Statistical Methods in Medical Research

Prospective randomized controlled trials are difficult to obtain if a promising new therapy has to be tested against seemingly obsolete alternatives. One method to address this problem is to compare the results of (multicentre) trials to literature results. However, previous treatment-era changes and population-dependent results complicate objective comparisons. The presented approach describes a method to objectify such comparisons in cases in which individual raw data regarding a new therapy have to be compared to summary results regarding a conventional alternative published in the literature. The chosen example is the introduction of bovine neck veins as a substitute for dysfunctional human pulmonary valves, and the conventional therapeutic alternative is pulmonary-artery homografts. Literature research, subgroup identification, filtering, endpoint remodelling, weighting and, if necessary, confidence-limit calculation yield adjusted comparisons. These individual comparisons are then aggregated, first by article and then over several articles (similar to meta-analyses), resulting in a differentiated panel of answers (Multiply Adjusted Comparisons). In situations in which extensive raw data regarding a new therapeutic alternative but no randomized controlled trials and no raw data from previous studies using the conventional therapeutic alternative are available, the proposed method identifies the best evidence and is by far superior to unadjusted direct comparisons or gut feelings.

Measurement of serum biomarkers by multiplex assays may be more variable as compared to single biomarker assays. Measurement error in these data may bias parameter estimates in regression analysis, which could mask true associations of serum biomarkers with an outcome. The Least Absolute Shrinkage and Selection Operator (LASSO) can be used for variable selection in these high-dimensional data. Furthermore, when the distribution of measurement error is assumed to be known or estimated with replication data, a simple measurement error correction method can be applied to the LASSO method. However, in practice the distribution of the measurement error is unknown and is expensive to estimate through replication both in monetary cost and need for greater amount of sample which is often limited in quantity. We adapt an existing bias correction approach by estimating the measurement error using validation data in which a subset of serum biomarkers are re-measured on a random subset of the study sample. We evaluate this method using simulated data and data from the Tucson Epidemiological Study of Airway Obstructive Disease (TESAOD). We show that the bias in parameter estimation is reduced and variable selection is improved.

Statistical models of breast cancer tumour progression have been used to further our knowledge of the natural history of breast cancer, to evaluate mammography screening in terms of mortality, to estimate overdiagnosis, and to estimate the impact of lead-time bias when comparing survival times between screen detected cancers and cancers found outside of screening programs. Multi-state Markov models have been widely used, but several research groups have proposed other modelling frameworks based on specifying an underlying biological continuous tumour growth process. These continuous models offer some advantages over multi-state models and have been used, for example, to quantify screening sensitivity in terms of mammographic density, and to quantify the effect of body size covariates on tumour growth and time to symptomatic detection. As of yet, however, the continuous tumour growth models are not sufficiently developed and require extensive computing to obtain parameter estimates. In this article, we provide a detailed description of the underlying assumptions of the continuous tumour growth model, derive new theoretical results for the model, and show how these results may help the development of this modelling framework. In illustrating the approach, we develop a model for mammography screening sensitivity, using a sample of 1901 post-menopausal women diagnosed with invasive breast cancer.

Stepped wedge and cluster randomised crossover trials are examples of cluster randomised designs conducted over multiple time periods that are being used with increasing frequency in health research. Recent systematic reviews of both of these designs indicate that the within-cluster correlation is typically taken account of in the analysis of data using a random intercept mixed model, implying a constant correlation between any two individuals in the same cluster no matter how far apart in time they are measured: within-period and between-period intra-cluster correlations are assumed to be identical. Recently proposed extensions allow the within- and between-period intra-cluster correlations to differ, although these methods require that all between-period intra-cluster correlations are identical, which may not be appropriate in all situations. Motivated by a proposed intensive care cluster randomised trial, we propose an alternative correlation structure for repeated cross-sectional multiple-period cluster randomised trials in which the between-period intra-cluster correlation is allowed to decay depending on the distance between measurements. We present results for the variance of treatment effect estimators for varying amounts of decay, investigating the consequences of the variation in decay on sample size planning for stepped wedge, cluster crossover and multiple-period parallel-arm cluster randomised trials. We also investigate the impact of assuming constant between-period intra-cluster correlations instead of decaying between-period intra-cluster correlations. Our results indicate that in certain design configurations, including the one corresponding to the proposed trial, a correlation decay can have an important impact on variances of treatment effect estimators, and hence on sample size and power. An R Shiny app allows readers to interactively explore the impact of correlation decay.

