Showing papers in "Statistical Methods in Medical Research in 2022"

Fitting to the UK COVID-19 outbreak, short-term forecasts and estimating the reproductive number

Abstract: The COVID-19 pandemic has brought to the fore the need for policy makers to receive timely and ongoing scientific guidance in response to this recently emerged human infectious disease. Fitting mathematical models of infectious disease transmission to the available epidemiological data provide a key statistical tool for understanding the many quantities of interest that are not explicit in the underlying epidemiological data streams. Of these, the effective reproduction number, R , has taken on special significance in terms of the general understanding of whether the epidemic is under control ( R<1 ). Unfortunately, none of the epidemiological data streams are designed for modelling, hence assimilating information from multiple (often changing) sources of data is a major challenge that is particularly stark in novel disease outbreaks. Here, focusing on the dynamics of the first wave (March–June 2020), we present in some detail the inference scheme employed for calibrating the Warwick COVID-19 model to the available public health data streams, which span hospitalisations, critical care occupancy, mortality and serological testing. We then perform computational simulations, making use of the acquired parameter posterior distributions, to assess how the accuracy of short-term predictions varied over the time course of the outbreak. To conclude, we compare how refinements to data streams and model structure impact estimates of epidemiological measures, including the estimated growth rate and daily incidence.

Statistical methods used to combine the effective reproduction number, R(t), and other related measures of COVID-19 in the UK

Abstract: In the recent COVID-19 pandemic, a wide range of epidemiological modelling approaches were used to predict the effective reproduction number, R(t), and other COVID-19-related measures such as the daily rate of exponential growth, r(t). These candidate models use different modelling approaches or differing assumptions about spatial or age-mixing, and some capture genuine uncertainty in scientific understanding of disease dynamics. Combining estimates using appropriate statistical methodology from multiple candidate models is important to better understand the variation of these outcome measures to help inform decision-making. In this paper, we combine estimates for specific UK nations/regions using random-effects meta-analyses techniques, utilising the restricted maximum-likelihood (REML) method to estimate the heterogeneity variance parameter, and two approaches to calculate the confidence interval for the combined estimate: the standard Wald-type and the Knapp and Hartung (KNHA) method. As estimates in this setting are derived using model predictions, each with varying degrees of uncertainty, equal-weighting is favoured over the standard inverse-variance weighting to avoid potential up-weighting of models providing estimates with lower levels of uncertainty that are not fully accounting for inherent uncertainties. Both equally-weighted models using REML alone and REML+KNHA approaches were found to provide similar variation for R(t) and r(t), with both approaches providing wider, and therefore more conservative, confidence intervals around the combined estimate compared to the standard inverse-variance weighting approach. Utilising these meta-analysis techniques has allowed for statistically robust combined estimates to be calculated for key COVID-19 outcome measures. This in turn allows timely and informed decision-making based on all available information.

Inferring risks of coronavirus transmission from community household data

Abstract: The response of many governments to the COVID-19 pandemic has involved measures to control within- and between-household transmission, providing motivation to improve understanding of the absolute and relative risks in these contexts. Here, we perform exploratory, residual-based, and transmission-dynamic household analysis of the Office for National Statistics COVID-19 Infection Survey data from 26 April 2020 to 15 July 2021 in England. This provides evidence for: (i) temporally varying rates of introduction of infection into households broadly following the trajectory of the overall epidemic and vaccination programme; (ii) susceptible-Infectious transmission probabilities of within-household transmission in the 15–35% range; (iii) the emergence of the Alpha and Delta variants, with the former being around 50% more infectious than wildtype and 35% less infectious than Delta within households; (iv) significantly (in the range of 25–300%) more risk of bringing infection into the household for workers in patient-facing roles pre-vaccine; (v) increased risk for secondary school-age children of bringing the infection into the household when schools are open; (vi) increased risk for primary school-age children of bringing the infection into the household when schools were open since the emergence of new variants.

