Title: Statistical analysis of an iron study

Key words: statistical analysis, statistical significance, patients, study, probability, ferritin, minimum number, 5% level, statistical power, iron intake, supplements,

Date: Sept 2006

Category: Measurements

Nutrimed Module:

Type: Article

Author: Morgan, G

**Statistical analysis of an iron study **

In the given example, to determine the number of patients needed in the study for it to reach statistical significance (P<0.05), if the power of the study was 80%, the following formula could be used:

n = __2 sigma ^{2} (Z
alpha/2 + Z beta )^{2}__

d^{2}

Substituting, with a probability of 5%, P = 0.05, Z alpha/2 =1.96 Power = 80% = 0.8 =1- beta, i.e. beta = 0.2= probability of making a Type II error and Z beta = 0.84 (from tables).

(Z alpha/2 + Z beta)^{2} = 7.85

Therefore, n = __2 X 5.4 ^{2} X 7.85 __

3^{2}

= 50.86

A minimum number of 51 patients are therefore required to show a statistically significant rise of ferritin of 3 mcg/l. If there were only resources to do a study on 30 patients, then the power of the study would diminish. Z beta, the number of standard deviations from the norm defining the probability of making a Type II error, can be deduced using the formula:

Z beta = __d √n/2__ _ Z
alpha/2

Sigma

i.e. Z beta = __3 √30/2__ _ 1.96 = 0.19

5.4

From tables: Z beta = 0.19, Beta = 0.425 and 1 - Beta = 0.575

The power of the study if only 30 patients were used would therefore be 57.5% With only 30 patients, if a power of 80% was required, the difference between the population means, d, would have to increase for this to be statistically significant at the 5% level.

The initial formula could be used, i.e

n = __2 sigma ^{2} (Z alpha/2 + Z beta )__

d^{2}

i.e. d^{2} = __2 X 5.4 ^{2} X (1.96 + 0.84)^{2}__

30

= 15.24 i.e. d = 3.90

Therefore, with only 30 patients in the study, with a power of 80%, a ferritin level difference between the population means of 4 mcg/l would need to be detected if the study was to approach a statistical significance of 5%. Assuming that the two groups were evenly matched and both had a normal distribution and the same standard deviations of their means, the only way to achieve this greater sensitivity and improve the chances of a successful outcome to the study would be to increase the iron intake of the supplemented group. Given the 6 month time limit of the study, it is unlikely that extending the length of this period would increase the response of the treated group.

Assuming that the response was dose related, the logical solution would be to increase the daily dose of the iron supplement by increasing the Kellogg’s breakfast bar allowance from one to two or more a day. This would increase the chances of detecting significant changes in ferritin levels.

References

1. Nelson M. (2001) Lecture notes. Surrey University

2. Riffenburgh RH. (1999) Statistics in Medicine. Academic Press, New York