Motivated by a study exploring differences in glycemic control between non-Hispanic black and non-Hispanic white veterans with type 2 diabetes, we aim to address a type of confounding that arises in spatially referenced observational studies. Specifically, we develop a spatial doubly robust propensity score estimator to reduce bias associated with geographic confounding, which occurs when measured or unmeasured confounding factors vary by geographic location, leading to imbalanced group comparisons. We augment the doubly robust estimator with spatial random effects, which are assigned conditionally autoregressive priors to improve inferences by borrowing information across neighboring geographic regions. Through a series of simulations, we show that ignoring spatial variation results in increased absolute bias and mean squared error, while the spatial doubly robust estimator performs well under various levels of spatial heterogeneity and moderate sample sizes. In the motivating application, we construct three global estimates of the risk difference between race groups: an unadjusted estimate, a doubly robust estimate that adjusts only for patient-level information, and a hierarchical spatial doubly robust estimate. Results indicate a gradual reduction in the risk difference at each stage, with the inclusion of spatial random effects providing a 20% reduction compared to an estimate that ignores spatial heterogeneity. Smoothed maps indicate poor glycemic control across Alabama and southern Georgia, areas comprising the so-called “stroke belt.” These results suggest the need for community-specific interventions to target diabetes in geographic areas of greatest need.

In this work we propose a method for optimal treatment assignment based on individual covariate information for a patient. For the K treatment ( K ≥ 2 ) scenario, we compare quantities that are suitable surrogates to true conditional probabilities of outcome variable of each treatment dominating outcome variables for all other treatments conditional on patient specific scores constructed from patient-specific covariates. As opposed to methods based on conditional means, our method can be applied for a broad set of models and error structures. Furthermore, the proposed method has very desirable large sample properties. We suggest Single Index Models as appropriate models connecting outcome variables to covariates and our empirical investigations show that correct treatment assignments are highly accurate. The proposed method is also rather robust against departures from a Single Index Model structure. Furthermore, selection of a treatment using the proposed metric appears to incur no losses in terms of the average reward for cases when two treatments are close in terms of this metric. We also conduct a real data analysis to show the applicability of the proposed procedure. This analysis highlights possible gains both in terms of average response and survival time if one were to use the proposed method.

Multistate models provide an important method for analyzing a wide range of life history processes including disease progression and patient recovery following medical intervention. Panel data consisting of the states occupied by an individual at a series of discrete time points are often used to estimate transition intensities of the underlying continuous-time process. When transition intensities depend on the time elapsed in the current state and back transitions between states are possible, this intermittent observation process presents difficulties in estimation due to intractability of the likelihood function. In this manuscript, we present an iterative stochastic expectation-maximization algorithm that relies on a simulation-based approximation to the likelihood function and implement this algorithm using rejection sampling. In a simulation study, we demonstrate the feasibility and performance of the proposed procedure. We then demonstrate application of the algorithm to a study of dementia, the Nun Study, consisting of intermittently-observed elderly subjects in one of four possible states corresponding to intact cognition, impaired cognition, dementia, and death. We show that the proposed stochastic expectation-maximization algorithm substantially reduces bias in model parameter estimates compared to an alternative approach used in the literature, minimal path estimation. We conclude that in estimating intermittently observed semi-Markov models, the proposed approach is a computationally feasible and accurate estimation procedure that leads to substantial improvements in back transition estimates.

When performing a repeated measures experiment, such as a clinical trial, there is a risk of subject drop-out during the experiment. If one or more subjects leave the study prematurely, a situation could arise where the eventual design is disconnected, implying that very few treatment contrasts for both direct effects and carryover effects are estimable. This paper aims to identify experimental conditions where this problem with the eventual design can be avoided. It is shown that in the class of uniformly balanced repeated measurement designs consisting of two or more Latin squares, there are planned designs with the following useful property. Provided that all subjects have completed the first two periods of study, such a design will not be replaced by a disconnected eventual design due to drop-out, irrespective of the type of drop-out behaviour that may occur. Designs with this property are referred to as perpetually connected. These experimental conditions are identified and examined in the paper and an example of at least one perpetually connected uniformly balanced repeated measurement design is given in each case. The results improve upon previous contributions in the literature that have been confined largely to cases in which drop-out occurs only in the final periods of study.

Incomplete block crossover trials with period-specific baseline and post-baseline (outcome) measures for each subject are often used in clinical drug development; without loss of generality, we focus on the three-treatment two-period ( 3 × 2 ) crossover. Data from such trials are commonly analyzed using a mixed effects model with indicator terms for treatment and period, and an unstructured covariance matrix for the vector of intra-subject measurements. It is well-known that treatment effect estimates from this analysis are complex functions of both within-subject and between-subject treatment contrasts. We caution that the associated type I error rate and power for hypothesis testing can be non-trivially influenced by how the baselines are utilized. Specifically, the mixed effects analysis which uses change from baseline as the dependent variable is shown to consistently underperform corresponding analyses in which the outcome is the dependent variable and linear combinations of the baselines are used as period-specific and/or period-invariant covariates. A simpler fixed effects analysis of covariance involving only within-subject contrasts is also described for small sample situations in which the mixed effects analyses can suffer from increased type I error rates. Theoretical insights, simulation results and an illustrative example with real data are used to develop the main points.

