Substantive model compatible multilevel multiple imputation: A joint modeling approach.

BACKGROUND: Substantive model compatible multiple imputation (SMC-MI) is a relatively novel imputation method that is particularly useful when the analyst's model includes interactions, non-linearities, and/or partially observed random slope variables. METHODS: Here we thoroughly investigate a SMC-MI strategy based on joint modeling of the covariates of the analysis model. We provide code to apply the proposed strategy and we perform an extensive simulation work to test it in various circumstances. We explore the impact on the results of various factors, including whether the missing data are at the individual or cluster level, whether there are non-linearities and whether the imputation model is correctly specified. Finally, we apply the imputation methods to the motivating example data. RESULTS: SMC-JM appears to be superior to standard JM imputation, particularly in presence of large variation in random slopes, non-linearities, and interactions. Results seem to be robust to slight mis-specification of the imputation model for the covariates. When imputing level 2 data, enough clusters have to be observed in order to obtain unbiased estimates of the level 2 parameters. CONCLUSIONS: SMC-JM is preferable to standard JM imputation in presence of complexities in the analysis model of interest, such as non-linearities or random slopes

Multiple imputation for discrete data: Evaluation of the joint latent normal model.

Missing data are ubiquitous in clinical and social research, and multiple imputation (MI) is increasingly the methodology of choice for practitioners. Two principal strategies for imputation have been proposed in the literature: joint modelling multiple imputation (JM-MI) and full conditional specification multiple imputation (FCS-MI). While JM-MI is arguably a preferable approach, because it involves specification of an explicit imputation model, FCS-MI is pragmatically appealing, because of its flexibility in handling different types of variables. JM-MI has developed from the multivariate normal model, and latent normal variables have been proposed as a natural way to extend this model to handle categorical variables. In this article, we evaluate the latent normal model through an extensive simulation study and an application on data from the German Breast Cancer Study Group, comparing the results with FCS-MI. We divide our investigation in four sections, focusing on (i) binary, (ii) categorical, (iii) ordinal, and (iv) count data. Using data simulated from both the latent normal model and the general location model, we find that in all but one extreme general location model setting JM-MI works very well, and sometimes outperforms FCS-MI. We conclude the latent normal model, implemented in the R package jomo, can be used with confidence by researchers, both for single and multilevel multiple imputation

How to check a simulation study

Simulation studies are powerful tools in epidemiology and biostatistics, but they can be hard to conduct successfully. Sometimes unexpected results are obtained. We offer advice on how to check a simulation study when this occurs, and how to design and conduct the study to give results that are easier to check. Simulation studies should be designed to include some settings in which answers are already known. They should be coded in stages, with data-generating mechanisms checked before simulated data are analysed. Results should be explored carefully, with scatterplots of standard error estimates against point estimates surprisingly powerful tools. Failed estimation and outlying estimates should be identified and dealt with by changing data-generating mechanisms or coding realistic hybrid analysis procedures. Finally, we give a series of ideas that have been useful to us in the past for checking unexpected results. Following our advice may help to prevent errors and to improve the quality of published simulation studies

The Smooth Away From Expected (SAFE) non-inferiority frontier: theory and implementation with an application to the D3 trial

Background In a non-inferiority trial, the choice of margin depends on the expected control event risk. If the true risk differs from expected, power and interpretability of results can be affected. A non-inferiority frontier pre-specifies an appropriate non-inferiority margin for each value of control event risk. D3 is a non-inferiority trial comparing two treatment regimens in children living with HIV, designed assuming a control event risk of 12%, a non-inferiority margin of 10%, 80% power and a significance level (α) of 0.025. We consider approaches to choosing and implementing a frontier for this already funded trial, where changing the sample size substantially would be difficult. Methods In D3, we fix the non-inferiority margin at 10%, 8% and 5% for control event risks of ≥9%, 5% and 1%, respectively. We propose four frontiers which fit these fixed points, including a Smooth Away From Expected (SAFE) frontier. Analysis approaches considered are as follows: using the pre-specified significance level (α=0.025); always using a reduced significance level (to achieve α≤0.025 across control event risks); reducing significance levels only when the control event risk differs significantly from expected (control event risk <9%); and using a likelihood ratio test. We compare power and type 1 error for SAFE with other frontiers. Results Changing the significance level only when the control event risk is <9% achieves approximately nominal (<3%) type I error rate and maintains reasonable power for control event risks between 1 and 15%. The likelihood ratio test method performs similarly, but the results are more complex to present. Other analysis methods lead to either inflated type 1 error or badly reduced power. The SAFE frontier gives more interpretable results with low control event risks than other frontiers (i.e. it uses more reasonable non-inferiority margins). Other frontiers do not achieve power close (i.e. within 1%) to SAFE across the range of likely control event risks while controlling type I error. Conclusions The SAFE non-inferiority frontier will be used in D3, and the non-inferiority margin and significance level will be modified if the control event risk is lower than expected. This ensures results will remain interpretable if design assumptions are incorrect, while achieving similar power. A similar approach could be considered for other non-inferiority trials where the control event risk is uncertain

Longitudinal associations between perceptions of the neighbourhood environment and physical activity in adolescents: evidence from the Olympic Regeneration in East London (ORiEL) study.