A comparison of analytical strategies for cluster randomized trials with survival outcomes in the presence of competing risks

Abstract: While statistical methods for analyzing cluster randomized trials with continuous and binary outcomes have been extensively studied and compared, little comparative evidence has been provided for analyzing cluster randomized trials with survival outcomes in the presence of competing risks. Motivated by the Strategies to Reduce Injuries and Develop Confidence in Elders trial, we carried out a simulation study to compare the operating characteristics of several existing population-averaged survival models, including the marginal Cox, marginal Fine and Gray, and marginal multi-state models. For each model, we found that adjusting for the intraclass correlations through the sandwich variance estimator effectively maintained the type I error rate when the number of clusters is large. With no more than 30 clusters, however, the sandwich variance estimator can exhibit notable negative bias, and a permutation test provides better control of type I error inflation. Under the alternative, the power for each model is differentially affected by two types of intraclass correlations—the within-individual and between-individual correlations. Furthermore, the marginal Fine and Gray model occasionally leads to higher power than the marginal Cox model or the marginal multi-state model, especially when the competing event rate is high. Finally, we provide an illustrative analysis of Strategies to Reduce Injuries and Develop Confidence in Elders trial using each analytical strategy considered.

Adjusting for time of infection or positive test when estimating the risk of a post-infection outcome in an epidemic

Abstract: When comparing the risk of a post-infection binary outcome, for example, hospitalisation, for two variants of an infectious pathogen, it is important to adjust for calendar time of infection. Typically, the infection time is unknown and positive test time used as a proxy for it. Positive test time may also be used when assessing how risk of the outcome changes over calendar time. We show that if time from infection to positive test is correlated with the outcome, the risk conditional on positive test time is a function of the trajectory of infection incidence. Hence, a risk ratio adjusted for positive test time can be quite different from the risk ratio adjusted for infection time. We propose a simple sensitivity analysis that indicates how risk ratios adjusted for positive test time and infection time may differ. This involves adjusting for a shifted positive test time, shifted to make the difference between it and infection time uncorrelated with the outcome. We illustrate this method by reanalysing published results on the relative risk of hospitalisation following infection with the Alpha versus pre-existing variants of SARS-CoV-2. Results indicate the relative risk adjusted for infection time may be lower than that adjusted for positive test time.

A comparison of two frameworks for multi-state modelling, applied to outcomes after hospital admissions with COVID-19

Abstract: We compare two multi-state modelling frameworks that can be used to represent dates of events following hospital admission for people infected during an epidemic. The methods are applied to data from people admitted to hospital with COVID-19, to estimate the probability of admission to intensive care unit, the probability of death in hospital for patients before and after intensive care unit admission, the lengths of stay in hospital, and how all these vary with age and gender. One modelling framework is based on defining transition-specific hazard functions for competing risks. A less commonly used framework defines partially-latent subpopulations who will experience each subsequent event, and uses a mixture model to estimate the probability that an individual will experience each event, and the distribution of the time to the event given that it occurs. We compare the advantages and disadvantages of these two frameworks, in the context of the COVID-19 example. The issues include the interpretation of the model parameters, the computational efficiency of estimating the quantities of interest, implementation in software and assessing goodness of fit. In the example, we find that some groups appear to be at very low risk of some events, in particular intensive care unit admission, and these are best represented by using ‘cure-rate’ models to define transition-specific hazards. We provide general-purpose software to implement all the models we describe in the flexsurv R package, which allows arbitrarily flexible distributions to be used to represent the cause-specific hazards or times to events.

On recurrent-event win ratio

Abstract: The win ratio approach proposed by Pocock et al. (2012) has become a popular tool for analyzing composite endpoints of death and non-fatal events like hospitalization. Its standard version, however, draws on the non-fatal event only through the first occurrence. For statistical efficiency and clinical interpretability, we construct and compare different win ratio variants that make fuller use of recurrent events. We pay special attention to a variant called last-event-assisted win ratio, which compares two patients on the cumulative frequency of the non-fatal event, with ties broken by the time of its latest episode. It is shown that last-event-assisted win ratio uses more data than the standard win ratio does but reduces to the latter when the non-fatal event occurs at most once. We further prove that last-event-assisted win ratio rejects the null hypothesis with large probability if the treatment stochastically delays all events. Simulations under realistic settings show that the last-event-assisted win ratio test consistently enjoys higher power than the standard win ratio and other competitors. Analysis of a real cardiovascular trial provides further evidence for the practical advantages of the last-event-assisted win ratio. Finally, we discuss future work to develop meaningful effect size estimands based on the extended rules of comparison. The R-code for the proposed methods is included in the package WR openly available on the Comprehensive R Archive Network.

