The effects of alternative study designs on the power of community randomized trials: evidence from three studies of human immunodeficiency virus prevention in East Africa

Jim Todd1, Lucy Carpenter2, Xianbin Li3, Jessica Nakiyingi4, Ron Gray3 and Richard Hayes1

1 London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK.
2 Department of Public Health, Institute of Health Sciences, University of Oxford, Old Road, Oxford OX3 7LF, UK.
3 Johns Hopkins University, Bloomberg School of Public Health, 615 N Wolfe Street, Baltimore, MD 21205, USA.
4 MRC Programme on AIDS in Uganda, PO Box 49, Entebbe, Uganda.

Jim Todd, ITD, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, UK. E-mail: jim.todd{at}lshtm.ac.uk


    Abstract
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 Statistical methods
 Results
 Discussion
 References
 
Background Randomized intervention trials in which the community is the unit of randomization are increasingly being used to evaluate the impact of public health interventions. In the design of community randomized trials (CRT), the power of the study is likely to be affected by two issues: the matching or stratification of communities, and the number and size of the communities to be randomized.

Methods Data from three East African community intervention trials, designed to evaluate the impact of interventions to reduce human immunodeficiency virus (HIV) incidence, are used to compare the efficiency of different trial designs.

Results Compared with an unmatched design, stratification reduced the between-community variation in the Mwanza trial (from 0.51 to 0.24) and in the Masaka trial (from 0.38 to 0.28). The reduction was smaller in the Rakai trial where the selected communities were more homogeneous (from 0.15 to 0.11). For all trials, individual matching of communities produced estimates of between-community variation similar to those from the stratified designs. The linear association between HIV prevalence and incidence was strong in the Mwanza trial (correlation coefficient R = 0.83) and the Masaka trial (R = 0.83), but weak in the Rakai trial (R = 0.28). Unmatched study designs that use smaller communities tend to increase between-community variation, but reduce the design effect and improve study power.

Conclusions These empirical data suggest that selection of homogeneous communities, or stratification of communities prior to randomization, may improve the power of CRT.


Keywords Intervention studies, community-randomized, between-community variance, sample size, stratification, matching, power, study design, HIV

Accepted 12 February 2003

Randomized controlled trials, in which groups of individuals (e.g. communities) are the units of randomization, are increasingly being used to evaluate the impact of public health interventions.1 Recently, a number of community randomized trials (CRT) have been undertaken to examine the effectiveness of different interventions in reducing human immunodeficiency virus (HIV) incidence in East Africa. Interventions used in these studies include intensifying the treatment and management of other sexually transmitted diseases (STD), which are known to enhance the spread of HIV, and community-wide education programmes that aim to bring about change in sexual behaviour.2 For studies such as these, where interventions need to be implemented at the community level, the CRT study design is usually the most logical choice. Use of this study design has important implications for sample size determination and the analysis of the results, but these issues are often overlooked.3

The number of communities included in CRT is usually small, as the cost of enrolling each community is often high. Randomizing a smaller number of units increases the risk of an imbalance in the intervention and control arms with respect to known risk factors for the outcome of interest. In order to overcome this problem, investigators using CRT designs often match communities on important risk factors prior to randomization.4–8 Much discussion has been generated on the advantages and disadvantages of matching in community intervention trials.4,5,8,9 By reducing the imbalance on known baseline risk factors for the outcome, matching can increase the credibility of the study to a critical scientific readership. However, communities should only be matched on factors known to be highly correlated with the outcome of interest.10 Inappropriate or inadequate matching can reduce the power of the study to detect a real effect, and hence care should be exercised in the choice of matching criteria.9

In CRT where prevalence or incidence of a disease is the outcome of interest, the between-community variation in the event rate is an important factor in determination of sample size and statistical power.11 Matching (or stratifying) affects the statistical power of the study and this needs to be taken into account in sample size determination. Other things being equal, matching or stratifying communities on important risk factors prior to randomization should result in a decrease in between-community variation compared with an unmatched study. The overall effect on statistical power, however, depends on whether this decrease is sufficient to offset the loss in degrees of freedom from using a matched or stratified study design.4

