BMJ 2014;349:g6435 doi: 10.1136/bmj.g6435 (Published 24 October 2014)
Page 1 of 2
Endgames
ENDGAMES STATISTICAL QUESTION
Randomised controlled trials: “within subject” versus “between subject” designs Philip Sedgwick reader in medical statistics and medical education Institute for Medical and Biomedical Education, St George’s, University of London, London, UK
A study investigated the effectiveness of morphine in relieving the sensation of breathlessness in patients in whom the underlying cause was maximally treated. A randomised double blind placebo controlled crossover (“within subjects”) design was used. The intervention was four days of 20 mg sustained release oral morphine or corresponding placebo. No washout period was included. Laxatives were provided as needed. Participants were 48 patients who had not previously been treated with opioids. Most of the patients had chronic obstructive pulmonary disease (42; 88%).1 The main outcome measures were dyspnoea, as measured in the morning and evening on a 100 mm visual analogue scale, plus quality of sleep and side effects. Outcome measures were recorded at the end of each four day treatment period. Participants reported significantly different dyspnoea scores when treated with morphine: an improvement of 6.6 mm (95% confidence interval 1.6 to 11.6; P=0.011) in the morning and 9.5 mm (3.0 to 16.1; P=0.006) in the evening. Participants also reported significantly better sleep during the period when taking morphine (P=0.039). Significantly more participants reported distressing constipation while taking morphine (P=0.021) despite the use of laxatives. It was concluded that sustained release oral morphine at low dosage provides significant symptomatic improvement in refractory dyspnoea. Which of the following statements, if any, are true? a) All trial participants acted as their own control
b) The crossover trial study design provided a more precise estimate of the treatment effects of oral morphine than if a “between subjects” design had been used c) Fewer subjects were needed for the “within subjects” study design than if a “between subjects” design had been used
Answers
Statements a, b, and c are all true.
The trial investigated the efficacy of oral morphine in relieving the sensation of breathlessness in patients in whom the
underlying cause was maximally treated. A randomised double blind placebo controlled crossover trial study design was used. The trial consisted of two treatment periods, and the participants received both treatments in successive order. For each patient, the order in which treatments were received—20 mg sustained release oral morphine followed by placebo, or vice versa—was determined at random. Each treatment period lasted for four days. The design did not include a washout period. The purpose of a washout period in a crossover trial is to minimise any carryover of effects, including pharmacological and psychological ones, of the treatment received in the first period to the second treatment period. To avoid any potential carryover of effects confounding the results in the above study, treatments were compared in outcome measures at the end of each treatment period. The crossover trial study design is described as a “within subjects” or “within group” study design. The study design is typically used when the condition being investigated is chronic and treatment is for the short term relief of symptoms rather than to provide a cure. Crossover trials have been described in detail in a previous question.2 Other types of “within subjects” design have been described in previous questions, including the “n of 1” trial study design.3
In the above study, patients received both morphine and placebo. The outcome measurements were therefore paired, and the effectiveness of oral morphine was compared with placebo within each patient. Hence, each participant acted as his or her own control (a is true). It would have been possible to investigate the effectiveness of oral morphine for the management of refractory dyspnoea using a “between subjects” randomised placebo controlled trial study design. Participants would have been randomly allocated to oral morphine or placebo, and in contrast to a “within subjects” design, they would have received the same treatment for the entire study period. The placebo group would have acted as the control. At the end of follow-up, the treatments would have been compared in their effectiveness by comparing the outcomes between the
[email protected] For personal use only: See rights and reprints http://www.bmj.com/permissions
Subscribe: http://www.bmj.com/subscribe
BMJ 2014;349:g6435 doi: 10.1136/bmj.g6435 (Published 24 October 2014)
Page 2 of 2
ENDGAMES
two independent groups of patients. A “between subjects” study design is sometimes referred to as a “between groups” design.
