Sensitivity models for missing covariates in the analysis of survival data from multiple surveys

Using individual patient data from five independent surveys, we evaluate regional variations in survival in cerebral palsy. The influence of four important variables measuring disability, which are only partially observed for many cases, are analysed. Results are compared between a naive complete case analysis; a full likelihood model in which the covariates are assumed to be missing at random and in which each of the binary predictor variables are modelled as independent Bernoulli random variables; a model in which the covariates are modelled by a conditionalwise sequence, accommodating dependencies between the likelihoods of having various mixtures of disabilities; and a model in which the likelihood of a predictor variable being observed is allowed to depend on the value of the covariate itself (NMAR). Fully parametric survival regression models are used and analysis carried out in BUGS. Results suggest that proportions recorded as having severe visual or cognitive impairments are substantially lower than the actual proportions severely impaired. Associations between the likelihood of a particular covariate being recorded and the likelihood of a more severe disability imply that life expectancies for those who are very severely impaired may be up to 20% less than inferences based on complete case analyses

Differences between European birthweight standards: impact on classification of ‘small for gestational age’

We describe a quantitative and comparative review of a selection of European birthweight standards for gestational age for singletons, to enable appropriate choices to be made for clinical and research use. Differences between median values at term across standards in 10 regions and misclassification of ‘small for gestational age’ (SGA), were studied. Sex and parity differences, exclusion criteria, and methods of construction were considered. There was wide variation between countries in exclusion criteria, methods of calculating standards, and median birthweight at term. The lightest standards (e.g. France's medians are 255g lower than Norway's medians) were associated with fewer exclusion criteria. Up to 20% of the population used in the construction of the Scottish standard would be classified as SGA using the Norwegian standard. Substantial misclassification of SGA is possible. Assumptions about variation used in the construction of some standards were not justified. It is not possible to conclude that there are real differences in birthweight standards between European countries. Country-based standards control for some population features but add misclassification due to the differing ways in which standards are derived. Standards should be chosen to reflect clinical or research need. If standards stratified by sex or parity are not available, adjustments should be made. In multinational studies, comparisons should be made between results using both a common standard and country-based standards

Stepped-wedge cluster randomised controlled trials : a generic framework including parallel and multiple-level designs

Stepped-wedge cluster randomised trials (SW-CRTs) are being used with increasing frequency in health service evaluation. Conventionally, these studies are cross-sectional in design with equally spaced steps, with an equal number of clusters randomised at each step and data collected at each and every step. Here we introduce several variations on this design and consider implications for power. One modification we consider is the incomplete cross-sectional SW-CRT, where the number of clusters varies at each step or where at some steps, for example, implementation or transition periods, data are not collected. We show that the parallel CRT with staggered but balanced randomisation can be considered a special case of the incomplete SW-CRT. As too can the parallel CRT with baseline measures. And we extend these designs to allow for multiple layers of clustering, for example, wards within a hospital. Building on results for complete designs, power and detectable difference are derived using a Wald test and obtaining the variance–covariance matrix of the treatment effect assuming a generalised linear mixed model. These variations are illustrated by several real examples. We recommend that whilst the impact of transition periods on power is likely to be small, where they are a feature of the design they should be incorporated. We also show examples in which the power of a SW-CRT increases as the intra-cluster correlation (ICC) increases and demonstrate that the impact of the ICC is likely to be smaller in a SW-CRT compared with a parallel CRT, especially where there are multiple levels of clustering. Finally, through this unified framework, the efficiency of the SW-CRT and the parallel CRT can be compared

Parametric dynamic survival models

A non-proportional hazards model is developed. The model can accommodate right censored, interval censored and double interval censored data sets. There is also an extension of the model to include multiplicative gamma frailties. The basic model is an extension of the dynamic Bayesian survival model developed by Gamerman (1987), but with some alterations and using a different method of model fitting. The model developed here, the Normal Dynamic Survival Model, models both the log-baseline hazard and covariate effects by a piecewise constant and correlated process, based on some division of the time axis. Neighbouring piecewise constant parameters are related by a simple evolution equation: normal with mean zero and unknown variance to be estimated. The method of estimation is to use Markov chain Monte Carlo simulations: Gibbs sampling with a Metropolis-Hastings step. For double interval censored data an iterative data augmentation procedure is considered: exploiting the comparative ease at which interval censored observations may be modelled. The model is applied within a range of well known, and illustrative data sets, with convincing results. In addition the impact of censoring is investigated by a simulation study

