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Crossover trials are widely used to assess the effect of a reversible exposure on an outcome of interest. To gain further insight into the underlying mechanisms of this effect, researchers may be interested in exploring whether or not it runs through a specific intermediate variable: the mediator. Mediation analysis in crossover designs has received scant attention so far and is mostly confined to the traditional Baron and Kenny approach. We aim to tackle mediation analysis within the counterfactual framework and elucidate the assumptions under which the direct and indirect effects can be identified in AB / BA crossover studies. Notably, we show that both effects are identifiable in certain statistical models, even in the presence of unmeasured time-independent (or upper-level) confounding of the mediator–outcome relation. Employing the mediation formula, we derive expressions for the direct and indirect effects in within-subject designs for continuous outcomes that lend themselves to linear modelling, under a large variety of settings. We discuss an estimation approach based on regressing differences in outcomes on differences in mediators and show how to allow for period effects as well as different types of moderation. The performance of this approach is compared to other existing methods through simulations and is illustrated with data from a neurobehavioural study. Lastly, we demonstrate how a sensitivity analysis can be performed that is able to assess the robustness of both the direct and indirect effect against violation of the “no unmeasured lower-level mediator–outcome confounding” assumption.

In survival analysis, the estimation of patient-specific survivor functions that are conditional on a set of patient characteristics is of special interest. In general, knowledge of the conditional survival probabilities of a patient at all relevant time points allows better assessment of the patient’s risk than summary statistics, such as median survival time. Nevertheless, standard methods for analysing survival data seldom estimate the survivor function directly. Therefore, we propose the application of conditional transformation models (CTMs) for the estimation of the conditional distribution function of survival times given a set of patient characteristics. We used the inverse probability of censoring weighting approach to account for right-censored observations. Our proposed modelling approach allows the prediction of patient-specific survivor functions. In addition, CTMs constitute a flexible model class that is able to deal with proportional as well as non-proportional hazards. The well-known Cox model is included in the class of CTMs as a special case. We investigated the performance of CTMs in survival data analysis in a simulation that included proportional and non-proportional hazard settings and different scenarios of explanatory variables. Furthermore, we re-analysed the survival times of patients suffering from chronic myelogenous leukaemia and studied the impact of the proportional hazards assumption on previously published results.

Selection of estimators is an essential task in modeling. A general framework is that the estimators of a distribution are obtained by minimizing a function (the estimating function) and assessed using another function (the assessment function). A classical case is that both functions estimate an information risk (specifically cross-entropy); this corresponds to using maximum likelihood estimators and assessing them by Akaike information criterion (AIC). In more general cases, the assessment risk can be estimated by leave-one-out cross-validation. Since leave-one-out cross-validation is computationally very demanding, we propose in this paper a universal approximate cross-validation criterion under regularity conditions (UACVR). This criterion can be adapted to different types of estimators, including penalized likelihood and maximum a posteriori estimators, and also to different assessment risk functions, including information risk functions and continuous rank probability score (CRPS). UACVR reduces to Takeuchi information criterion (TIC) when cross-entropy is the risk for both estimation and assessment. We provide the asymptotic distributions of UACVR and of a difference of UACVR values for two estimators. We validate UACVR using simulations and provide an illustration on real data both in the psychometric context where estimators of the distributions of ordered categorical data derived from threshold models and models based on continuous approximations are compared.

Length bias in survival data occurs in observational studies when, for example, subjects with shorter lifetimes are less likely to be present in the recorded data. In this paper, we consider estimating the causal exposure (treatment) effect on survival time from observational data when, in addition to the lack of randomization and consequent potential for confounding, the data constitute a length-biased sample; we hence term this a double-bias problem. We develop estimating equations that can be used to estimate the causal effect indexing the structural Cox proportional hazard and accelerated failure time models for point exposures in double-bias settings. The approaches rely on propensity score-based adjustments, and we demonstrate that estimation of the propensity score must be adjusted to acknowledge the length-biased sampling. Large sample properties of the estimators are established and their small sample behavior is studied using simulations. We apply the proposed methods to a set of, partly synthesized, length-biased survival data collected as part of the Canadian Study of Health and Aging (CSHA) to compare survival of subjects with dementia among institutionalized patients versus those recruited from the community and depict their adjusted survival curves.

Generalized additive models (GAMs) based on the binomial and Poisson distributions can be used to provide flexible semi-parametric modelling of binary and count outcomes. When used with the canonical link function, these GAMs provide semi-parametrically adjusted odds ratios and rate ratios. For adjustment of other effect measures, including rate differences, risk differences and relative risks, non-canonical link functions must be used together with a constrained parameter space. However, the algorithms used to fit these models typically rely on a form of the iteratively reweighted least squares algorithm, which can be numerically unstable when a constrained non-canonical model is used. We describe an application of a combinatorial EM algorithm to fit identity link Poisson, identity link binomial and log link binomial GAMs in order to estimate semi-parametrically adjusted rate differences, risk differences and relative risks. Using smooth regression functions based on B-splines, the method provides stable convergence to the maximum likelihood estimates, and it ensures that the estimates always remain within the parameter space. It is also straightforward to apply a monotonicity constraint to the smooth regression functions. We illustrate the method using data from a clinical trial in heart attack patients.

