Statistical Methods in Medical Research

Propensity score (PS) matching is a very popular causal estimator usually used to estimate the average treatment effect on the treated (ATT) from observational data. However, opting for this estimator may raise some efficiency issues when the sample size is limited. Therefore, we aimed to evaluate the performance of propensity score matching in this context. We started with a motivating example based on a cohort of 66 children with sickle cell anemia who received either allogeneic bone-marrow transplant or chronic transfusion. We found substantial differences in the ATT estimate according to the model selected for propensity score estimation and subsequent matching. Then, we assessed the performance of the different propensity score matching methods and post-matching analyses to estimate the ATT using a simulation study. Although all selected propensity score matching methods were based of previous recommendations, we found important discrepancies in the estimation of treatment effect between them, underlining the importance of thorough sensitivity analyses when using propensity score matching in the context of small sample sizes.

This paper concerns estimation of subgroup treatment effects with observational data. Existing propensity score methods are mostly developed for estimating overall treatment effect. Although the true propensity scores balance covariates in any subpopulations, the estimated propensity scores may result in severe imbalance in subgroup samples. Indeed, subgroup analysis amplifies a bias-variance tradeoff, whereby increasing complexity of the propensity score model may help to achieve covariate balance within subgroups, but it also increases variance. We propose a new method, the subgroup balancing propensity score, to ensure good subgroup balance as well as to control the variance inflation. For each subgroup, the subgroup balancing propensity score chooses to use either the overall sample or the subgroup (sub)sample to estimate the propensity scores for the units within that subgroup, in order to optimize a criterion accounting for a set of covariate-balancing moment conditions for both the overall sample and the subgroup samples. We develop two versions of subgroup balancing propensity score corresponding to matching and weighting, respectively. We devise a stochastic search algorithm to estimate the subgroup balancing propensity score when the number of subgroups is large. We demonstrate through simulations that the subgroup balancing propensity score improves the performance of propensity score methods in estimating subgroup treatment effects. We apply the subgroup balancing propensity score method to the Italy Survey of Household Income and Wealth (SHIW) to estimate the causal effects of having debit card on household consumption for different income groups.

The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure or treatment effects in observational studies. Routine practice is often based on stepwise selection procedures that use hypothesis testing, change-in-estimate assessments or the lasso, which have all been criticised for – amongst other things – not giving sufficient priority to the selection of confounders. This has prompted vigorous recent activity in developing procedures that prioritise the selection of confounders, while preventing the selection of so-called instrumental variables that are associated with exposure, but not outcome (after adjustment for the exposure). A major drawback of all these procedures is that there is no finite sample size at which they are guaranteed to deliver treatment effect estimators and associated confidence intervals with adequate performance. This is the result of the estimator jumping back and forth between different selected models, and standard confidence intervals ignoring the resulting model selection uncertainty. In this paper, we will develop insight into this by evaluating the finite-sample distribution of the exposure effect estimator in linear regression, under a number of the aforementioned confounder selection procedures. We will show that by making clever use of propensity scores, a simple and generic solution is obtained in the context of generalized linear models, which overcomes this concern (under weaker conditions than competing proposals). Specifically, we propose to use separate regularized regressions for the outcome and propensity score models in order to construct a doubly robust ‘g-estimator’; when these models are sufficiently sparse and correctly specified, standard confidence intervals for the g-estimator implicitly incorporate the uncertainty induced by the variable selection procedure.

In observational studies with a survival outcome, treatment initiation may be time dependent, which is likely to be affected by both time-invariant and time-varying covariates. In situations where the treatment is necessary for the study population, all or most subjects may be exposed to the treatment sooner or later. In this scenario, the causal effect of interest is the delay in treatment reception. A simple comparison of those receiving treatment early vs. those receiving treatment late might not be appropriate, as the timing of the treatment reception is not randomized. Extending Lu’s matching design with time-varying covariates, we propose a propensity score matching strategy to estimate the treatment delay effect. The goal is to balance the covariate distribution between on-time treatment and delayed treatment groups at each time point using risk set matching. Our simulation study shows that, in the presence of treatment delay effects, the matching-based analyses clearly outperform the conventional regression analysis using the naive Cox proportional hazards model. We apply this method to study the treatment delay effect of 17 alpha-hydroxyprogesterone caproate (17P) for patients with recurrent preterm birth.