In some settings there may be a choice in the size of the community to be randomized. On purely statistical grounds, the randomization of a larger number of smaller units is preferable to randomizing a small number of large communities as the design effect will be smaller.11 A further advantage of using a large number of smaller units is that there may be less need for prior matching or stratification. Against this must be weighed the fact that smaller communities are likely to have larger between-community variation. Also smaller communities may result in higher levels of contamination from individuals outside of the community.2

While simulation experiments have been performed to examine the impact of stratification and size of randomization unit on estimates of between-community variation,9,10 few empirical data have been reported. The data from three CRT implemented to evaluate HIV prevention in East Africa have been used to examine the effect of matching or stratification of the randomization units on the between-community variation in HIV prevalence and incidence. This paper also examines how the size of the community affects the coefficient of variation and design effect in these CRT.


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 Methods
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An overview of the three trials is shown in Table 1Go.


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Table 1 Overview of three community randomized trials to assess the impact of different interventions on the incidence of human immunodeficiency virus (HIV) in East Africa
 
The CRT in rural Mwanza, conducted between 1991 and 1994, assessed the impact of improved syndromic management of STD on HIV incidence in a cohort of 12 500 adults.12 Twelve communities were used with approximately 1400 person years of follow-up in each. The communities were matched into six pairs, based on the type of community, geographical location, and the number of STD patients treated in the health centre. In each pair, one community was randomly assigned to the intervention and the other acted as a control community.13 Within each community, random cluster sampling was used to identify households and all adults aged 15–54 years were enrolled into the trial. The study was designed to detect a 50% decrease in the HIV incidence with 80% power, assuming an initial annual incidence of 1.0%, and a coefficient of variation between communities of 0.25. Data on HIV prevalence at baseline, and for incidence during the 2-year period of follow-up, are available for the communities and for the smaller clusters within each community.

The Masaka trial was a three-arm CRT, conducted between 1994 and 2000 to assess the effectiveness of an information, education, and communication (IEC) programme aimed at modifying sexual behaviour, with and without improved syndromic management of STD as implemented through existing government health units.14,15 Eighteen parishes were selected for the study and, prior to randomization, were matched into six triplets according to the type of road passing through the parish (major, secondary, or no secondary road), distance from Masaka town (<20 km, 20–40 km, >40 km) and quality of health facility (subjectively graded +, ++, or +++). There were three arms to the trial: arm A parishes received IEC alone, while those in arm B received IEC together with improved syndromic management of STD, and arm C was the control arm where parishes received general community development activities.14 All study parishes contained a government health unit and all adults (aged >=13 years) residing in the two to five villages closest to the health unit were enrolled into the study so as to achieve a target study population of 750 adults per parish. This study was designed to detect a 50% reduction in HIV incidence in either intervention arm compared with the control arm assuming a background annual incidence rate of 1.5%, 80% power, and a coefficient of variation of 0.25.14,15 Data on HIV prevalence at baseline, and for HIV incidence, are available for the communities and for the smaller villages within each community.

The Rakai trial was a two-arm CRT, conducted between 1994 and 1998 to evaluate the effectiveness of mass, presumptive STD treatment on STD rates, HIV incidence, and maternal– infant health.16 The presumptive STD treatment was provided to all consenting adults aged 15–59 in the intervention communities, and mass treatment with anti-helminthics and vitamins was provided in the control communities. From prior epidemiological studies in Rakai District, 56 small communities with HIV prevalence and incidence data were aggregated into 10 larger communities.16,17 Each larger community approximated a social and presumably a sexual network. Predicted HIV incidence and prevalence were used to stratify the 10 communities into three strata, and randomization was conducted within strata to obtain 5 intervention and 5 control communities per arm. All consenting individuals in randomized communities were enrolled and followed-up. The study was designed to detect a 35% reduction in HIV incidence, estimated at 1.5–2.0%, with a coefficient of variation of 0.15. Data on HIV prevalence and incidence are available for each of the 10 larger communities.