Sample size calculations are needed to design and assess the feasibility of case-control studies. Although such calculations are readily available for simple case-control designs and univariate analyses, there is limited theory and software for multivariate unconditional logistic analysis of case-control data. Here we outline the theory needed to detect scalar exposure effects or scalar interactions while controlling for other covariates in logistic regression. Both analytical and simulation methods are presented, together with links to the corresponding software.

Characterization of long-term disease dynamics, from disease-free to end-stage, is integral to understanding the course of neurodegenerative diseases such as Parkinson’s and Alzheimer’s, and ultimately, how best to intervene. Natural history studies typically recruit multiple cohorts at different stages of disease and follow them longitudinally for a relatively short period of time. We propose a latent time joint mixed effects model to characterize long-term disease dynamics using this short-term data. Markov chain Monte Carlo methods are proposed for estimation, model selection, and inference. We apply the model to detailed simulation studies and data from the Alzheimer’s Disease Neuroimaging Initiative.

How people use their time has been linked with their health. For example, spending more time being physically active is known to be beneficial for health, whereas long durations of sitting have been associated with unfavourable health outcomes. Accordingly, public health messages have advocated swapping strategies to promote the reallocation of time between parts of the time-use composition, such as “Move More, Sit Less”, with the aim of achieving optimal distribution of time for health. However, the majority of research underpinning these public health messages has not considered daily time use as a composition, and has ignored the relative nature of time-use data. We present a way of applying compositional data analysis to estimate change in a health outcome when fixed durations of time are reallocated from one part of a particular time-use composition to another, while the remaining parts are kept constant, based on a multiple linear regression model on isometric log ratio coordinates. In an example, we examine the expected differences in Body Mass Index z-scores for reallocations of time between sleep, physical activity and sedentary behaviour.

Longitudinal data are often collected in biomedical applications in such a way that measurements on more than one response are taken from a given subject repeatedly overtime. For some problems, these multiple profiles need to be modeled jointly to get insight on the joint evolution and/or association of these responses over time. In practice, such longitudinal outcomes may have many zeros that need to be accounted for in the analysis. For example, in dietary intake studies, as we focus on in this paper, some food components are eaten daily by almost all subjects, while others are consumed episodically, where individuals have time periods where they do not eat these components followed by periods where they do. These episodically consumed foods need to be adequately modeled to account for the many zeros that are encountered. In this paper, we propose a joint model to analyze multivariate hierarchical semicontinuous data characterized by many zeros and more than one replicate observations at each measurement occasion. This approach allows for different probability mechanisms for describing the zero behavior as compared with the mean intake given that the individual consumes the food. To deal with the potentially large number of multivariate profiles, we use a pairwise model fitting approach that was developed in the context of multivariate Gaussian random effects models with large number of multivariate components. The novelty of the proposed approach is that it incorporates: (1) multivariate, possibly correlated, response variables; (2) within subject correlation resulting from repeated measurements taken from each subject; (3) many zero observations; (4) overdispersion; and (5) replicate measurements at each visit time.

Data on rates, percentages, or proportions arise frequently in many different applied disciplines like medical biology, health care, psychology, and several others. In this paper, we develop a robust inference procedure for the beta regression model, which is used to describe such response variables taking values in (0, 1) through some related explanatory variables. In relation to the beta regression model, the issue of robustness has been largely ignored in the literature so far. The existing maximum likelihood-based inference has serious lack of robustness against outliers in data and generate drastically different (erroneous) inference in the presence of data contamination. Here, we develop the robust minimum density power divergence estimator and a class of robust Wald-type tests for the beta regression model along with several applications. We derive their asymptotic properties and describe their robustness theoretically through the influence function analyses. Finite sample performances of the proposed estimators and tests are examined through suitable simulation studies and real data applications in the context of health care and psychology. Although we primarily focus on the beta regression models with a fixed dispersion parameter, some indications are also provided for extension to the variable dispersion beta regression models with an application.

Outcome reporting bias occurs when outcomes in research studies are selectively reported, the selection being influenced by the study results. For benefit outcomes, we have shown how risk assessments using the Outcome Reporting Bias in Trials risk classification scale can be used to calculate bias-adjusted treatment effect estimates. This paper presents a new and simpler version of the benefits method, and shows how it can be extended to cover the partial reporting and non-reporting of harm outcomes. Our motivating example is a Cochrane systematic review of 12 studies of Topiramate add-on therapy for drug-resistant partial epilepsy. Bias adjustments for partially reported or unreported outcomes suggest that the review has overestimated the benefits and underestimated the harms of the test treatment.