Unified approach to optimal estimation of mean and standard deviation from sample summaries

Abstract: Recently, various methods have been developed to estimate the sample mean and standard deviation when only the sample size, and other selected sample summaries are reported. In this paper, we provide a unified approach to optimal estimation that can be easily adopted when only some summary statistics are reported. We show that the proposed estimators have the lowest variance among linear unbiased estimators. We also show that in the most commonly reported cases, that is, when only a three-number or five-number summary is reported, the newly proposed estimators match the previously developed estimators. Finally, we demonstrate the performance of the estimators numerically.

Re-randomisation trials in multi-episode settings: Estimands and independence estimators

Abstract: Often patients may require treatment on multiple occasions. The re-randomisation design can be used in such multi-episode settings, as it allows patients to be re-enrolled and re-randomised for each new treatment episode they experience. We propose a set of estimands that can be used in multi-episode settings, focusing on issues unique to multi-episode settings, namely how each episode should be weighted, how the patient's treatment history in previous episodes should be handled, and whether episode-specific effects or average effects across all episodes should be used. We then propose independence estimators for each estimand, and show the manner in which many re-randomisation trials have been analysed in the past (a simple comparison between all intervention episodes vs. all control episodes) corresponds to a per-episode added-benefit estimand, that is, the average effect of the intervention across all episodes, over and above any benefit conferred from the intervention in previous episodes. We show this estimator is generally unbiased, and describe when other estimators will be unbiased. We conclude that (i) consideration of these estimands can help guide the choice of which analysis method is most appropriate; and (ii) the re-randomisation design with an independence estimator can be a useful approach in multi-episode settings.

A general method for calculating power for GEE analysis of complete and incomplete stepped wedge cluster randomized trials

Abstract: Stepped wedge designs have uni-directional crossovers at randomly assigned time points (steps) where clusters switch from control to intervention condition. Incomplete stepped wedge designs are increasingly used in cluster randomized trials of health care interventions and have periods without data collection due to logistical, resource and patient-centered considerations. The development of sample size formulae for stepped wedge trials has primarily focused on complete designs and continuous responses. Addressing this gap, a general, fast, non-simulation based power procedure is proposed for generalized estimating equations analysis of complete and incomplete stepped wedge designs and its predicted power is compared to simulated power for binary and continuous responses. An extensive set of simulations for six and twelve clusters is based upon the Connect-Home trial with an incomplete stepped wedge design. Results show that empirical test size is well controlled using a t-test with bias-corrected sandwich variance estimator for as few as six clusters. Analytical power agrees well with a simulated power in scenarios with twelve clusters. For six clusters, analytical power is similar to simulated power with estimation using the correctly specified model-based variance estimator. To explore the impact of study design choice on power, the proposed fast GEE power method is applied to the Connect-Home trial design, four alternative incomplete stepped wedge designs and one complete design.

Challenges of modelling approaches for network meta-analysis of time-to-event outcomes in the presence of non-proportional hazards to aid decision making: Application to a melanoma network

Abstract: Background Synthesis of clinical effectiveness from multiple trials is a well-established component of decision-making. Time-to-event outcomes are often synthesised using the Cox proportional hazards model assuming a constant hazard ratio over time. However, with an increasing proportion of trials reporting treatment effects where hazard ratios vary over time and with differing lengths of follow-up across trials, alternative synthesis methods are needed. Objectives To compare and contrast five modelling approaches for synthesis of time-to-event outcomes and provide guidance on key considerations for choosing between the modelling approaches. Methods The Cox proportional hazards model and five other methods of estimating treatment effects from time-to-event outcomes, which relax the proportional hazards assumption, were applied to a network of melanoma trials reporting overall survival: restricted mean survival time, generalised gamma, piecewise exponential, fractional polynomial and Royston-Parmar models. Results All models fitted the melanoma network acceptably well. However, there were important differences in extrapolations of the survival curve and interpretability of the modelling constraints demonstrating the potential for different conclusions from different modelling approaches. Conclusion The restricted mean survival time, generalised gamma, piecewise exponential, fractional polynomial and Royston-Parmar models can accommodate non-proportional hazards and differing lengths of trial follow-up within a network meta-analysis of time-to-event outcomes. We recommend that model choice is informed using available and relevant prior knowledge, model transparency, graphically comparing survival curves alongside observed data to aid consideration of the reliability of the survival estimates, and consideration of how the treatment effect estimates can be incorporated within a decision model.

