Assessment Task -
You become interested in the non-skeletal effects of vitamin D and review the literature. On the basis of your reading you find that there is some evidence to suggest that vitamin D deficiency is linked to chronic lung disease. On further reading you come across the large cross-sectional study by Black and Scragg (2005, Chest; 128:3792) showing that low vitamin D levels are associated with poor lung function. On the basis of this prior evidence you decide to conduct a small randomised controlled trial to determine the effect of vitamin D supplementation (versus a placebo) on the FEV1/FVC ratio (a measure of airway obstruction) in "healthy" adults.
Q1. Formulate a null and alternative hypothesis for your study.
Having established your hypothesis, you begin to refine your "population of interest". You have already decided to focus on "healthy" adults so you have a series of exclusion criteria that eliminate people from your study with existing acute (e.g. virus/infection) or chronic (e.g. asthma, heart disease etc) conditions. You also have a limited budget for your study so you decide to limit the population to female adults (18-25 years of age) living in Hobart with circulating 25(OH)D levels < 50 nmol/L (i.e. they have existing vitamin D deficiency).
Q2. What are the advantages and disadvantages of having such a selective population?
Having decided on your population, you manage to recruit a random sample of 20 individuals to your study and randomise them to receive either weekly doses of 120,000IU of vitamin D or placebo for 4 weeks. One week after the final dose you measure the participants' lung function and obtain the following data:
|
Vitamin D
|
Placebo
|
|
FEV1(L)
|
FEV1/FVC
|
FEV1(L)
|
FEV1/FVC
|
|
3.6
|
0.87
|
3.7
|
0.93
|
|
4.9
|
0.74
|
3.9
|
1.01
|
|
3.5
|
0.80
|
3.3
|
0.88
|
|
4.6
|
0.85
|
3.5
|
0.94
|
|
3.6
|
0.91
|
4.6
|
0.84
|
|
3.6
|
0.90
|
3.6
|
0.87
|
|
3.8
|
0.72
|
4.9
|
0.92
|
|
3.4
|
0.86
|
3.4
|
0.98
|
|
3.6
|
0.94
|
4.7
|
0.97
|
|
4.7
|
0.81
|
3.5
|
0.79
|
Q3. Calculate the mean, median and standard deviation of the FEV1 for the two groups.
Q4. Based on the relationship between the mean and median of the FEV1 data what can you say about the skewness of these data?
Q5. Calculate the median, interquartile range (IQR) and range for FEV1/FVC ratio for both groups and draw two box plots (on the same graph) showing these data.
Q6. Based on these box plots, are the data for FEV1/FVC substantially skewed?
Q7. Conduct an appropriate statistical test to compare the mean FEV1/FVC ratios between the vitamin D treated group and the placebo group and report i) the value for the test statistic, ii) the P-value and iii) the degrees of freedom.
Q8. What can you conclude from this test?
Someone with a much larger budget manages to conduct a study that recruits every "healthy" vitamin D deficient adult in the country and repeats your trial comparing the effect of vitamin D supplementation on the FEV1/FVC ratio. They analyse their data and find the mean(SD) of the FEV1/FVC ratio for the vitamin D supplemented group and placebo group were 0.86(0.12) and 0.85(0.13) respectively with a P - value of 0.78.
Q9. Explain what type of error is likely to have occurred in your study.