Two studies employed an individually matched design: matched pairs in Mwanza and matched triplets in Masaka. The Rakai study used randomization within strata, but communities were retrospectively matched into pairs for the analysis. The present analysis estimates the coefficient of variation for HIV prevalence and HIV incidence in these studies. The coefficient of variation of baseline HIV prevalence is used to compare the expected power for alternative study designs—unmatched and individually matched study designs for all three studies and a stratified study design for the Mwanza and Masaka trials. The strata for the Mwanza study were formed using the type of community: islands (two communities), roadside (two communities) and rural (eight communities), and for the Masaka trial using the baseline prevalence of HIV (high, medium, and low).


    Statistical methods
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Sample size formulae for randomized trials where individuals are the unit of randomization have been amended to give the number of communities required where whole communities are randomized.2 For an unmatched study, the number of communities, c, required in each arm is given approximately as:



where {lambda}0 and {lambda}1 are the average incidence rates across communities in the control and intervention arms respectively, y is the average person-years of observation in each community (assumed roughly equal in each community), k is the coefficient of variation (standard deviation/mean) of the (true) incidence rates between communities (assumed the same in each arm), and z{alpha}/2 and zß are the standard normal deviates corresponding to the required significance level ({alpha}) and power (1 – ß) of the trial.

For any given trial, it is possible to rewrite the above equation to obtain the power of the study for the trial outcome.



For study designs involving strata or matched pairs of communities, the above formula can be used with two modifications. The constant 1 is replaced with 2 and k is replaced with km, where km is the between-community coefficient of variation of incidence rates within the matched strata in the absence of intervention, where strata consist of two or more communities.11

From this formula the importance of calculating the true between-community variance of the rates is shown. To calculate k, a random effects model is assumed where the number of events in each community is assumed to follow a Poisson distribution. Under this model, following the notation of Hayes and Bennett,11 the between-community variance, {sigma}b2, is estimated as:



where s2 is the empirical (observed) between-community variance, r is the overall incidence rate computed from all communities combined, yj is the person-years at risk in community j, and m is the total number of communities used in the analysis. The empirical between-community variance, s2 is estimated as:



where rj is the observed incidence rate in community j and is the average of the community-specific rates. The coefficient of variation, k, is obtained as b/r.

For stratified studies (communities matched into strata) the same steps apply, but each stratum will have a different expected rate. In this case the formula should be applied for each stratum separately (for i = 1 through t, the number of strata in the study), which gives the following estimate for {sigma}b2:



where in stratum i, mi is the number of communities, ri is the rate, si2 the between-community variance, and t is the number of strata. For stratified designs, km can be obtained in the same way b/r, where r is the overall incidence rate computed from all communities combined. Note that the matched pair study design is a special case of the stratified design with mi = 2 for all strata.

For prevalence surveys where the outcome of interest is a proportion and the within-community variation is assumed to be binomial, an analogous result is obtained for the calculation of k and km.11 The between-community variation can be calculated by subtracting the sum of the within-community binomial variance from the empirical observed variance of the proportions. For the unmatched study this becomes:



where p is the overall proportion of interest, nj is the number of individuals in community j, and the other notation as before. The coefficient of variation, k, is given as b/p.

The design effect for any study design represents the increased size of the study compared with a design that randomizes individual subjects.18 We have calculated the design effect for all three studies by comparing the actual sample size used in these trials with a design using individual randomization.


In HIV prevention trials, baseline HIV prevalence is sometimes used as a proxy for HIV incidence when estimating between-community variation and calculating power and sample size at the design stage. We applied the above methods for prevalence measures to observed HIV prevalences in the three trials in East Africa, to compare the coefficient of variation, design effect, and power for three alternative study designs. We then applied the methods for incidence rates to the observed HIV incidence in the three trials to calculate the actual coefficient of variation during follow-up, assuming an unmatched study design.

To evaluate the use of baseline prevalence as a proxy for incidence, Pearson correlation coefficients were used to assess the strength of linear relationship between prevalence and incidence rates. In all three trials, the correlation coefficient was calculated separately for the intervention and control arms and the mean of the separate correlation coefficients is presented.