On estimating the area under the ROC curve in ranked set sampling

Abstract: In medical research, the receiver operating characteristic curve is widely used to evaluate accuracy of a continuous biomarker. The area under this curve is known as an index for overall performance of the biomarker. This article develops three new estimators of the area under the receiver operating characteristic curve in ranked set sampling. The first estimator is obtained under normality assumption. The two other estimators are constructed by applying a Box–Cox transformation on data, and then using either a parametric estimator or a kernel-density-based estimator. A simulation study is carried out to compare the proposed estimators with those available in the literature. It emerges that the new estimators offer some advantages in specific situations. Application of the methods is demonstrated using real data in the context of medicine.

A distribution-free control charting technique based on change-point analysis for detection of epidemics

Abstract: Worldwide, the detection of epidemics has been recognized as a continuing problem of crucial importance to public health surveillance. Various approaches for detecting and quantifying epidemics of infectious diseases in the recent literature are directly influenced by methods of Statistical Process Control (SPC). However, implementing SPC quality tools directly to the general health care monitoring problem, in a similar manner as in industrial quality control, is not feasible since many assumptions such as stationarity, known asymptotic distribution etc. are not met. Toward this end, in this paper, some of the open statistical research issues involved in this field are discussed, and a distribution-free control charting technique based on change-point analysis is applied and evaluated for detection of epidemics. The main tool in this methodology is the detection of unusual trends, in the sense that the beginning of an unusual trend marks a switch from a control state to an epidemic state. The in-control and out-of-control performance of the adapted control scheme from SPC is thoroughly investigated using Monte Carlo simulations, and the applied scheme is found to outperform its parametric and nonparametric competitors in many cases. Moreover, the empirical comparative study provides evidence that the adapted change-point detection scheme has several appealing properties compared to the current practice for detection of epidemics.

A permutation-based approach to inference for weighted sum regression with correlated chemical mixtures

Abstract: There is a growing demand for methods to determine the effects that chemical mixtures have on human health. One statistical challenge is identifying true “bad actors” from a mixture of highly correlated predictors, a setting in which standard approaches such as linear regression become highly variable. Weighted Quantile Sum regression has been proposed to address this problem, through a two-step process where mixture component weights are estimated using bootstrap aggregation in a training dataset and inference on the overall mixture effect occurs in a held-out test set. Weighted Quantile Sum regression is popular in applied papers, but the reliance on data splitting is suboptimal, and analysts who use the same data for both steps risk inflating the Type I error rate. We therefore propose a modification of Weighted Quantile Sum regression that uses a permutation test for inference, which allows for weight estimation using the entire dataset and preserves Type I error. To minimize computational burden, we propose replacing the bootstrap with L1 or L2 penalization and describe how to choose the appropriate penalty given expert knowledge about a mixture of interest. We apply our method to a national pregnancy cohort study of prenatal phthalate exposure and child health outcomes.

Online control of the False Discovery Rate in group-sequential platform trials

Abstract: When testing multiple hypotheses, a suitable error rate should be controlled even in exploratory trials. Conventional methods to control the False Discovery Rate assume that all p-values are available at the time point of test decision. In platform trials, however, treatment arms enter and leave the trial at different times during its conduct. Therefore, the actual number of treatments and hypothesis tests is not fixed in advance and hypotheses are not tested at once, but sequentially. Recently, for such a setting the concept of online control of the False Discovery Rate was introduced. We propose several heuristic variations of the LOND procedure (significance Levels based On Number of Discoveries) that incorporate interim analyses for platform trials, and study their online False Discovery Rate via simulations. To adjust for the interim looks spending functions are applied with O’Brien-Fleming or Pocock type group-sequential boundaries. The power depends on the prior distribution of effect sizes, for example, whether true alternatives are uniformly distributed over time or not. We consider the choice of design parameters for the LOND procedure to maximize the overall power and investigate the impact on the False Discovery Rate by including both concurrent and non-concurrent control data.