Propensity score methods are a part of the standard toolkit for applied researchers who wish to ascertain causal effects from observational data. While they were originally developed for binary treatments, several researchers have proposed generalizations of the propensity score methodology for non-binary treatment regimes. Such extensions have widened the applicability of propensity score methods and are indeed becoming increasingly popular themselves. In this article, we closely examine two methods that generalize propensity scores in this direction, namely, the propensity function (PF), and the generalized propensity score (GPS), along with two extensions of the GPS that aim to improve its robustness. We compare the assumptions, theoretical properties, and empirical performance of these methods. On a theoretical level, the GPS and its extensions are advantageous in that they are designed to estimate the full dose response function rather than the average treatment effect that is estimated with the PF. We compare GPS with a new PF method, both of which estimate the dose response function. We illustrate our findings and proposals through simulation studies, including one based on an empirical study about the effect of smoking on healthcare costs. While our proposed PF-based estimator preforms well, we generally advise caution in that all available methods can be biased by model misspecification and extrapolation.

Matching on an estimated propensity score is frequently used to estimate the effects of treatments from observational data. Since the 1970s, different authors have proposed methods to combine matching at the design stage with regression adjustment at the analysis stage when estimating treatment effects for continuous outcomes. Previous work has consistently shown that the combination has generally superior statistical properties than either method by itself. In biomedical and epidemiological research, survival or time-to-event outcomes are common. We propose a method to combine regression adjustment and propensity score matching to estimate survival curves and hazard ratios based on estimating an imputed potential outcome under control for each successfully matched treated subject, which is accomplished using either an accelerated failure time parametric survival model or a Cox proportional hazard model that is fit to the matched control subjects. That is, a fitted model is then applied to the matched treated subjects to allow simulation of the missing potential outcome under control for each treated subject. Conventional survival analyses (e.g., estimation of survival curves and hazard ratios) can then be conducted using the observed outcome under treatment and the imputed outcome under control. We evaluated the repeated-sampling bias of the proposed methods using simulations. When using nearest neighbor matching, the proposed method resulted in decreased bias compared to crude analyses in the matched sample. We illustrate the method in an example prescribing beta-blockers at hospital discharge to patients hospitalized with heart failure.

Pseudo-values provide a method to perform regression analysis for complex quantities with right-censored data. A further complication, interval-censored data, appears when events such as dementia are studied in an epidemiological cohort. We propose an extension of the pseudo-value approach for interval-censored data based on a semi-parametric estimator computed using penalised likelihood and splines. This estimator takes interval-censoring and competing risks into account in an illness-death model. We apply the pseudo-value approach to three mean value parameters of interest in studies of dementia: the probability of staying alive and non-demented, the restricted mean survival time without dementia and the absolute risk of dementia. Simulation studies are conducted to examine properties of pseudo-values based on this semi-parametric estimator. The method is applied to the French cohort PAQUID, which included more than 3,000 non-demented subjects, followed for dementia for more than 25 years.

This paper focuses on hypothesis testing in lasso regression, when one is interested in judging statistical significance for the regression coefficients in the regression equation involving a lot of covariates. To get reliable p-values, we propose a new lasso-type estimator relying on the idea of induced smoothing which allows to obtain appropriate covariance matrix and Wald statistic relatively easily. Some simulation experiments reveal that our approach exhibits good performance when contrasted with the recent inferential tools in the lasso framework. Two real data analyses are presented to illustrate the proposed framework in practice.

Recently, a new estimation procedure has been developed to assess bias and precision of a new measurement method, relative to a reference standard. However, the author did not develop confidence bands around the bias and standard deviation curves. Therefore, the goal in this paper is to extend this methodology in several important directions. First, by developing simultaneous confidence bands for the various parameters estimated to allow formal comparisons between different measurement methods. Second, by proposing a new index of agreement. Third, by providing a series of new graphs to help the investigator to assess bias, precision, and agreement between the two measurement methods. The methodology requires repeated measurements on each individual for at least one of the two measurement methods. It works very well to estimate the differential and proportional biases, even with as few as two to three measurements by one of the two methods and only one by the other. The repeated measurements need not come from the reference standard but from either measurement methods. This is a great advantage as it may sometimes be more feasible to gather repeated measurements with the new measurement method.

