Improper analysis of trials randomised using stratified blocks or minimisation

Many clinical trials restrict randomisation using stratified blocks or minimisation to balance prognostic factors across treatment groups. It is widely acknowledged in the statistical literature that the subsequent analysis should reflect the design of the study, and any stratification or minimisation variables should be adjusted for in the analysis. However, a review of recent general medical literature showed only 14 of 41 eligible studies reported adjusting their primary analysis for stratification or minimisation variables. We show that balancing treatment groups using stratification leads to correlation between the treatment groups. If this correlation is ignored and an unadjusted analysis is performed, standard errors for the treatment effect will be biased upwards, resulting in 95% confidence intervals that are too wide, type I error rates that are too low and a reduction in power. Conversely, an adjusted analysis will give valid inference. We explore the extent of this issue using simulation for continuous, binary and time-to-event outcomes where treatment is allocated using stratified block randomisation or minimisation

Analysis of multicentre trials with continuous outcomes: when and how should we account for centre effects?

In multicentre trials, randomisation is often carried out using permuted blocks stratified by centre. It has previously been shown that stratification variables used in the randomisation process should be adjusted for in the analysis to obtain correct inference. For continuous outcomes, the two primary methods of accounting for centres are fixed-effects and random-effects models. We discuss the differences in interpretation between these two models and the implications that each pose for analysis. We then perform a large simulation study comparing the performance of these analysis methods in a variety of situations. In total, we assessed 378 scenarios. We found that random centre effects performed as well or better than fixed-effects models in all scenarios. Random centre effects models led to increases in power and precision when the number of patients per centre was small (e.g. 10 patients or less) and, in some scenarios, when there was an imbalance between treatments within centres, either due to the randomisation method or to the distribution of patients across centres. With small samples sizes, random-effects models maintained nominal coverage rates when a degree-of-freedom (DF) correction was used. We assessed the robustness of random-effects models when assumptions regarding the distribution of the centre effects were incorrect and found this had no impact on results. We conclude that random-effects models offer many advantages over fixed-effects models in certain situations and should be used more often in practice

Reporting and analysis of trials using stratified randomisation in leading medical journals: review and reanalysis

To assess how often stratified randomisation is used, whether analysis adjusted for all balancing variables, and whether the method of randomisation was adequately reported, and to reanalyse a previously reported trial to assess the impact of ignoring balancing factors in the analysis

Analysis of multicenter clinical trials with very low event rates

INTRODUCTION: In a five-arm randomized clinical trial (RCT) with stratified randomization across 54 sites, we encountered low primary outcome event proportions, resulting in multiple sites with zero events either overall or in one or more study arms. In this paper, we systematically evaluated different statistical methods of accounting for center in settings with low outcome event proportions. METHODS: We conducted a simulation study and a reanalysis of a completed RCT to compare five popular methods of estimating an odds ratio for multicenter trials with stratified randomization by center: (i) no center adjustment, (ii) random intercept model, (iii) Mantel-Haenszel model, (iv) generalized estimating equation (GEE) with an exchangeable correlation structure, and (v) GEE with small sample correction (GEE-small sample correction). We varied the number of total participants (200, 500, 1000, 5000), number of centers (5, 50, 100), control group outcome percentage (2%, 5%, 10%), true odds ratio (1, > 1), intra-class correlation coefficient (ICC) (0.025, 0.075), and distribution of participants across the centers (balanced, skewed). RESULTS: Mantel-Haenszel methods generally performed poorly in terms of power and bias and led to the exclusion of participants from the analysis because some centers had no events. Failure to account for center in the analysis generally led to lower power and type I error rates than other methods, particularly with ICC = 0.075. GEE had an inflated type I error rate except in some settings with a large number of centers. GEE-small sample correction maintained the type I error rate at the nominal level but suffered from reduced power and convergence issues in some settings when the number of centers was small. Random intercept models generally performed well in most scenarios, except with a low event rate (i.e., 2% scenario) and small total sample size (n ≤ 500), when all methods had issues. DISCUSSION: Random intercept models generally performed best across most scenarios. GEE-small sample correction performed well when the number of centers was large. We do not recommend the use of Mantel-Haenszel, GEE, or models that do not account for center. When the expected event rate is low, we suggest that the statistical analysis plan specify an alternative method in the case of non-convergence of the primary method

A comparison of methods to adjust for continuous covariates in the analysis of randomised trials

BACKGROUND: Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy. METHODS: We compared several methods of adjustment to determine which is best when the association between covariate and outcome is unknown. We assessed (a) dichotomisation or categorisation; (b) assuming a linear association with outcome; (c) using fractional polynomials with one (FP1) or two (FP2) polynomial terms; and (d) using restricted cubic splines with 3 or 5 knots. We evaluated each method using simulation and through a re-analysis of trial datasets. RESULTS: Methods which kept covariates as continuous typically had higher power than methods which used categorisation. Dichotomisation, categorisation, and assuming a linear association all led to large reductions in power when the true association was non-linear. FP2 models and restricted cubic splines with 3 or 5 knots performed best overall. CONCLUSIONS: For the analysis of randomised trials we recommend (1) adjusting for continuous covariates even if their association with outcome is unknown; (2) keeping covariates as continuous; and (3) using fractional polynomials with two polynomial terms or restricted cubic splines with 3 to 5 knots when a linear association is in doubt