Uncertainty quantification for epidemiological forecasts of COVID-19 through combinations of model predictions

Abstract: Scientific advice to the UK government throughout the COVID-19 pandemic has been informed by ensembles of epidemiological models provided by members of the Scientific Pandemic Influenza group on Modelling. Among other applications, the model ensembles have been used to forecast daily incidence, deaths and hospitalizations. The models differ in approach (e.g. deterministic or agent-based) and in assumptions made about the disease and population. These differences capture genuine uncertainty in the understanding of disease dynamics and in the choice of simplifying assumptions underpinning the model. Although analyses of multi-model ensembles can be logistically challenging when time-frames are short, accounting for structural uncertainty can improve accuracy and reduce the risk of over-confidence in predictions. In this study, we compare the performance of various ensemble methods to combine short-term (14-day) COVID-19 forecasts within the context of the pandemic response. We address practical issues around the availability of model predictions and make some initial proposals to address the shortcomings of standard methods in this challenging situation.

Robust statistical inference for matched win statistics

Abstract: As alternatives to the time-to-first-event analysis of composite endpoints, the win statistics, that is, the net benefit, the win ratio, and the win odds have been proposed to assess treatment effects, using a hierarchy of prioritized component outcomes based on clinical relevance or severity. Whether we are using paired organs of a human body or pair-matching patients by risk profiles or propensity scores, we can leverage the level of granularity of matched win statistics to assess the treatment effect. However, inference for the matched win statistics (net benefit, win ratio, and win odds)—quantities related to proportions—is either not available or unsatisfactory, especially in samples of small to moderate size or when the proportion of wins (or losses) is near 0 or 1. In this paper, we present methods to address these limitations. First, we introduce a different statistic to test for the null hypothesis of no treatment effect and provided a sample size formula. Then, we use the method of variance estimates recovery to derive reliable, boundary-respecting confidence intervals for the matched net benefit, win ratio, and win odds. Finally, a simulation study demonstrates the performance of the proposed methods. We illustrate the proposed methods with two data examples.

Risk difference tests for stratified binary data under Dallal’s model

Abstract: In medical studies, the binary data is often encountered when the paired organs or body parts receive treatment. However, the same treatment may lead to different therapeutic effects based on the stratified factors or confounding effects. Under Dallal’s model, the paper proposes the homogeneity test of risk difference to determine the necessity of stratified treatment. When the stratification is not necessary, common test is introduced to investigate if the risk difference is equal to a fixed constant between two groups. Several statistical tests are derived to analyze homogeneity and common hypotheses, respectively. Monte Carlo simulations show that the score tests behave well in both of hypotheses. Wald-type and Rosner’s statistics are always liberal but have higher empirical powers. Especially, the likelihood ratio statistic is better for the homogeneity test in the case of smaller data with larger strata. Two real examples are provided to illustrate the effectiveness of the proposed methods in ankle instability and otolaryngology studies.

CFO: Calibration-free odds design for phase I/II clinical trials

Abstract: Recent revolution in oncology treatment has witnessed emergence and fast development of the targeted therapy and immunotherapy. In contrast to traditional cytotoxic agents, these types of treatment tend to be more tolerable and thus efficacy is of more concern. As a result, seamless phase I/II trials have gained enormous popularity, which aim to identify the optimal biological dose (OBD) rather than the maximum tolerated dose (MTD). To enhance the accuracy and robustness for identification of OBD, we develop a calibration-free odds (CFO) design. For toxicity monitoring, the CFO design casts the current dose in competition with its two neighboring doses to obtain an admissible set. For efficacy monitoring, CFO selects the dose that has the largest posterior probability to achieve the highest efficacy under the Bayesian paradigm. In contrast to most of the existing designs, the prominent merit of CFO is that its main dose-finding component is model-free and calibration-free, which can greatly ease the burden on artificial input of design parameters and thus enhance the robustness and objectivity of the design. Extensive simulation studies demonstrate that the CFO design strikes a good balance between efficiency and safety for MTD identification under phase I trials, and yields comparable or sometimes slightly better performance for OBD identification than the competing methods under phase I/II trials.