In the above study, the crossover study design provided a more precise estimate of the treatment effect of morphine than if a “between subjects” design had been used (b is true). This was because morphine and placebo were compared within individual patients. Because the difference in outcome between treatments was measured within patients, any natural biological variation in the measurements was removed. Furthermore, because the outcome measurements between treatments were paired, any potential confounding was removed. By contrast, the randomisation of participants to treatment groups for a “between subjects” study design will minimise but not necessarily remove confounding; any effects of confounding will be reduced as sample size increases. Confounding in clinical trials has been described in a previous question.4 Because the crossover trial provides a more precise estimate of the treatment effect than a “between subjects” trial design, the sample size needed to observe the smallest effect of clinical interest when comparing treatments is smaller than for a “between subjects” design (c is true). Sample size calculations in trials have been described in a previous question.5 The crossover trial study design is prone to methodological problems that would not arise if a “between subjects” design were used. In the above study patients dropped out after the first treatment period in both treatment groups and therefore did not receive the second treatment. Drop out may be related to side effects as in any trial. However, if patients do not receive the second treatment then the outcome measurements recorded in the first period will probably not be included in the analysis, limiting the available data and therefore statistical power of the trial. Statistical power has been described in a previous question.6 A treatment period interaction may also exist in crossover trials—that is, a systematic difference between the
For personal use only: See rights and reprints http://www.bmj.com/permissions
treatment periods in the outcome scores for a treatment. The researchers did not report whether a significant period interaction existed. However, if an interaction had existed, the outcome measures for patients who received—for example, morphine in the first treatment period—would have differed (either better or worse) from those seen in patients who received morphine in the second period. If the period effect is sufficiently large enough, the outcome measurements recorded for the second period in a crossover trial may have to be discarded. If so, the statistical power of the trial would be severely reduced. As described, a “within subjects” design provided a more precise estimate of the treatment effect of morphine than would have been the case if a “between subjects” design had been used. It was important that the paired nature of the data was accounted for during statistical analysis, because statistical power would be reduced if it were ignored. Statistical tests to compare two related treatment groups in paired outcome measurements have been described in previous questions.7 8 Competing interests: None declared. 1 2 3 4 5 6 7 8
Abernethy AP, Currow DC Frith P, Fazekas BS, McHugh A, Bui C. Randomised, double blind, placebo controlled crossover trial of sustained release morphine for the management of refractory dyspnoea. BMJ 2003;327:523. Sedgwick P. What is a crossover trial? BMJ 2014;348:g3191. Sedgwick P. What is an “n-of-1” trial? BMJ 2014;348:g2674. Sedgwick P. Confounding in clinical trials. BMJ 2012;345:e7951. Sedgwick P. Sample size: how many participants are needed in a trial? BMJ 2013;346:f1041. Sedgwick P. The importance of statistical power. BMJ 2013;347:f6282. Sedgwick P. Parametric statistical tests for two related groups: numerical data. BMJ 2014;348:g124. Sedgwick P. Non-parametric statistical tests for two related groups: numerical data. BMJ 2012;344:e2537.
Cite this as: BMJ 2014;349:g6435 © BMJ Publishing Group Ltd 2014
Subscribe: http://www.bmj.com/subscribe
Page 1 of 2
Endgames
ENDGAMES STATISTICAL QUESTION
Randomised controlled trials: “within subject” versus “between subject” designs Philip Sedgwick reader in medical statistics and medical education Institute for Medical and Biomedical Education, St George’s, University of London, London, UK
A study investigated the effectiveness of morphine in relieving the sensation of breathlessness in patients in whom the underlying cause was maximally treated. A randomised double blind placebo controlled crossover (“within subjects”) design was used. The intervention was four days of 20 mg sustained release oral morphine or corresponding placebo. No washout period was included. Laxatives were provided as needed. Participants were 48 patients who had not previously been treated with opioids. Most of the patients had chronic obstructive pulmonary disease (42; 88%).1 The main outcome measures were dyspnoea, as measured in the morning and evening on a 100 mm visual analogue scale, plus quality of sleep and side effects. Outcome measures were recorded at the end of each four day treatment period. Participants reported significantly different dyspnoea scores when treated with morphine: an improvement of 6.6 mm (95% confidence interval 1.6 to 11.6; P=0.011) in the morning and 9.5 mm (3.0 to 16.1; P=0.006) in the evening. Participants also reported significantly better sleep during the period when taking morphine (P=0.039). Significantly more participants reported distressing constipation while taking morphine (P=0.021) despite the use of laxatives. It was concluded that sustained release oral morphine at low dosage provides significant symptomatic improvement in refractory dyspnoea. Which of the following statements, if any, are true? a) All trial participants acted as their own control
b) The crossover trial study design provided a more precise estimate of the treatment effects of oral morphine than if a “between subjects” design had been used c) Fewer subjects were needed for the “within subjects” study design than if a “between subjects” design had been used
Answers
Statements a, b, and c are all true.