With group randomized trials complete groups of subject are randomized to treatment conditions. Such grouping also occurs in individually randomized trials where treatment is administered in groups. Outcomes may be measured at the level of the subject, but also at the level of the group. The optimal design determines the number of groups and the number of subjects per group in the intervention and control conditions. It is found by taking a budgetary constraint into account, where costs are associated with implementing the intervention and control, and with taking measurements on subject and groups. The optimal design is found such that the effect of treatment is estimated with highest efficiency, and the total costs do not exceed the budget that is available. The design that is optimal for the outcome at the subject level is not necessarily optimal for the outcome at the group level. Multiple-objective optimal designs consider both outcomes simultaneously. Their aim is to find a design that has high efficiencies for both outcome measures. An Internet application for finding the multiple-objective optimal design is demonstrated on the basis of an example from smoking prevention in primary education, and another example on consultation time in primary care.

Non-response is a commonly encountered problem in many population-based surveys. Broadly speaking, non-response can be due to refusal or failure to contact the sample units. Although both types of non-response may lead to bias, there is much evidence to indicate that it is much easier to reduce the proportion of non-contacts than to do the same with refusals. In this article, we use data collected from a nationally representative survey under the Demographic and Health Surveys program to study non-response due to refusals to HIV testing in Malawi. We review existing estimation methods and propose novel approaches to the estimation of HIV prevalence that adjust for refusal behaviour. We then explain the data requirement and practical implications of the conventional and proposed approaches. Finally, we provide some general recommendations for handling non-response due to refusals and we highlight the challenges in working with Demographic and Health Surveys and explore different approaches to statistical estimation in the presence of refusals. Our results show that variation in the estimated HIV prevalence across different estimators is due largely to those who already know their HIV test results. In the case of Malawi, variations in the prevalence estimates due to refusals for women are larger than those for men.

A multi-treatment response adaptive procedure is developed considering “comparison with the best” philosophy of multiple comparison procedures for clinical trials with ordinal categorical responses, when there is no shared control. For each response category, we arbitrarily create two outcome groups; one by combining the categories more favorable to it and the other by merging the categories at most as favorable to it and hence define the odds (i.e. cumulative odds). Pairwise ratios of such odds (i.e. cumulative odds ratios) based on pairs of treatments are combined conveniently to derive a measure of relative superiority and hence the allocation probability functions. For practical implementation, we suggest response-adaptive randomization (RAR), that is, update the allocation probabilities dynamically using the available allocation and response information to favor the treatment doing better. Empirical as well as large sample properties following the randomization are investigated in detail. Moreover, a real clinical trial with trauma patients is redesigned using the proposed RAR to envisage practical applicability.

We propose new summary measures of biomarker accuracy which can be used as companions to existing diagnostic accuracy measures. Conceptually, our summary measures are tantamount to the so-called Hellinger affinity and we show that they can be regarded as measures of agreement constructed from similar geometrical principles as Pearson correlation. We develop a covariate-specific version of our summary index, which practitioners can use to assess the discrimination performance of a biomarker, conditionally on the value of a predictor. We devise nonparametric Bayes estimators for the proposed indexes, derive theoretical properties of the corresponding priors, and assess the performance of our methods through a simulation study. The proposed methods are illustrated using data from a prostate cancer diagnosis study.

The attributable fraction is the candidate tool to quantify individual shares of each risk factor on the disease burden in a population, expressing the proportion of cases ascribable to the risk factors. The original formula ignored the presence of other factors (i.e. multiple risk factors and/or confounders), and several adjusting methods for potential confounders have been proposed. However, crude and adjusted attributable fractions do not sum up to their joint attributable fraction (i.e. the number of cases attributable to all risk factors together) and their sum may exceed one. A different approach consists of partitioning the joint attributable fraction into exposure-specific shares leading to sequential and average attributable fractions. We provide an example using Italian case–control data on oral cavity cancer comparing crude, adjusted, sequential, and average attributable fractions for smoking and alcohol and provide an overview of the available software routines for their estimation. For each method, we give interpretation and discuss shortcomings. Crude and adjusted attributable fractions added up over than one, whereas sequential and average methods added up to the joint attributable fraction = 0.8112 (average attributable fractions for smoking and alcohol were 0.4894 and 0.3218, respectively). The attributable fraction is a well-known epidemiological measure that translates risk factors prevalence and disease occurrence in useful figures for a public health perspective. This work endorses their proper use and interpretation.

