Excess Body Weight and Sleep Apnea

Research conducted by: Kari Johansson, Erik Hemmingsson, Richard Harlid, Ylva Trolle Lagerros, Fredrik Granath, Stephan Rössner, and Martin Neovius

Statistical article authored by: Philip Sedgwick

Case study prepared by: Robert F. Houser and Georgette Baghdady

Overview
In his statistical article, “Standard deviation versus standard error,” UK researcher Philip Sedgwick presents us with an interesting discussion of the proper use of standard deviation (SD) and standard error of the mean (SEM).  He uses an example of a weight loss study of 63 obese men suffering from obstructive sleep apnea who were being treated with continuous positive airway pressure (CPAP).  The weight loss program lasted one year.  Outcome measures included change in body weight measured in kilograms (kg).

More than 60% of people experiencing obstructive sleep apnea are obese.  CPAP therapy is the most common treatment.  It uses a machine and mask to prevent the airway from collapsing, thus enabling a person to breathe more easily during sleep.  Weight loss is an effective treatment for sleep apnea.


Questions to Answer
What is the proper use of the SD?  What is the proper use of the SEM?

Design Issues
None for the Sedgwick article.

Descriptions of Variables
Variable Description
Weight

Body weight at baseline in kg
Weight change Change in body weight at one year from baseline in kg


References

Sedgwick, P. (2011). Standard deviation versus standard error. BMJ, 343, d8010.

Johansson, K., Hemmingsson, E., Harlid, R., Lagerros, Y. T., Granath, F., Rössner, S., Neovius, M. (2011). Longer term effects of very low energy diet on obstructive sleep apnoea in cohort derived from randomised controlled trial: prospective observational follow-up study. BMJ, 342, d3017.


Links

What Is Sleep Apnea?
t Table (two-tailed) for significance and calculation of confidence interval
Johansson et al. article


Exercises

Please perform the following exercises first, and then read the Sedgwick article to check your answers.  Also, please read the original research article by Johansson et al.

Exercises contain quotes and notes from Sedgwick’s article.

  1. “At baseline the sample had a mean weight of 113.1 kg (SD=14.2 kg).”
    1. At baseline the sample had a mean weight of ____ pounds.
    2. Approximately 68% of the sample had a weight at baseline that was no further than one standard deviation away from the sample mean—that is, from ____ kg to ____ kg.
    3. Approximately 95% of the sample had a weight at baseline that was no further than two standard deviations away from the sample mean—that is, from ____ kg to ____ kg.
    4. Approximately 99% of the sample had a weight at baseline that was no further than three standard deviations away from the sample mean—that is, from ____ kg to ____ kg.

  2. There was a statistically significant decrease in body weight from baseline to the weight assessment one year later for the 63 men.  “The mean change in body weight at one year from baseline was a reduction of 12.1 kg (95% confidence interval 9.8 to 14.3) (SD=9 kg; SEM=1.13 kg).”
    1. The mean change in body weight at one year from baseline was a reduction of ____ pounds.
    2. How did the researchers obtain a SEM of 1.13?
    3. How did the researchers obtain a 95% CI of 9.8 to 14.3?
    4. It is estimated with 95% confidence that the mean weight loss after being on the weight loss program for one year for the entire population could be as little as ____ kg or as much as ____ kg.

  3. Perform a t test for a single mean comparing the mean change in body weight (M=12.1 kg, SD=9 kg) with zero change.
    1. What is t?
    2. What is the degrees of freedom (df)?
    3. At what level is t statistically significant?

  4. “The weight loss programme lasted one year and consisted of a very low energy diet for nine weeks followed by a weight loss maintenance programme.”  How could the study design be improved in order to strengthen the evidence of a cause-and-effect relationship between the weight loss program and the reduction in body weight?

  5. In the article, Sedgwick asks …

“Which of the following, if any, are true?”  (pick all that apply)

    1. “The standard deviation of body weight at baseline provides a measure of the spread of observations of weight in the sample before participants began the weight loss programme.”
    2. “At baseline, approximately 95% of sample members had a body weight that was within two standard deviations of the sample mean.”
    3. “The standard error of the mean change in body weight at one year provides a measure of precision of the sample mean as an estimate of the population parameter.”
    4. “After one year on the weight loss programme, 95% of the population would have a reduction in body weight between 9.8 kg and 14.3 kg.”