Optimal Study Designs for Cluster Randomised Trials: An Overview of Methods and Results

There are multiple cluster randomised trial designs that vary in when the clusters cross between control and intervention states, when observations are made within clusters, and how many observations are made at that time point. Identifying the most efficient study design is complex though, owing to the correlation between observations within clusters and over time. In this article, we present a review of statistical and computational methods for identifying optimal cluster randomised trial designs. We also adapt methods from the experimental design literature for experimental designs with correlated observations to the cluster trial context. We identify three broad classes of methods: using exact formulae for the treatment effect estimator variance for specific models to derive algorithms or weights for cluster sequences; generalised methods for estimating weights for experimental units; and, combinatorial optimisation algorithms to select an optimal subset of experimental units. We also discuss methods for rounding weights to whole numbers of clusters and extensions to non-Gaussian models. We present results from multiple cluster trial examples that compare the different methods, including problems involving determining optimal allocation of clusters across a set of cluster sequences, and selecting the optimal number of single observations to make in each cluster-period for both Gaussian and non-Gaussian models, and including exchangeable and exponential decay covariance structures

What type of cluster randomized trial for which setting?

The cluster randomized trial allows a randomized evaluation when it is either not possible to randomize the individual or randomizing individuals would put the trial at high risk of contamination across treatment arms. There are many variations of the cluster randomized design, including the parallel design with or without baseline measures, the cluster randomized cross-over design, the stepped-wedge cluster randomized design, and more recently-developed variants such as the batched stepped-wedge design and the staircase design. Once it has been clearly established that there is a need for cluster randomization, one ever important question is which form the cluster design should take. If a design in which time is split into multiple trial periods is to be adopted (e.g. as in a stepped-wedge), researchers must decide whether the same participants should be measured in multiple trial periods (cohort sampling); or if different participants should be measured in each period (continual recruitment or cross-sectional sampling). Here we outline the different possible options and weigh up the pros and cons of the different design choices, which revolve around statistical efficiency, study logistics and the assumptions required.</p

Systematic review finds major deficiencies in sample size methodology and reporting for stepped-wedge cluster randomised trials

BACKGROUND: Stepped-wedge cluster randomised trials (SW-CRT) are increasingly being used in health policy and services research, but unless they are conducted and reported to the highest methodological standards, they are unlikely to be useful to decision-makers. Sample size calculations for these designs require allowance for clustering, time effects and repeated measures. METHODS: We carried out a methodological review of SW-CRTs up to October 2014. We assessed adherence to reporting each of the 9 sample size calculation items recommended in the 2012 extension of the CONSORT statement to cluster trials. RESULTS: We identified 32 completed trials and 28 independent protocols published between 1987 and 2014. Of these, 45 (75%) reported a sample size calculation, with a median of 5.0 (IQR 2.5–6.0) of the 9 CONSORT items reported. Of those that reported a sample size calculation, the majority, 33 (73%), allowed for clustering, but just 15 (33%) allowed for time effects. There was a small increase in the proportions reporting a sample size calculation (from 64% before to 84% after publication of the CONSORT extension, p=0.07). The type of design (cohort or cross-sectional) was not reported clearly in the majority of studies, but cohort designs seemed to be most prevalent. Sample size calculations in cohort designs were particularly poor with only 3 out of 24 (13%) of these studies allowing for repeated measures. DISCUSSION: The quality of reporting of sample size items in stepped-wedge trials is suboptimal. There is an urgent need for dissemination of the appropriate guidelines for reporting and methodological development to match the proliferation of the use of this design in practice. Time effects and repeated measures should be considered in all SW-CRT power calculations, and there should be clarity in reporting trials as cohort or cross-sectional designs