The intraclass correlation coefficient (ICC) is defined as the ratio of the between-cluster variance to the total variance.19,20 Although ICC have been used extensively to compare study designs for quantitative data and proportions, there is no corresponding definition of ICC for rates based on person-years analysis.21 For proportions, using the previously defined notation with p as the overall prevalence across all communities, the ICC was calculated as:



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 Statistical methods
 Results
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 References
 
Effect of stratification
The average prevalence of HIV estimated from the baseline survey round in the 12 communities included in the Mwanza intervention trial was 4.1%, (range: 1.5–8.7%). For the unmatched study design, the coefficient of variation for HIV prevalence was 0.51 giving a design effect of 4.37 and a power of 40% (Table 2Go). Stratifying communities into three strata (roadside, islands, and rural) dramatically reduced the between-community variance. The coefficient of variation was halved to 0.24, giving a design effect of 2.00 and a power of 66%. Using the matched pairs study design gave a very similar coefficient of variation of 0.25, but the design effect was larger at 2.36, and the power lower at 64%. Across the three study designs, the ICC was 0.0109 for the unmatched design, 0.0025 for the stratified design, and 0.0027 for the matched pairs design (Table 2Go).


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Table 2 The effect of matching on the coefficient of variation, intraclass correlation coefficient, design effect and power of trial designs for the Mwanza, Masaka, and Rakai trials, using baseline human immunodeficiency virus (HIV) prevalence as a proxy for the outcome of interest
 
Average prevalence of HIV in the baseline survey of the 18 communities included in the Masaka trial was 9.8% (range: 4.1–20.6%). For the unmatched study design, the coefficient of variation for HIV prevalence was 0.37, giving a design effect of 5.55, and a power of 67%. Stratification of the communities into three strata of six communities reduced the coefficient of variation to 0.27, giving a design effect of 3.63 and increasing the power of the study to 78%. Using a study design with matched triplets, the coefficient of variation was slightly more than for the stratified design at 0.30, the design effect 4.68, and a power of 71% (Table 2Go). One of the matched triplets showed a substantial imbalance in HIV prevalence and if this triplet was removed then the coefficient of variation would have been reduced to 0.18, a gain of 50% over the unmatched study design. The ICC was 0.0152 for the unmatched design, 0.0080 for the stratified design, and 0.0099 for the individually matched design.

In the baseline survey of the 10 clusters in the Rakai trial the average prevalence of HIV was 15.1% (range: 12.1–19.8%) which was substantially higher than in the other 2 trials. The Rakai communities were selected to be relatively homogeneous, and consequently in the unmatched design the coefficient of variation was 0.15, the design effect was 1.84, and the power of the study 67% (Table 2Go). Using a pair matched design gave a coefficient of variation of 0.11, a design effect of 1.62, and a power of 61%. The ICC for the two study designs was 0.0039 for the unmatched design, and 0.0024 for the individually matched design.

Prevalence versus incidence
HIV incidence rates in the Mwanza trial were 5.9 per 1000 person-years at risk for the intervention arm and 9.5 per 1000 for the control arm communities. Assuming an unmatched study design, estimates of the between-community variance for HIV incidence in the Mwanza trial were obtained separately for each arm and then pooled to obtain combined estimates controlling for the effect of the intervention (Table 3Go). The coefficient of variation for incidence in the intervention arm was somewhat higher than that for the control arm, but the combined estimate of 0.50 was very similar to that for baseline HIV prevalence in the unmatched study design. In the Mwanza trial there was a strong correlation (R = 0.83) between HIV prevalence at baseline and HIV incidence in the 12 communities (Figure 1aGo).


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Table 3 The coefficient of variation for human immunodeficiency virus (HIV) incidence in the Mwanza, Masaka, and Rakai community randomized intervention trials assuming an unmatched study design
 


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Figure 1 (A) Incidence and prevalence of human immunodeficiency virus (HIV) in 12 communities in the Mwanza trial: by arm of trial; (B) Incidence and prevalence of human immunodeficiency virus (HIV) in 18 communities in the Masaka trial: by arm of trial; (C) Incidence and prevalence of human immunodeficiency virus (HIV) in 10 communities in the Rakai trial: by arm of trial

 
Overall HIV incidence in the Masaka trial was 7.8 per 1000 person-years at risk, with no significant difference between the three arms of the trial. The overall estimate of between-community variation was similar in all three arms, with the overall coefficient of variation for HIV incidence (k = 0.53) higher than for baseline HIV prevalence (k = 0.37) (Table 3Go). There was a strong correlation (R = 0.83) between HIV prevalence and HIV incidence in the 18 communities (Figure 1bGo). However, two communities had a very high prevalence and incidence of HIV, and if these communities were excluded the correlation was reduced (R = 0.55).