For a continuous-scale diagnostic test, the receiver operating characteristic (ROC) curve is a popular tool for displaying the ability of the test to discriminate between healthy and diseased subjects. In some studies, verification of the true disease status is performed only for a subset of subjects, possibly depending on the test result and other characteristics of the subjects. Estimators of the ROC curve based only on this subset of subjects are typically biased; this is known as verification bias. Methods have been proposed to correct verification bias, in particular under the assumption that the true disease status, if missing, is missing at random (MAR). MAR assumption means that the probability of missingness depends on the true disease status only through the test result and observed covariate information. However, the existing methods require parametric models for the (conditional) probability of disease and/or the (conditional) probability of verification, and hence are subject to model misspecification: a wrong specification of such parametric models can affect the behavior of the estimators, which can be inconsistent. To avoid misspecification problems, in this paper we propose a fully nonparametric method for the estimation of the ROC curve of a continuous test under verification bias. The method is based on nearest-neighbor imputation and adopts generic smooth regression models for both the probability that a subject is diseased and the probability that it is verified. Simulation experiments and an illustrative example show the usefulness of the new method. Variance estimation is also discussed.

In medical and other related sciences, clinical or experimental measurements usually serve as a basis for diagnostic, prognostic, therapeutic, and performance evaluations. Examples can be assessing the reliability of multiple raters (or measurement methods), assessing the suitability for tumor evaluation of using a local laboratory or a central laboratory in a randomized clinical trial (RCT), validating surrogate endpoints in a study, determining that the important outcome measurements are interchangeable among the evaluators in an RCT. Any elegant study design cannot overcome the damage by unreliable measurement. Many methods have been developed to assess the agreement of two measurement methods. However, there is little attention to quantify how good the agreement of two measurement methods is. In this paper, similar to the type I error and the power in describing a hypothesis testing, we propose quantifying an agreement assessment using two rates: the discordance rate and the tolerance probability. This approach is demonstrated through examples.

Exposure misclassification in case–control studies leads to bias in odds ratio estimates. There has been considerable interest recently to account for misclassification in estimation so as to adjust for bias as well as more accurately quantify uncertainty. These methods require users to elicit suitable values or prior distributions for the misclassification probabilities. In the event where exposure misclassification is highly uncertain, these methods are of limited use, because the resulting posterior uncertainty intervals tend to be too wide to be informative. Posterior inference also becomes very dependent on the subjectively elicited prior distribution. In this paper, we propose an alternative “robust Bayesian” approach, where instead of eliciting prior distributions for the misclassification probabilities, a feasible region is given. The extrema of posterior inference within the region are sought using an inequality constrained optimization algorithm. This method enables sensitivity analyses to be conducted in a useful way as we do not need to restrict all of our unknown parameters to fixed values, but can instead consider ranges of values at a time.

In disease registries, bivariate survival data are typically collected under interval sampling. It refers to a situation when entry into a registry is at the time of the first failure event (i.e., HIV infection) within a calendar time window. For all the cases in the registry, time of the initiating event (i.e., birth) is retrospectively identified, and subsequently the second failure event (i.e., death) is observed during follow-up. In this paper we discuss how interval sampling introduces bias into the data. Given the sampling design that the first event occurs within a specific time interval, the first failure time is doubly truncated, and the second failure time is possibly informatively right censored. Consider semi-stationary condition that the disease progression is independent of when the initiating event occurs. Under this condition, this paper adopts copula models to assess association between the bivariate survival times with interval sampling. We first obtain bias-corrected estimators of marginal survival functions, and estimate association parameter of copula model by a two-stage procedure. In the second part of the work, covariates are incorporated into the survival distributions via the proportional hazards models. Inference of the association measure in copula model is established, where the association is allowed to depend on covariates. Asymptotic properties of proposed estimators are established, and finite sample performance is evaluated by simulation studies. The method is applied to a community-based AIDS study in Rakai to investigate dependence between age at infection and residual lifetime without and with adjustment for HIV subtype.

We compare splitting methods for constructing survival trees that are used as a model of survival time based on covariates. A number of splitting criteria on the classification and regression tree (CART) have been proposed by various authors, and we compare nine criteria through simulations. Comparative studies have been restricted to criteria that suppose the survival model for each terminal node in the final tree as a non-parametric model. As the main results, the criteria using the exponential log-likelihood loss, log-rank test statistics, the deviance residual under the proportional hazard model, or square error of martingale residual are recommended when it appears that the data have constant hazard with the passage of time. On the other hand, when the data are thought to have decreasing hazard with passage of time, the criterion using the two-sample test statistic, or square error of deviance residual would be optimal. Moreover, when the data are thought to have increasing hazard with the passage of time, the criterion using the exponential log-likelihood loss, or impurity that combines observed times and the proportion of censored observations would be the best. We also present the results of an actual medical research to show the utility of survival trees.