On estimating a constrained bivariate random effects model for meta-analysis of test accuracy studies

Abstract: Tailored meta-analysis uses setting-specific knowledge for the test positive rate and disease prevalence to constrain the possible values for a test's sensitivity and specificity. The constrained region is used to select those studies relevant to the setting for meta-analysis using an unconstrained bivariate random effects model (BRM). However, sometimes there may be no studies to aggregate, or the summary estimate may lie outside the plausible or “applicable” region. Potentially these shortcomings may be overcome by incorporating the constraints in the BRM to produce a constrained model. Using a penalised likelihood approach we developed an optimisation algorithm based on co-ordinate ascent and Newton-Raphson iteration to fit a constrained bivariate random effects model (CBRM) for meta-analysis. Using numerical examples based on simulation studies and real datasets we compared its performance with the BRM in terms of bias, mean squared error and coverage probability. We also determined the ‘closeness’ of the estimates to their true values using the Euclidian and Mahalanobis distances. The CBRM produced estimates which in the majority of cases had lower absolute mean bias and greater coverage probability than the BRM. The estimated sensitivities and specificity for the CBRM were, in general, closer to the true values than the BRM. For the two real datasets, the CBRM produced estimates which were in the applicable region in contrast to the BRM. When combining setting-specific data with test accuracy meta-analysis, a constrained model is more likely to yield a plausible estimate for the sensitivity and specificity in the practice setting than an unconstrained model.

Modified Brier score for evaluating prediction accuracy for binary outcomes

Abstract: The Brier score has been a popular measure of prediction accuracy for binary outcomes. However, it is not straightforward to interpret the Brier score for a prediction model since its value depends on the outcome prevalence. We decompose the Brier score into two components, the mean squares between the estimated and true underlying binary probabilities, and the variance of the binary outcome that is not reflective of the model performance. We then propose to modify the Brier score by removing the variance of the binary outcome, estimated via a general sliding window approach. We show that the new proposed measure is more sensitive for comparing different models through simulation. A standardized performance improvement measure is also proposed based on the new criterion to quantify the improvement of prediction performance. We apply the new measures to the data from the Breast Cancer Surveillance Consortium and compare the performance of predicting breast cancer risk using the models with and without its most important predictor.

Benchmarking survival outcomes: A funnel plot for survival data

Abstract: Benchmarking is commonly used in many healthcare settings to monitor clinical performance, with the aim of increasing cost-effectiveness and safe care of patients. The funnel plot is a popular tool in visualizing the performance of a healthcare center in relation to other centers and to a target, taking into account statistical uncertainty. In this paper, we develop a methodology for constructing funnel plots for survival data. The method takes into account censoring and can deal with differences in censoring distributions across centers. Practical issues in implementing the methodology are discussed, particularly in the setting of benchmarking clinical outcomes for hematopoietic stem cell transplantation. A simulation study is performed to assess the performance of the funnel plots under several scenarios. Our methodology is illustrated using data from the European Society for Blood and Marrow Transplantation benchmarking project.

Integrating relative survival in multi-state models—a non-parametric approach

Abstract: Multi-state models provide an extension of the usual survival/event-history analysis setting. In the medical domain, multi-state models give the possibility of further investigating intermediate events such as relapse and remission. In this work, a further extension is proposed using relative survival, where mortality due to population causes (i.e. non-disease-related mortality) is evaluated. The objective is to split all mortality in disease and non-disease-related mortality, with and without intermediate events, in datasets where cause of death is not recorded or is uncertain. To this end, population mortality tables are integrated into the estimation process, while using the basic relative survival idea that the overall mortality hazard can be written as a sum of a population and an excess part. Hence, we propose an upgraded non-parametric approach to estimation, where population mortality is taken into account. Precise definitions and suitable estimators are given for both the transition hazards and probabilities. Variance estimating techniques and confidence intervals are introduced and the behaviour of the new method is investigated through simulations. The newly developed methodology is illustrated by the analysis of a cohort of patients followed after an allogeneic hematopoietic stem cell transplantation. The work has been implemented in the R package mstate.