A common problem in biomedical research is to calculate the sample size required to learn a classifier using a (possibly high-dimensional) panel of biomarkers. This paper describes a simple method based on a Gaussian approximation for calculating the predictive performance of the learned classifier given the size of the biomarker panel, the size of the training sample, and the optimal predictive performance (expressed as C-statistic C opt ) of the biomarker panel that could be obtained if a training sample of unlimited size were available. Under the assumption that the biomarker effect sizes have the same correlation structure as the biomarkers, the required sample size does not depend upon these correlations, but only upon C opt and upon the sparsity of the distribution of effect sizes, defined by the proportion of biomarkers that have nonzero effects. To learn a classifier that extracts 80% of the predictive information, the required case sample size varies from about 0.1 cases per variable for a panel with C opt = 0 . 9 and a sparse distribution of effect sizes (such that 1% of biomarkers have nonzero effect sizes) to nine cases per variable for a panel with C opt = 0 . 75 and a diffuse distribution of effect sizes.

There is a need for statistical methods appropriate for the analysis of clinical trials from a personalized-medicine viewpoint as opposed to the common statistical practice that simply examines average treatment effects. This article proposes an approach to quantifying, reporting and analyzing individual benefits of medical or behavioral treatments to severely ill patients with chronic conditions, using data from clinical trials. The approach is a new development of a published framework for measuring the severity of a chronic disease and the benefits treatments provide to individuals, which utilizes regression models with random coefficients. Here, a patient is considered to be severely ill if the patient’s basal severity is close to one. This allows the derivation of a very flexible family of probability distributions of individual benefits that depend on treatment duration and the covariates included in the regression model. Our approach may enrich the statistical analysis of clinical trials of severely ill patients because it allows investigating the probability distribution of individual benefits in the patient population and the variables that influence it, and we can also measure the benefits achieved in specific patients including new patients. We illustrate our approach using data from a clinical trial of the anti-depressant imipramine.

The GH-2000 score has been developed as a powerful and unique technique for the detection of growth hormone misuse by sportsmen and women. The score depends upon the measurement of two growth hormone sensitive markers, insulin-like growth factor-I and the amino-terminal pro-peptide of type III collagen. It also includes a term to adjust for the age of the athlete. Decision limits for the GH-2000 score have been developed and are incorporated into the guidelines of the World Anti-Doping Agency. These decision limits are derived by setting a 1 in 10,000 false-positive rate rule. As these decision limits are estimated from samples of GH-2000 scores, they carry uncertainty. In previous work, this uncertainty has been addressed by establishing an upper 95% confidence interval for the true decision limits based on a normal approximation which has been shown to be appropriate if sample sizes are large (such as 1000 and above). Here, we show that these approximations, whether reasonable or not, can be entirely avoided by developing an upper 95% confidence interval for the true decision limits using an approach based upon the t-distribution. While there are considerable differences for smaller sample sizes, these become negligible when the sample size is large such as 1000 and above.

We develop variable selection approaches for accelerated failure time models, consisting of a group of algorithms based on a synthesis of two widely used techniques in the area of variable selection for survival analysis—the Buckley–James method and the Dantzig selector. Two algorithms are based on proposed modified Buckley–James estimating methods that are designed for high-dimensional censored data. Another two algorithms are based on a two-stage weighted Dantzig selector method where weights are obtained from the two proposed synthesis-based algorithms. The methods are easy to understand and they perform estimation and variable selection simultaneously. Furthermore, they can deal with collinearity among the covariates. We conducted several simulation studies and one empirical analysis with a microarray dataset; these studies demonstrated satisfactory variable selection performance. In addition, the microarray data analysis shows the methods performing similarly to three other correlation-based greedy variable selection techniques in the literature—sure independence screening, tilted correlation screening (TCS), and partial correlation (PC) simple. This empirical study also found that the sure independence screening technique considerably improves the performance of most of the proposed methods.

Subgroup analyses in clinical trials are becoming increasingly important. In cancer research, more and more targeted therapies are explored from which probably only a portion of the whole population will benefit. An adaptive design for subgroup selection with identification of a subgroup, the adaptive signature design, was proposed in the literature. Unfortunately, measuring and validating the variables defining the subgroup (i.e. biomarkers) can be extremely expensive. For this reason, we propose an extension of this design where subgroup analysis is not performed when the overall results suggest that it is unlikely to achieve statistical significance in the subgroup. Avoiding measuring and validating expensive biomarkers in this case can save resources that could be used on more promising research.