Adjusting for multiple prognostic factors in the analysis of randomised trials

Background: When multiple prognostic factors are adjusted for in the analysis of a randomised trial, it is unclear (1) whether it is necessary to account for each of the strata, formed by all combinations of the prognostic factors (stratified analysis), when randomisation has been balanced within each stratum (stratified randomisation), or whether adjusting for the main effects alone will suffice, and (2) the best method of adjustment in terms of type I error rate and power, irrespective of the randomisation method. Methods: We used simulation to (1) determine if a stratified analysis is necessary after stratified randomisation, and (2) to compare different methods of adjustment in terms of power and type I error rate. We considered the following methods of analysis: adjusting for covariates in a regression model, adjusting for each stratum using either fixed or random effects, and Mantel-Haenszel or a stratified Cox model depending on outcome. Results: Stratified analysis is required after stratified randomisation to maintain correct type I error rates when (a) there are strong interactions between prognostic factors, and (b) there are approximately equal number of patients in each stratum. However, simulations based on real trial data found that type I error rates were unaffected by the method of analysis (stratified vs unstratified), indicating these conditions were not met in real datasets. Comparison of different analysis methods found that with small sample sizes and a binary or time-to-event outcome, most analysis methods lead to either inflated type I error rates or a reduction in power; the lone exception was a stratified analysis using random effects for strata, which gave nominal type I error rates and adequate power. Conclusions: It is unlikely that a stratified analysis is necessary after stratified randomisation except in extreme scenarios. Therefore, the method of analysis (accounting for the strata, or adjusting only for the covariates) will not generally need to depend on the method of randomisation used. Most methods of analysis work well with large sample sizes, however treating strata as random effects should be the analysis method of choice with binary or time-to-event outcomes and a small sample size

A re-randomisation design for clinical trials

Background: Recruitment to clinical trials is often problematic, with many trials failing to recruit to their target sample size. As a result, patient care may be based on suboptimal evidence from underpowered trials or non-randomised studies. Methods: For many conditions patients will require treatment on several occasions, for example, to treat symptoms of an underlying chronic condition (such as migraines, where treatment is required each time a new episode occurs), or until they achieve treatment success (such as fertility, where patients undergo treatment on multiple occasions until they become pregnant). We describe a re-randomisation design for these scenarios, which allows each patient to be independently randomised on multiple occasions. We discuss the circumstances in which this design can be used. Results: The re-randomisation design will give asymptotically unbiased estimates of treatment effect and correct type I error rates under the following conditions: (a) patients are only re-randomised after the follow-up period from their previous randomisation is complete; (b) randomisations for the same patient are performed independently; and (c) the treatment effect is constant across all randomisations. Provided the analysis accounts for correlation between observations from the same patient, this design will typically have higher power than a parallel group trial with an equivalent number of observations. Conclusions: If used appropriately, the re-randomisation design can increase the recruitment rate for clinical trials while still providing an unbiased estimate of treatment effect and correct type I error rates. In many situations, it can increase the power compared to a parallel group design with an equivalent number of observations

Implementation and Evaluation of Iron Deficiency Anemia Content in Prenatal Education Classes

Purpose/Background The purpose of this quality improvement project is to provide and increase educational awareness and knowledge regarding iron deficiency anemia (IDA) in pregnant patients at an urban primary care clinic in Memphis, TN. This project is intended to decrease the number of individuals with IDA in pregnancy while decreasing the occurrence of IDA-related complications in pregnancy. The study aimed to introduce a cost-effective approach to help decrease or eradicate complications related to IDA during pregnancy. The World Health Organization (WHO) estimates the prevalence of anemia-complicating pregnancies to be more than 40 percent. Pregnant women with IDA residing in low and middle-income countries are at a higher risk of low birth weight, preterm birth, perinatal mortality, and neonatal mortality. Memphis is known as an urban, predominantly Black city, in which studies have shown that the prevalence of Black gravidas was \u3e15 percent in the first trimester, around 20 percent in the second trimester, and close to 50 percent in the third trimester. Introducing IDA educational sessions can beneficially impact Memphis maternal and infant mortality rates and the number of complications and interventions related to IDA. Methods Researchers collaborated with the Midwives at Regional One Health Center’s (ROH) Hollywood Primary Care Clinic in Memphis, TN, to educate 25 pregnant women. The participants were administered a pretest before reviewing the IDA content. After completion of the pretest, an infographic was given to and reviewed with the patient during a 10-minute session. After reviewing the infographic, the participant took a post-test. All women gave consent to participate in this study in their first trimester (before 13 weeks gestation), were 18 or older, and had no known blood disorders or medical conditions that interfere with liver function. Results The pretest/post-test showed a significant correlation between IDA educational sessions and increased awareness. The results show the benefits of education in increasing awareness to help prevent pregnant women in Memphis, TN, from developing IDA and related complications. IDA educational sessions will continue to increase awareness amongst pregnant women. The likelihood of pregnant women complying with iron supplement regimens will steadily increase, thus decreasing the risk of IDA-related complications. Therefore, the results show that providing short educational sessions to mothers in their first trimester are not only cost-effective, but will also improve maternal and infant mortality rates, especially in underserved communities like Memphis, TN. Implication in Nursing Practice Pre- and post-tests will be administered before and after the iron deficiency anemia education session. The pre- and post-tests will be used to collect data regarding patient education on iron deficiency anemia in pregnancy before and after the education. This information will help determine if there is a correlation between patients receiving one-on-one education on iron deficiency anemia and their knowledge of patient compliance with iron supplementation. Once the education and data collection is completed, strengths and weaknesses should be identified for improvement throughout the project for more organized and efficient education

Assessing potential sources of clustering in individually randomised trials

Recent reviews have shown that while clustering is extremely common in individually randomised trials (for example, clustering within centre, therapist, or surgeon), it is rarely accounted for in the trial analysis. Our aim is to develop a general framework for assessing whether potential sources of clustering must be accounted for in the trial analysis to obtain valid type I error rates (non-ignorable clustering), with a particular focus on individually randomised trials