Brain functional connectivity is a widely investigated topic in neuroscience. In recent years, the study of brain connectivity has been largely aided by graph theory. The link between time series recorded at multiple locations in the brain and the construction of a graph is usually an adjacency matrix. The latter converts a measure of the connectivity between two time series, typically a correlation coefficient, into a binary choice on whether the two brain locations are functionally connected or not. As a result, the choice of a threshold τ over the correlation coefficient is key. In the present work, we propose a multiple testing approach to the choice of τ that uses the Bayes false discovery rate and a new estimator of the statistical power called average power function to balance the two types of statistical error. We show that the proposed average power function estimator behaves well both in case of independence and weak dependence of the tests and it is reliable under several simulated dependence conditions. Moreover, we propose a robust method for the choice of τ using the 5% and 95% percentiles of the average power function and False Discovery Rate bootstrap distributions, respectively, to improve stability. We applied our approach to functional magnetic resonance imaging and high density electroencephalogram data.

Understanding the limitation of solely relying on statistical significance, researchers have proposed methods to draw biomedical conclusions based on clinical significance. The minimal clinically important significance is one of the most fundamental concepts to study clinical significance. Based on an anchor question usually available in the patients' reported outcome, Hedayat et al. presented a method to estimate minimal clinically important significance using the classification technique. However, their method implicitly requires that the binary outcome of the anchor question is equally likely, i.e. the balanced outcome assumption. This assumption cannot be guaranteed a priori when one designs the study; hence, it cannot be satisfied in general. In this paper, we propose a data adaptive method, which can overcome this limitation. Compared to Hedayat et al., our method uses a faster gradient based algorithm and adopts a more flexible structure of the minimal clinically important significance at the individual level. We conduct comprehensive simulation studies and apply our method to the chondral lesions and meniscus procedure study to demonstrate its usefulness and also its outperformance.

Sensitive questions are often involved in healthcare or medical survey research. Much empirical evidence has shown that the randomized response technique is useful for the collection of truthful responses. However, few studies have discussed methods to estimate the dependence of sensitive responses of multiple types. This study aims to fill that gap by considering a method based on moment estimation and without using the joint distribution of the responses. In addition to the construction of a covariance matrix for the multiple sensitive questions despite incomplete information due to the randomized response technique design, we can calculate the conditional mean of continuous sensitive responses given as categorical responses and partial correlations among continuous sensitive responses. We conduct a simulation experiment to study the bias and variance of the moment estimator with various sample sizes. We apply the proposed method in a healthcare study of the dependence structure among the responses of a survey concerning health and pressure on college students.

Non-adherence to assigned treatment is a common issue in cluster randomised trials. In these settings, the efficacy estimand may also be of interest. Many methodological contributions in recent years have advocated using instrumental variables to identify and estimate the local average treatment effect. However, the clustered nature of randomisation in cluster randomised trials adds to the complexity of such analyses. In this paper, we show that the local average treatment effect can be estimated via two-stage least squares regression using cluster-level summaries of the outcome and treatment received under certain assumptions. We propose the use of baseline variables to adjust the cluster-level summaries before performing two-stage least squares in order to improve efficiency. Implementation needs to account for the reduced sample size, as well as the possible heteroscedasticity, to obtain valid inferences. Simulations are used to assess the performance of two-stage least squares of cluster-level summaries under cluster-level or individual-level non-adherence, with and without weighting and robust standard errors. The impact of adjusting for baseline covariates and of appropriate degrees of freedom correction for inference is also explored. The methods are then illustrated by re-analysing a cluster randomised trial carried out in a specific UK primary care setting. Two-stage least squares estimation using cluster-level summaries provides estimates with small to negligible bias and coverage close to nominal level, provided the appropriate small sample degrees of freedom correction and robust standard errors are used for inference.

To optimize designs for longitudinal studies analyzed by mixed-effect models with binary outcomes, the Fisher information matrix can be used. Optimal design approaches, however, require a priori knowledge of the model. We aim to propose, for the first time, a robust design approach accounting for model uncertainty in longitudinal trials with two treatment groups, assuming mixed-effect logistic models. To optimize designs given one model, we compute several optimality criteria based on Fisher information matrix evaluated by the new approach based on Monte-Carlo/Hamiltonian Monte-Carlo. We propose to use the DD_S-optimality criterion, as it ensures a compromise between the precision of estimation of the parameters, and hence the Wald test power, and the overall precision of parameter estimation. To account for model uncertainty, we assume candidate models with their respective weights. We compute robust design across these models using compound DD_S-optimality. Using the Fisher information matrix, we propose to predict the average power over these models. Evaluating this approach by clinical trial simulations, we show that the robust design is efficient across all models, allowing one to achieve good power of test. The proposed design strategy is a new and relevant approach to design longitudinal studies with binary outcomes, accounting for model uncertainty.