MEGH: A parametric class of general hazard models for clustered survival data

Abstract: In many applications of survival data analysis, the individuals are treated in different medical centres or belong to different clusters defined by geographical or administrative regions. The analysis of such data requires accounting for between-cluster variability. Ignoring such variability would impose unrealistic assumptions in the analysis and could affect the inference on the statistical models. We develop a novel parametric mixed-effects general hazard (MEGH) model that is particularly suitable for the analysis of clustered survival data. The proposed structure generalises the mixed-effects proportional hazards and mixed-effects accelerated failure time structures, among other structures, which are obtained as special cases of the MEGH structure. We develop a likelihood-based algorithm for parameter estimation in general subclasses of the MEGH model, which is implemented in our R package MEGH. We propose diagnostic tools for assessing the random effects and their distributional assumption in the proposed MEGH model. We investigate the performance of the MEGH model using theoretical and simulation studies, as well as a real data application on leukaemia.

Standard error estimation in meta-analysis of studies reporting medians

Abstract: We consider the setting of an aggregate data meta-analysis of a continuous outcome of interest. When the distribution of the outcome is skewed, it is often the case that some primary studies report the sample mean and standard deviation of the outcome and other studies report the sample median along with the first and third quartiles and/or minimum and maximum values. To perform meta-analysis in this context, a number of approaches have recently been developed to impute the sample mean and standard deviation from studies reporting medians. Then, standard meta-analytic approaches with inverse-variance weighting are applied based on the (imputed) study-specific sample means and standard deviations. In this article, we illustrate how this common practice can severely underestimate the within-study standard errors, which results in poor coverage for the pooled mean in common effect meta-analyses and overestimation of between-study heterogeneity in random effects meta-analyses. We propose a straightforward bootstrap approach to estimate the standard errors of the imputed sample means. Our simulation study illustrates how the proposed approach can improve the estimation of the within-study standard errors and consequently improve coverage for the pooled mean in common effect meta-analyses and estimation of between-study heterogeneity in random effects meta-analyses. Moreover, we apply the proposed approach in a meta-analysis to identify risk factors of a severe course of COVID-19.

A potential outcomes approach to defining and estimating gestational age-specific exposure effects during pregnancy

Abstract: Many studies seek to evaluate the effects of potentially harmful pregnancy exposures during specific gestational periods. We consider an observational pregnancy cohort where pregnant individuals can initiate medication usage or become exposed to a drug at various times during their pregnancy. An important statistical challenge involves how to define and estimate exposure effects when pregnancy loss or delivery can occur over time. Without proper consideration, the results of standard analysis may be vulnerable to selection bias, immortal time-bias, and time-dependent confounding. In this study, we apply the “target trials” framework of Hernán and Robins in order to define effects based on the counterfactual approach often used in causal inference. This effect is defined relative to a hypothetical randomized trial of timed pregnancy exposures where delivery may precede and thus potentially interrupt exposure initiation. We describe specific implementations of inverse probability weighting, G-computation, and Targeted Maximum Likelihood Estimation to estimate the effects of interest. We demonstrate the performance of all estimators using simulated data and show that a standard implementation of inverse probability weighting is biased. We then apply our proposed methods to a pharmacoepidemiology study to evaluate the potentially time-dependent effect of exposure to inhaled corticosteroids on birthweight in pregnant people with mild asthma.

Approximate Bayesian computation design for phase I clinical trials

Abstract: In the development of new cancer treatment, an essential step is to determine the maximum tolerated dose in a phase I clinical trial. In general, phase I trial designs can be classified as either model-based or algorithm-based approaches. Model-based phase I designs are typically more efficient by using all observed data, while there is a potential risk of model misspecification that may lead to unreliable dose assignment and incorrect maximum tolerated dose identification. In contrast, most of the algorithm-based designs are less efficient in using cumulative information, because they tend to focus on the observed data in the neighborhood of the current dose level for dose movement. To use the data more efficiently yet without any model assumption, we propose a novel approximate Bayesian computation approach to phase I trial design. Not only is the approximate Bayesian computation design free of any dose–toxicity curve assumption, but it can also aggregate all the available information accrued in the trial for dose assignment. Extensive simulation studies demonstrate its robustness and efficiency compared with other phase I trial designs. We apply the approximate Bayesian computation design to the MEK inhibitor selumetinib trial to demonstrate its satisfactory performance. The proposed design can be a useful addition to the family of phase I clinical trial designs due to its simplicity, efficiency and robustness.