In Rakai, overall HIV incidence was 17 per 1000 person-years (Table 3Go). There was a low correlation between baseline HIV prevalence and HIV incidence on follow-up (R = 0.28), largely because of the homogeneity of the selected communities (Figure 1cGo). The between-community variation for HIV incidence was similar in both arms, and the overall coefficient of variation (k = 0.24) higher than the coefficient for variation for baseline HIV prevalence (k = 0.15). In previous studies in Rakai which sampled heterogeneous communities there was a much stronger correlation (R = 0.96) between HIV prevalence and incidence (Ron Gray, unpublished observations).

Size of randomization unit
In the Mwanza trial, the 12 communities comprised 94 randomly selected smaller units (balozis), while the 18 communities included in the Masaka trial consisted of 67 villages. An unmatched study trial design that used these smaller units as the units of randomization would have a slightly higher coefficient of variation and ICC, but a much smaller design effect (Table 4Go). However, these smaller units formed part of larger communities in both studies, and the lack of statistical independence between the smaller units implies that the coefficient of variation should be treated with caution. When a large number of small communities are randomized, the power of the study is largely unaffected by an increase in the coefficient of variation (Figure 2Go). However, for a study with few, large communities, the power decreases rapidly as the coefficient of variation increases.22 Keeping the overall sample size constant, Figure 2Go shows the relationship between the number of communities, the coefficient of variation, and the power of the study.


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Table 4 The coefficient of variation, intraclass correlation coefficient, design effect and power of trial designs for the Mwanza and Masaka trials for larger and smaller units of randomization, using human immunodeficiency virus (HIV) prevalence as a proxy for the outcome of interest and an unmatched study design
 


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Figure 2 Relationship between the power of the study and the coefficient of variation (k) between communities for a prospective cohort study with 8000 person years of follow-up (PYO) in each arm of the study, for 5 communities of 1600 PYO, 10 of 800 PYO, 20 of 400 PYO, and 40 communities of 200 PYO per arm

 

    Discussion
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The community randomized intervention trial is proving to be a useful tool for assessing the benefits of a variety of community interventions.2,9,22 For example, in the context of HIV prevention in East Africa, community randomization has the advantage of capturing the full effect of the intervention. Both improved STD treatment and IEC may have an impact both on acquisition and transmission of HIV and the community randomized design maximizes the impact observed as well as minimizing the ‘contamination’ of the intervention and comparison arms of the trial.2

Trials to evaluate the impact of such interventions are expensive, time-consuming, and difficult to mount. It is important for the trial design to maximize the power of any study to detect the effect of the intervention. These three trials were designed to detect a reduction in the incidence of HIV in the intervention communities, although the power and size of effect differed in each trial. In all three trials, the between-community coefficient of variation calculated from baseline HIV prevalence was greater than the initial assumptions in the planning of the trials. However, both stratification and pair matching reduced the between-community variation for HIV prevalence and therefore increased the power of the studies. Stratification has the additional advantage of allowing the intervention effect and the coefficient of variation of the outcome to be assessed within strata, while this cannot be done in pair matched studies. Even when the matching variables are highly correlated with the outcome of interest, pair matching of individual communities may not provide additional benefits over stratification, and loses additional degrees of freedom in the analysis, leading to a loss of power.

In most CRT, there are no reliable directly observed estimates for the outcome variable at the time of stratification. It is common, therefore, to use proxy measures for the stratification or matching of communities.22 In HIV prevention trials, baseline HIV prevalence is often used as a proxy for HIV incidence as, especially in the early stages of the HIV epidemic, the two measures are highly correlated. The correlation between HIV prevalence and incidence was high in the Mwanza and Masaka trials, but weaker in the Rakai trial. In Rakai, the purposeful selection of more homogeneous communities not only reduced the coefficient of variation and increased the power of the study, but also reduced the correlation between the prevalence and incidence of HIV in the communities.

