting the Independent variable versus the dependent variable. The SPSS output for Levene’s test for equal variance, shows a value >0.05 in this case 0.654. The Ho is the variances in the different groups are equal, so we want p>0.05 and we can discard the bottom row of data in the table.   An Independent T test was run on the data with a 95% confidence Interval for the mean difference. This showed a significant difference between the total cholesterol levels in the treatment group and the placebo group. As this p value is less the 0.05 we would reject the null hypothesis of no difference between the means and state that in all probability the difference in Cholesterol levels is statistically significant. So, in all probability this result is not a chance finding. This led to rejection of the null hypothesis in favour of the alternative hypothesis.

9. State/explain the overall outcome in language for the lay reader (1 paragraph maximum).       [20%]

The overall outcome from this study is that the new drug is more effective at lowering cholesterol levels in the treatment group compare to the placebo group.  A study was performed involving 80 patients with higher than normal cholesterol levels who were randomly assigned to 2 groups (i) Placebo and (ii) Treatment (40 in each group).  The treatment group each received an equal single dose of the test drug, once a day, for a month.  The placebo group received a placebo under the same conditions.  All participants followed a prescribed healthy diet plan.  After one month the cholesterol levels of all participants was measured. At the end of the study the control group given the placebo showed a higher level of cholesterol in their blood with a mean of 6.57, while the group taking the new drug had a lower cholesterol level in their blood with a mean of 4.94. From these simple statistics it seems that the drug might work but this could be due to chance. To test this an Independent t-test is carried out using a statistical package SPSS to find out if the results are repeatable for an entire population. A high t value generated from this test indicates the results are repeatable. The t value is a ratio of the difference between two groups and the difference within the groups. A t-value of 9 was obtained and this tells you the groups are different. Every t-value has a p-value and a p value is the probability that the results from the sample data could have occurred by chance. Low p values are good and a value of 0.000 was given in the output. In most cases a p value of 0.05 or less is accepted to mean the data is valid and did not occur due to chance and ultimately the results show the new drug has the potential to lower cholesterol levels in patients with Cardiovascular disease. (Word press, 2019)

10 Comment on the design of the original study in terms of its advantages and also limitations and suggest modifications/changes.                                 [20%]

This study used a randomised control trial which gave a numerical result of the difference between the drug treatment group and the placebo group and the probability that this difference is due to the intervention rather than any other factor. The subjects were randomly assigned to one of two groups one receiving the intervention being tested and the other a control group receiving a placebo. The probability of an individual being assigned to each group is decided by chance.

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This study has the 3 major characteristics of a RCT of manipulation administering the new drug, a control condition using a control group on a placebo, and randomisation with the random assignment of participants resulting in groups equivalent in many characteristics. The participants all have higher than normal cholesterol levels and are following the same diet plan. Validity of research is assured by using a control group and randomly assigning subjects to experimental and control groups. (Kendall, 2003)

The study could be improved and strengthened by collecting data on more than one occasion at a single point in time in order to collect a body of quantitative data in connection with the two variables which are analysed for patterns of association. The cholesterol levels before the experiment takes place were not provided and no base line variable measurements performed. A further set of data could have been provided by taking cholesterol levels at another point in time or with an increase in dose of the cholesterol lowering drug. Statistical analysis using ANOVA testing could be used to compare more than 2 means. ANOVA allows significant differences between treatments as a whole to be determined. 

We do not know if the groups were balanced in all the important variables that affect the outcome for example each group needs similar proportions of men and women, young and old, similar heights and weights and physical activity. Both groups were given a diet plan to follow which indicates this variable was considered. The high levels of cholesterol in the control group would indicate the change in diet did not contribute much to cholesterol level reduction, however we do not know if all participants stuck to the diet plan or what level of physical activity they maintained therefore confounding factors were not controlled int this study.

The sample size of 80 subjects is relatively small. The number of subjects used in the trial should be ascertained to have a power of test that permits the detection of a significant difference. The study duration and size should be sufficient to apply further statistical analysis. There was no mention of follow up of all patients who entered the study to find out if there were drop outs, non-compliers or withdrawals. A Larger sample size would allow for a more accurate result as more accurate effects of treatment can be assessed and statistically analysed.

The randomisation of the patients allocated to each group should be concealed from the investigator. A stratified allocation of patients should have been performed to ensure the important baseline variable predicting outcome of high cholesterol levels and the degree of this is evenly distributed between groups. After randomisation of the patients to the groups, it is more ideal for the participants, the researchers and those performing the data analysis to not to be aware of the groups assignment.  Bias can be introduced as extra attention is given to treatment group. Double blinding of both the investigator and patient eliminates this confounding factor and is the most ideal study design. (Bhide, 2018)

A well designed randomised controlled trial evaluating an intervention provides strong evidence of a cause-effect relation. It is powerful in changing practice to improve patient’s outcome, and therefore the study design is important as a poorly designed studies could wrongly influence practice.

It is necessary to ensure the results are properly quality controlled and an operations manual followed to standardise all procedures followed. All data transferred and stored should be accurate and safely stored.

Early involvement and support of peer review and of a local ethical review committee is essential in developing correct protocol.  A questionnaire to gather statistical data about participants or interviewing of selected members to carry out more in-depth research into variables and association between variables present in individual participants that may affect the data.  Application of strict criteria for eligibility of participants can narrow outcome measures and protect against bias and confounding however it may represent an artificial setting for different patient groups and environments in which the treatment may be applied. (Kendall, 2003)

Exposing patients to an intervention believed to be inferior to the current treatment raises ethical concerns. Comparing one treatment regimen against another would be considered ethical compared to the use of a placebo (Bhide, 2018)

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