Table 1.2: Description of the quality of sample size reporting identified in published reviews of cluster randomised trials Author Reported sample size calculation % Reported appropriate sample size calculation % Donner (1990)34 NA 3/16 19% Simpson (1995)35 5/21 24% 4/21 19% Chuang (2000)36 1/24 4% 0/24 0% Isaakidis (2003)23 47/51 92% 10/51 20% Puffer (2003)37 NA 20/36 56% Eldridge (2004)25 68/152 45% 21/152 14% Varnell (2004)22 NA 9/60 15% Murray(2008)38 40/75 53% 18/75 24% Eldridge (2008)39 29/34 85% 21/34 62% Bowater (2009)40 17/35 49% 10/35 29% Handlos (2009)27 33/35 94% 25/35 71% Mdege (2010)24 8/15 53% 3/15 20% Ivers (2011)30 164/300 55% 100/300 33% Walleser (2011)41 87/106 82% 63/106 59% Froud(2012)45 21/23 91% 15/23 65% Diaz-Ordaz (2013)28 43/73 59% 20/73 27% Sutton (2013)46 NA 12/15 80%
1.5
Ordinal outcomes
1.5.1
Definition
An ordinal variable is one which consists of a set of categories which can be ordered or ranked. Disease severity (mild, moderate, severe) or measures of agreement (completely agree, agree, do not agree, disagree, do not agree at all) are examples of ordinal variables. The difference between participants in adjacent categories may not be the same, and are often unmeasurable. For example the difference in disease severity between moderate and severe could be much greater than the difference between mild and moderate.
Where the outcome consist of categories which cannot be ordered, therefore each level does not differ in magnitude for example marital status (single, married, divorced) the variable is referred to as categorical, or nominal, within this thesis.
1.5. ORDINAL OUTCOMES
1.5.2
Example of a trial with an ordinal outcome
Encouraging lifestyle changes such as smoking cessation, decreasing fat intake and increasing regular physical activity can help prevent cardiovascular disease. Visits to primary healthcare can be an opportunity for those at high risk of coronary heart disease to receive advice about changing their lifestyle. In a trial by Steptoe et al 20 general practices were randomised to lifestyle counselling or usual health promotion.56 Patients with one or more risk factors for coronary heart disease were included in the study. Each patient completed a questionnaire prior to their physician visit and four and twelve months after. This questionnaire measured a patient’s stage of motivation concerning regular exercise and patients were categorised into one of five stages of change: Pre-contemplation (patients are not eating a low-fat diet or currently exercising or are smokers, and they are not seriously considering changing behaviour), contemplation (patients are considering a change in behaviour but are not confident they will carry this out within the next month), preparation (patients are seriously planning to change behaviour and are confident that they will make changes within the next month), action (patients have changed behaviour within the last 6 months) and maintenance (patients have maintained the change for at least 6 months).
1.5.3
Sample size approaches
In the Steptoe study the authors chose to dichotomise the ordinal outcome. Those in the action and maintenance stages were combined and those in the remaining categories were combined. The benefits of using a binary outcome are: sample size and analysis methods are well established; parameter estimates are likely to be available; the dichotomised version may be more clinically relevant; and it avoids problems in the analysis caused by a small number of observations in one of the ordinal categories.
Had the authors analysed the outcome in its ordinal form they would have likely increased the power of their study, as dichotomisation of the outcome results in a loss of information. For individually randomised trials using a sample size calculation appropriate for the ordinal version of the outcome can result in trials being on average 28% smaller compared to those powered on the dichotomous version.57 It is unknown how conservative the dichotomous approach would be for the clustered case. For a cluster randomised trial there is likely to be a large cost associated with recruiting an
1.5. ORDINAL OUTCOMES
additional cluster as compared to recruiting an additional subject in an individually randomised trial. Therefore to calculate a conservative estimate of sample size could be considered wasteful. In addition to the dichotomisation approach there are two other valid approaches that can be taken to arrive at a sample size estimate. The first is to choose an alternative primary outcome for which sample size can be calculated easily. In some situations this may be a reasonable approach if several outcome measures all of clinical relevance are being considered. The Core Outcome Measures in Effectiveness Trials (COMET) initiative was set up in 2010 to develop a set of standardised core outcomes that should be measured and reported in all trials of a certain condition. The consistent use of these core outcomes in trials will ensure that more trials can be included in meta-analyses and, most importantly, as each set of proposed core outcomes were chosen to be relevant to patients, clinicians and policy makers the findings from the trial are likely to influence current practice.58 These are important justifications for the choice of outcome measure, convenience for the sample size calculation is not.
The second method is to calculate the sample size via simulation methods. It can be computationally intensive but provides a lot of flexibility, allowing full control of all parameters and so giving a closer representation of real life. The procedure involves simulating a large number of data sets, each one to represent a potential data set of results from the trial. For each simulated data set the planned analysis is conducted and the empirical power calculated as the percentage of tests where the null hypothesis is rejected. Changes in the input parameters can be made until adequate power is achieved. This is a valid approach to use for ordinal outcomes and user written commands are available in the statistical computer package Stata to aid the implementation.59 However, this approach has disadvantages in both the time taken to compile the simulation and its potential complexity. The aim of my research is to recommend an approach that is simpler to implement, even if its use is only to provide an initial benchmark estimate that may be further refined with more complex procedures.
1.5.4
The importance of this research
The literature around sample size calculations for cluster randomised trials has focused heavily on continuous and binary outcomes. There is little guidance around sample size methods for ordinal