In both the Mwanza and Masaka intervention trials, a separate survey to measure HIV prevalence was not undertaken directly before the start of the trial.12,13 In Rakai, pre-existing data and models to correlate community characteristics with HIV prevalence and incidence allowed identification of appropriate communities for the CRT.17 In the Mwanza trial, the subsequent matching reduced the coefficient of variation for HIV prevalence by 50% and the outcome of interest, HIV incidence, was highly correlated with HIV prevalence. In the Masaka trial, the effect of one triplet with a substantial imbalance in HIV prevalence between the three communities reduced the gains from matching from 50% to only 25%. This illustrates the important benefits that may be gained by undertaking a baseline survey for HIV prevalence before stratification or matching in a study of HIV incidence.

In any intervention trial, the size of the community to be used as the randomization unit in the trial must be governed by practical considerations for the intervention.2 In the HIV trials in East Africa, large communities were needed to minimize the contamination from outside of the community. The evaluation of the intervention was undertaken in a smaller sub-sample within the larger community, but as the intervention was delivered through health units, this restricted the number of communities available for randomization. The lack of statistical independence between the smaller units analysed in this paper implies that the coefficient of variation and ICC may have been underestimated. Our results suggest that although smaller units may increase the coefficient of variation and ICC, they require fewer individuals in each cluster, which reduces the design effect and improves the power of the study.22

For prevalence studies both the coefficient of variation and ICC can be used to measure between-community variation, and either can be used for sample size estimation. When heterogeneous communities are used, both measures identify the improvements in study design brought about by stratification or matching of communities. For incidence studies based on person-years analysis, the ICC cannot be derived because of difficulties in defining appropriate sampling units.21 We therefore prefer to use the coefficient of variation, k, which provides a unified approach to sample size estimation for proportions, rates and quantitative variables.11

In the analysis of CRT, it is often desirable to adjust for confounding variables, since the number of units randomized may be insufficient to ensure balance between study arms. All three of these East African trials adjusted the final results for individual-level factors observed at follow-up.12,15,16 In addition, factors that were not balanced between randomized groups at baseline can be adjusted for in the analysis.23


KEY MESSAGES

  • Community randomized trials (CRT) are an important tool in the evaluation of many public health interventions.
  • The between-community coefficient of variation is a statistical tool used to assess the effect of alternative study designs in CRT.
  • Purposeful selection of homogeneous communities reduces the between-community coefficient of variation and increases the power of the trial.
  • Stratification of heterogeneous communities prior to randomization may reduce the between-community coefficient of variation and increase the power of the trial.

 


    Acknowledgments
 
This paper could not have been written without the work of the study teams in Mwanza, Masaka, and Rakai. We would specifically thank the following people: Heiner Grosskurth, Frank Mosha, David Mabey, and John Changalucha in the Mwanza study team, Jimmy Whitworth, Peter Kintu, Silvia Kiwuwa, Anatoli Kamali, Maria Quigley, Jane Kengeya-Kayondo, and Dominic Ricard in the Masaka trial team, and Maria Wawer, David Serwadda, and Nelson Sewankambo in the Rakai study team. We would like to thank David Ross and Jim Lewsey for their advice and comments on draft versions of this paper.


    References
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20 Ukoumunne OC, Gulliford MC, Chinn S, Strene JAC, Burney PGJ. Methods for evaluating area-wide and organisation-based interventions in health and health care: a systematic review. Health Technol Assess 1999;3:21–32.

21 Donner A, Klar N. Design and Analysis of Cluster Randomised Trials in Health Research. London: Arnold, 2000, p. 131.

22 Hayes RJ, Alexander NDE, Bennett S, Cousens SN. Design and analysis issues in cluster-randomized trials of interventions against infectious diseases. Statistical Methods in Medical Research 2000;9:95–116.[ISI][Medline]

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