BACKGROUND: Most UK adolescents do not achieve recommended levels of physical activity. Previous studies suggested that perceptions of the neighbourhood environment could contribute to explain differences in physical activity behaviours. We aimed to examine whether five measures of perceptions - perceived bus stop proximity, traffic safety, street connectivity, enjoyment of the neighbourhood for walking/cycling, and personal safety - were longitudinally associated with common forms of physical activity, namely walking to school, walking for leisure, and a composite measure of outdoor physical activity. We further aimed to investigate the moderating role of gender. METHODS: We used longitudinal data from the Olympic Regeneration in East London (ORiEL) study, a prospective cohort study. In 2012, 3106 adolescents aged 11 to 12 were recruited from 25 schools in 4 deprived boroughs of East London. Adolescents were followed-up in 2013 and 2014. The final sample includes 2260 adolescents surveyed at three occasions. We estimated logistic regression models using Generalised Estimating Equations to test the plausibility of hypotheses on the nature of the longitudinal associations (general association, cumulative effect, co-varying trajectories), adjusting for potential confounders. Item non-response was handled using multiple imputation. RESULTS: Longitudinal analyses indicate little evidence that perceptions of the neighbourhood are important predictors of younger adolescent physical activity. There was weak evidence that greater perceived proximity to bus stops is associated with a small decrease in the probability of walking for leisure. Results also indicate that poorer perception of personal safety decreases the probability of walking for leisure. There was some indication that better perception of street connectivity is associated with more outdoor physical activity. Finally, we found very little evidence that the associations between perceptions of the neighbourhood and physical activity differed by gender. CONCLUSIONS: This study suggests that younger adolescents' perceptions of their neighbourhood environment, and changes in these perceptions, did not consistently predict physical activity in a deprived and ethnically diverse urban population. Future studies should use situation-specific measures of the neighbourhood environment and physical activity to better capture the hypothesised processes and explore the relative roles of the objective environment, parental and adolescents' perceptions in examining differences in types of physical activity

How to design a MAMS-ROCI (aka DURATIONS) randomised trial: the REFINE-Lung case study

Background. The DURATIONS design has been recently proposed as a practical alternative to a standard two-arm non-inferiority design when the goal is to optimise some continuous aspect of treatment administration, e.g. duration or frequency, preserving efficacy but improving on secondary outcomes such as safety, costs or convenience. The main features of this design are that (i) it randomises patients to a moderate number of arms across the continuum and (ii) it uses a model to share information across arms. While papers published to date about the design have focused on analysis aspects, here we show how to design such a trial in practice. We use the REFINE-Lung trial as an example; this is a trial seeking the optimal frequency of immunotherapy treatment for non-small cell lung cancer patients. Because the aspect of treatment administration to optimise is frequency, rather than duration, we propose to rename the design as Multi-Arm Multi-Stage Response Over Continuous Intervention (MAMS-ROCI). Methods. We show how simulations can be used to design such a trial. We propose to use the ADEMP framework to plan such simulations, clearly specifying aims, data generating mechanisms, estimands, methods and performance measures before coding and analysing the simulations. We discuss the possible choices to be made using the REFINE-Lung trial as an example. Results. We describe all the choices made while designing the REFINE-Lung trial, and the results of the simulations performed. We justify our choice of total sample size based on these results. Conclusions. MAMS-ROCI trials can be designed using simulation studies that have to be carefully planned and conducted. REFINE-Lung has been designed using such an approach and we have shown how researchers could similarly design their own MAMS-ROCI trial.Comment: 25 pages, 1 table, 5 figure

What is the optimal duration, dose and frequency for anti-PD1 therapy of non-small cell lung cancer?

Over the past decade, immune checkpoint inhibitors (ICIs) have transformed the management of multiple malignancies including lung cancer. However, the optimal use of these agents in terms of duration, dose and administration frequency remains unknown. Focusing on anti-PD1 agents nivolumab and pembrolizumab in the context of non-small cell lung cancer, we argue that several lines of evidence suggest current administration regimens of these drugs may result in overtreatment with potentially important implications for cost, quality of life and toxicity. This review summarizes evidence for the scope to optimize anti-PD1 regimens, the limitations of existing data and potential approaches to solve these problems including with a novel multi-arm clinical trial design implemented in the recently opened REFINE-Lung study

The DURATIONS randomised trial design: estimation targets, analysis methods and operating characteristics

Background. Designing trials to reduce treatment duration is important in several therapeutic areas, including TB and antibiotics. We recently proposed a new randomised trial design to overcome some of the limitations of standard two-arm non-inferiority trials. This DURATIONS design involves randomising patients to a number of duration arms, and modelling the so-called duration-response curve. This article investigates the operating characteristics (type-1 and type-2 errors) of different statistical methods of drawing inference from the estimated curve. Methods. Our first estimation target is the shortest duration non-inferior to the control (maximum) duration within a specific risk difference margin. We compare different methods of estimating this quantity, including using model confidence bands, the delta method and bootstrap. We then explore the generalisability of results to estimation targets which focus on absolute event rates, risk ratio and gradient of the curve. Results. We show through simulations that, in most scenarios and for most of the estimation targets, using the bootstrap to estimate variability around the target duration leads to good results for DURATIONS design-appropriate quantities analogous to power and type-1 error. Using model confidence bands is not recommended, while the delta method leads to inflated type-1 error in some scenarios, particularly when the optimal duration is very close to one of the randomised durations. Conclusions. Using the bootstrap to estimate the optimal duration in a DURATIONS design has good operating characteristics in a wide range of scenarios, and can be used with confidence by researchers wishing to design a DURATIONS trial to reduce treatment duration. Uncertainty around several different targets can be estimated with this bootstrap approach.Comment: 4 figures, 1 table + additional materia