The trial investigated the efficacy of oral morphine in relieving the sensation of breathlessness in patients in whom the
underlying cause was maximally treated. A randomised double blind placebo controlled crossover trial study design was used. The trial consisted of two treatment periods, and the participants received both treatments in successive order. For each patient, the order in which treatments were received—20 mg sustained release oral morphine followed by placebo, or vice versa—was determined at random. Each treatment period lasted for four days. The design did not include a washout period. The purpose of a washout period in a crossover trial is to minimise any carryover of effects, including pharmacological and psychological ones, of the treatment received in the first period to the second treatment period. To avoid any potential carryover of effects confounding the results in the above study, treatments were compared in outcome measures at the end of each treatment period. The crossover trial study design is described as a “within subjects” or “within group” study design. The study design is typically used when the condition being investigated is chronic and treatment is for the short term relief of symptoms rather than to provide a cure. Crossover trials have been described in detail in a previous question.2 Other types of “within subjects” design have been described in previous questions, including the “n of 1” trial study design.3
In the above study, patients received both morphine and placebo. The outcome measurements were therefore paired, and the effectiveness of oral morphine was compared with placebo within each patient. Hence, each participant acted as his or her own control (a is true). It would have been possible to investigate the effectiveness of oral morphine for the management of refractory dyspnoea using a “between subjects” randomised placebo controlled trial study design. Participants would have been randomly allocated to oral morphine or placebo, and in contrast to a “within subjects” design, they would have received the same treatment for the entire study period. The placebo group would have acted as the control. At the end of follow-up, the treatments would have been compared in their effectiveness by comparing the outcomes between the
[email protected] For personal use only: See rights and reprints http://www.bmj.com/permissions
Subscribe: http://www.bmj.com/subscribe
BMJ 2014;349:g6435 doi: 10.1136/bmj.g6435 (Published 24 October 2014)
Page 2 of 2
ENDGAMES
two independent groups of patients. A “between subjects” study design is sometimes referred to as a “between groups” design.
In the above study, the crossover study design provided a more precise estimate of the treatment effect of morphine than if a “between subjects” design had been used (b is true). This was because morphine and placebo were compared within individual patients. Because the difference in outcome between treatments was measured within patients, any natural biological variation in the measurements was removed. Furthermore, because the outcome measurements between treatments were paired, any potential confounding was removed. By contrast, the randomisation of participants to treatment groups for a “between subjects” study design will minimise but not necessarily remove confounding; any effects of confounding will be reduced as sample size increases. Confounding in clinical trials has been described in a previous question.4 Because the crossover trial provides a more precise estimate of the treatment effect than a “between subjects” trial design, the sample size needed to observe the smallest effect of clinical interest when comparing treatments is smaller than for a “between subjects” design (c is true). Sample size calculations in trials have been described in a previous question.5 The crossover trial study design is prone to methodological problems that would not arise if a “between subjects” design were used. In the above study patients dropped out after the first treatment period in both treatment groups and therefore did not receive the second treatment. Drop out may be related to side effects as in any trial. However, if patients do not receive the second treatment then the outcome measurements recorded in the first period will probably not be included in the analysis, limiting the available data and therefore statistical power of the trial. Statistical power has been described in a previous question.6 A treatment period interaction may also exist in crossover trials—that is, a systematic difference between the
For personal use only: See rights and reprints http://www.bmj.com/permissions
treatment periods in the outcome scores for a treatment. The researchers did not report whether a significant period interaction existed. However, if an interaction had existed, the outcome measures for patients who received—for example, morphine in the first treatment period—would have differed (either better or worse) from those seen in patients who received morphine in the second period. If the period effect is sufficiently large enough, the outcome measurements recorded for the second period in a crossover trial may have to be discarded. If so, the statistical power of the trial would be severely reduced. As described, a “within subjects” design provided a more precise estimate of the treatment effect of morphine than would have been the case if a “between subjects” design had been used. It was important that the paired nature of the data was accounted for during statistical analysis, because statistical power would be reduced if it were ignored. Statistical tests to compare two related treatment groups in paired outcome measurements have been described in previous questions.7 8 Competing interests: None declared. 1 2 3 4 5 6 7 8
Abernethy AP, Currow DC Frith P, Fazekas BS, McHugh A, Bui C. Randomised, double blind, placebo controlled crossover trial of sustained release morphine for the management of refractory dyspnoea. BMJ 2003;327:523. Sedgwick P. What is a crossover trial? BMJ 2014;348:g3191. Sedgwick P. What is an “n-of-1” trial? BMJ 2014;348:g2674. Sedgwick P. Confounding in clinical trials. BMJ 2012;345:e7951. Sedgwick P. Sample size: how many participants are needed in a trial? BMJ 2013;346:f1041. Sedgwick P. The importance of statistical power. BMJ 2013;347:f6282. Sedgwick P. Parametric statistical tests for two related groups: numerical data. BMJ 2014;348:g124. Sedgwick P. Non-parametric statistical tests for two related groups: numerical data. BMJ 2012;344:e2537.
Cite this as: BMJ 2014;349:g6435 © BMJ Publishing Group Ltd 2014
Subscribe: http://www.bmj.com/subscribe