Estimation of the proportion of true null hypotheses under sparse dependence: Adaptive FDR controlling in microarray data

Abstract: The proportion of non-differentially expressed genes is an important quantity in microarray data analysis and an appropriate estimate of the same is used to construct adaptive multiple testing procedures. Most of the estimators for the proportion of true null hypotheses based on the thresholding, maximum likelihood and density estimation approaches assume independence among the gene expressions. Usually, sparse dependence structure is natural in modelling associations in microarray gene expression data and hence it is necessary to develop methods for accommodating the sparse dependence well within the framework of existing estimators. We propose a clustering based method to put genes in the same group that are not coexpressed using the estimated high dimensional correlation structure under sparse assumption as dissimilarity matrix. This novel method is applied to three existing estimators for the proportion of true null hypotheses. Extensive simulation study shows that the proposed method improves an existing estimator by making it less conservative and the corresponding adaptive Benjamini-Hochberg algorithm more powerful. The proposed method is applied to a microarray gene expression dataset of colorectal cancer patients and the results show gain in terms of number of differentially expressed genes. The R code is available at https://github.com/aniketstat/Proportiontion-of-true-null-under-sparse-dependence-2021.

Estimating latent, dynamic processes of breast cancer tumour growth and distant metastatic spread from mammography screening data

Abstract: We propose a framework for jointly modelling tumour size at diagnosis and time to distant metastatic spread, from diagnosis, based on latent dynamic sub-models of growth of the primary tumour and of distant metastatic detection. The framework also includes a sub-model for screening sensitivity as a function of latent tumour size. Our approach connects post-diagnosis events to the natural history of cancer and, once refined, may prove useful for evaluating new interventions, such as personalised screening regimes. We evaluate our model-fitting procedure using Monte Carlo simulation, showing that the estimation algorithm can retrieve the correct model parameters, that key patterns in the data can be captured by the model even with misspecification of some structural assumptions, and that, still, with enough data it should be possible to detect strong misspecifications. Furthermore, we fit our model to observational data from an extension of a case-control study of post-menopausal breast cancer in Sweden, providing model-based estimates of the probability of being free from detected distant metastasis as a function of tumour size, mode of detection (of the primary tumour), and screening history. For women with screen-detected cancer and two previous negative screens, the probabilities of being free from detected distant metastases 5 years after detection and removal of the primary tumour are 0.97, 0.89 and 0.59 for tumours of diameter 5, 15 and 35 mm, respectively. We also study the probability of having latent/dormant metastases at detection of the primary tumour, estimating that 33% of patients in our study had such metastases.

A dose-effect network meta-analysis model with application in antidepressants using restricted cubic splines.

Abstract: Network meta-analysis has been used to answer a range of clinical questions about the preferred intervention for a given condition. Although the effectiveness and safety of pharmacological agents depend on the dose administered, network meta-analysis applications typically ignore the role that drugs dosage plays in the results. This leads to more heterogeneity in the network. In this paper, we present a suite of network meta-analysis models that incorporate the dose-effect relationship using restricted cubic splines. We extend existing models into a dose-effect network meta-regression to account for study-level covariates and for groups of agents in a class-effect dose-effect network meta-analysis model. We apply our models to a network of aggregate data about the efficacy of 21 antidepressants and placebo for depression. We find that all antidepressants are more efficacious than placebo after a certain dose. Also, we identify the dose level at which each antidepressant's effect exceeds that of placebo and estimate the dose beyond which the effect of antidepressants no longer increases. When covariates were introduced to the model, we find that studies with small sample size tend to exaggerate antidepressants efficacy for several of the drugs. Our dose-effect network meta-analysis model with restricted cubic splines provides a flexible approach to modelling the dose-effect relationship in multiple interventions. Decision-makers can use our model to inform treatment choice.