How should randomised trials including multiple pregnancies be analysed?

OBJECTIVE

To compare the effects of four methods of analysis on the results of randomised controlled trials that recruit women with multiple pregnancies and measure outcomes on their babies.

DESIGN

Analysis of one real and two simulated data sets.

SETTING

Secondary analysis of perinatal randomised controlled trials.

POPULATION

Randomised controlled trials including women with multiple pregnancies.

METHODS

The analytical methods compared were (a) assuming independence among babies, (b) analysing outcomes per women, counting a woman as having an outcome if any of her babies had it (equivalent to selecting the worst outcome among any of a woman's babies), (c) randomly selecting one baby from each set of multiples for inclusion in the analysis, (d) adjustment of the analysis to take account of non-independence of babies from multiple pregnancies, using methods developed for analysis of cluster randomised trials.

MAIN OUTCOME MEASURES

Odds ratios for trials' main outcomes.

RESULTS

Results from application of cluster trial methods were similar to those from assuming independence among babies, but with slightly wider confidence intervals, reflecting the reduced effective sample size caused by non-independence between babies from the same pregnancy. Results were more variable using the other two methods, and in some cases, departed markedly from the results of the cluster trial methods.

CONCLUSIONS

Cluster trial methods provide a simple way of adjusting the analysis to take account of non-independence between babies from the same pregnancy. Random selection and analysis by pregnancy (methods (b) and (c)) have disadvantages and do not report outcomes for all of the babies in the trial. This may cause problems with incorporating trials analysed using these methods into systematic reviews.

Effect of within-household reinfestation on design sensitivity

The effect of within-household reinfestation on design sensitivity is investigated through statistical modeling of the reinfestation process. When reinfestation is present, household randomization tends to magnify treatment differences when compared with individual randomization or a randomized blocking design in the simple setting of two patients per household. The effect of reinfestation under more general household randomization settings is investigated by determining the relationship between the treatment effect and the number of patients per household. In an actual clinical study of treatment for head lice infestation, household randomization with proper stratification was adopted. The results from the study were consistent with theoretical expectations. This seeming contradiction to the blocking principle demonstrates the need to check whether all conditions are met before applying standard design principles.

Sample size calculations for clustered binary data

In this paper we propose a sample size calculation method for testing on a binomial proportion when binary observations are dependent within clusters. In estimating the binomial proportion in clustered binary data, two weighting systems have been popular: equal weights to clusters and equal weights to units within clusters. When the number of units varies cluster by cluster, performance of these two weighting systems depends on the extent of correlation among units within each cluster. In addition to them, we will also use an optimal weighting method that minimizes the variance of the estimator. A sample size formula is derived for each of the estimators with different weighting schemes. We apply these methods to the sample size calculation for the sensitivity of a periodontal diagnostic test. Simulation studies are conducted to evaluate a finite sample performance of the three estimators. We also assess the influence of misspecified input parameter values on the calculated sample size. The optimal estimator requires equal or smaller sample sizes and is more robust to the misspecification of an input parameter than those assigning equal weights to units or clusters.

Sample size and design considerations for phase II clinical trials with correlated observations

Several methods are available for the design of phase II clinical trials with binary endpoints. A primary assumption for most methods is that observations on the endpoint of interest are uncorrelated; however, this assumption is violated if an individual patient provides more than one observation on the endpoint of interest. In such cases, one solution is to use a summary measure for each patient; an alternative solution is to perform an observation-specific analysis using a technique that properly accounts for the correlation. In this paper, we investigate the effect that ignoring correlated observations can have on the design properties of the typical phase II clinical trial. In cases in which an observation-specific analysis is desirable, we propose a simple method that adjusts a standard one- or two-stage phase II design to account for loss of information due to correlated observations. Simulations demonstrate that the method ensures that type I and type II error rate design requirements are met even in the presence of strong correlation. We develop the method in the context of phase II oncology trials, but the method applies readily to other clinical areas in which multiple responses per patient are of interest.

Estimating intraclass correlation for binary data

This paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study. Some of the estimators are very specific, while others result from general methods such as pseudo-likelihood and extended quasi-likelihood estimation. The simulation study identifies several useful estimators, one of which does not seem to have been considered previously for binary data. Estimators based on extended quasi-likelihood are found to have a substantial bias in some circumstances.

An application of the Zucker-Wittes modified ratio estimate statistic in the Post Coronary Artery Bypass Graft (CABG) clinical trial

In the Post Coronary Artery Bypass Graft (POST CABG) clinical trial, the primary outcome is substantial worsening (i.e., narrowing of the lumen diameter) of the vein grafts upon comparison of the baseline and follow-up angiograms. The patients had one to five non-occluded vein grafts at entry, so there may be from one to five primary outcome responses per patient. A modified ratio estimate (MRE) statistic, as described previously by Zucker and Wittes, may be used to analyze data of this kind. In the present paper we propose a more powerful MRE statistic when the event rates and/ or intraclass correlations vary according to number of grafts per patient. We also adapt this statistic to the factorial treatment design of the POST CABG clinical trial.

Estimation and sample size considerations for clustered binary responses

Although there is much literature on sample size determination for clinical trials or experiments with independent responses, there is a lack of methodology to obtain sample sizes for dependent outcomes. This paper presents a simple way to calculate sample size for estimating treatment effects and diagnostic accuracy in the case of correlated binary outcomes. The proposed weighted procedure also has use in estimation, whose advantages we demonstrate through simulation. Recommendations are made for practical application.

"Within patient"-dependent outcomes in graft occlusion after coronary artery bypass. SINBA Group

In clinical trials aimed at assessing the efficacy of drugs after coronary artery grafting, statistical analysis is usually carried out on a per-patient basis and on a per-graft basis. Owing to the independence of responses among patients, the former outcome is analyzed by assuming a binomial model. However, this model cannot be directly adopted in analyzing the latter outcome because multiple vein grafts in the same patient do not act independently. It has been suggested that patients be considered as clusters of distal anastomoses, subsequently comparing the frequencies of occlusion under different treatments after adjusting the variance of each frequency for the size of the cluster. Alternatively, one can measure the intraclass (intrapatient) correlation coefficient and adopt distribution functions that include this quantity as one of the parameters. This approach has been adopted by many authors although the studies differed in the statistical model used to represent this kind of data. Two probability functions, Altham's and beta-binomial, have found wide application in different biomedical fields. Both are able to model the extrabinomial variability since their tails tend to zero more slowly than those of the binomial distribution. An alternative to adopting a specific probabilistic model consists of specifying a mixed model or a Markov-like susceptibility model. These models follow the same rationale since they assume the existence of two processes, one that causes an individual to become susceptible to occlusion, the other that determines the subsequent probability of occlusion in the individual. After presenting these models in a unified framework, this paper compares the estimates obtained by fitting the models to data gathered at coronary angiography 1 year after surgery by the SINBA group on a total of 847 saphenous vein anastomoses in 349 patients. Finally, the issue concerning the contribution of each patient to the effective sample size is discussed.