Volume 13, Issue 1 -

Multiple comparisons and small sample size, common characteristics of many types of “Big Data” including those that are produced by genomic studies, present specific challenges that affect reliability of inference. Use of multiple testing procedures necessitates calculation of very small tail probabilities of a test statistic distribution. Results based on large deviation theory provide a formal condition that is necessary to guarantee error rate control given practical sample sizes, linking the number of tests and the sample size; this condition, however, is rarely satisfied. Using methods that are based on Edgeworth expansions (relying especially on the work of Peter Hall), we explore the impact of departures of sampling distributions from typical assumptions on actual error rates. Our investigation illustrates how far the actual error rates can be from the declared nominal levels, suggesting potentially wide-spread problems with error rate control, specifically excessive false positives. This is an important factor that contributes to “reproducibility crisis”. We also review some other commonly used methods (such as permutation and methods based on finite sampling inequalities) in their application to multiple testing/small sample data. We point out that Edgeworth expansions, providing higher order approximations to the sampling distribution, offer a promising direction for data analysis that could improve reliability of studies relying on large numbers of comparisons with modest sample sizes.

Though widely used in applications, reinforced random walk on graphs have never been the subject of a valid statistical inference. We develop in this paper a statistical framework for a general two-colored urn model. The probability to draw a ball at each step depends on the number of balls of each color and on a multidimensional parameter through a function, called choice function. We introduce two estimators of the parameter: the maximum likelihood estimator and a weighted least squares estimator which is less efficient, but is closer to the calibration techniques used in the applied literature. In general, the model is an inhomogeneous Markov chain and this property makes the estimation of the parameter impossible on a single path, even if it were infinite. Therefore we assume that we observe i.i.d. experiments, each of a predetermined finite length. This is coherent with the usual experimental set-ups. We apply the statistical framework to a real life experiment: the selection of a path among pre-existing channels by an ant colony. We performed experiments, which consisted of letting ants pass through the branches of a fork. We consider the particular urn model proposed by J.-L. Deneubourg et al. in 1990 to describe this phenomenon. We simulate this model for several parameter values in order to assess the accuracy of the MLE and the WLSE. Then we estimate the parameter from the experimental data and evaluate confident regions with Bootstrap algorithms. The findings of this paper do not contradict the biological literature, but give statistical significance to the values of the parameter found therein.

Abstract: We introduce combinatorial mixtures – a flexible class of models for inference on mixture distributions whose components have multidimensional parameters. The key idea is to allow each element of the component-specific parameter vectors to be shared by a subset of other components. This approach allows for mixtures that range from very flexible to very parsimonious and unifies inference on component-specific parameters with inference on the number of components. We develop Bayesian inference and computational approaches for this class of distributions, and illustrate them in an application. This work was originally motivated by the analysis of cancer subtypes: in terms of biological measures of interest, subtypes may be characterized by differences in location, scale, correlations or any of the combinations. We illustrate our approach using publicly available data on molecular subtypes of lung and prostate cancers.

Conditional power of survival endpoints at interim analyses can support decisions on continuing a trial or stopping it for futility. When a cure fraction becomes apparent, conditional power cannot be calculated accurately using simple survival models, e.g. the exponential model. Non-mixture models consider such cure fractions. In this paper, we derive conditional power functions for non-mixture models, namely the non-mixture exponential, the non-mixture Weibull, and the non-mixture Gamma models. Formulae were implemented in the R package CP . For an example data set of a clinical trial, we calculated conditional power under the non-mixture models and compared results with those under the simple exponential model.

When multiple treatment alternatives are available for a certain psychological or medical problem, an important challenge is to find an optimal treatment regime, which specifies for each patient the most effective treatment alternative given his or her pattern of pretreatment characteristics. The focus of this paper is on tree-based treatment regimes, which link an optimal treatment alternative to each leaf of a tree; as such they provide an insightful representation of the decision structure underlying the regime. This paper compares the absolute and relative performance of four methods for estimating regimes of that sort (viz., Interaction Trees, Model-based Recursive Partitioning, an approach developed by Zhang et al. and Qualitative Interaction Trees) in an extensive simulation study. The evaluation criteria were, on the one hand, the expected outcome if the entire population would be subjected to the treatment regime resulting from each method under study and the proportion of clients assigned to the truly best treatment alternative, and, on the other hand, the Type I and Type II error probabilities of each method. The method of Zhang et al. was superior regarding the first two outcome measures and the Type II error probabilities, but performed worst in some conditions of the simulation study regarding Type I error probabilities.

To estimate or test the treatment effect in randomized clinical trials, it is important to adjust for the potential influence of covariates that are likely to affect the association between the treatment or control group and the response. If these covariates are known at the start of the trial, random assignment of the treatment within each stratum would be considered. On the other hand, if these covariates are not clear at the start of the trial, or if it is difficult to allocate the treatment within each stratum, completely randomized assignment of the treatment would be performed. In both sampling structures, the use of a stratified adjusted test is a useful way to evaluate the significance of the overall treatment effect by reducing the variance and/or bias of the result. If the trial has a binary endpoint, the Cochran and Mantel-Haenszel tests are generally used. These tests are constructed based on the assumption that the number of patients within a stratum is fixed. However, in practice, the stratum sizes are not fixed at the start of the trial in many situations, and are instead allowed to vary. Therefore, there is a risk that using these tests under such situations would result in an error in the estimated variation of the test statistics. To handle the problem, we propose new test statistics under both sampling structures based on multinomial distributions. Our proposed approach is based on the Cochran test, and the difference between the two tests tends to have similar values in the case of a large number of patients. When the total number of patients is small, our approach yields a more conservative result. Through simulation studies, we show that the new approach could correctly maintain the type I error better than the traditional approach.

Motivated by risk prediction studies with ultra-high dimensional bio markers, we propose a novel improvement screening methodology. Accurate risk prediction can be quite useful for patient treatment selection, prevention strategy or disease management in evidence-based medicine. The question of how to choose new markers in addition to the conventional ones is especially important. In the past decade, a number of new measures for quantifying the added value from the new markers were proposed, among which the integrated discrimination improvement (IDI) and net reclassification improvement (NRI) stand out. Meanwhile, C-statistics are routinely used to quantify the capacity of the estimated risk score in discriminating among subjects with different event times. In this paper, we will examine these improvement statistics as well as the norm-based approach for evaluating the incremental values of new markers and compare these four measures by analyzing ultra-high dimensional censored survival data. In particular, we consider Cox proportional hazards models with varying coefficients. All measures perform very well in simulations and we illustrate our methods in an application to a lung cancer study.

Matched case-control designs are currently used in many biomedical applications. To ensure high efficiency and statistical power in identifying features that best discriminate cases from controls, it is important to account for the use of matched designs. However, in the setting of high dimensional data, few variable selection methods account for matching. Bayesian approaches to variable selection have several advantages, including the fact that such approaches visit a wider range of model subsets. In this paper, we propose a variable selection method to account for case-control matching in a Bayesian context and apply it using simulation studies, a matched brain imaging study conducted at Massachusetts General Hospital, and a matched cardiovascular biomarker study conducted by the High Risk Plaque Initiative.

The generalized odds ratio (GOR) for paired sample is considered to measure the relative treatment effect on patient responses in ordinal data. Under a three-treatment two-period incomplete block crossover design, both asymptotic and exact procedures are developed for testing equality between treatments with ordinal responses. Monte Carlo simulation is employed to evaluate and compare the finite-sample performance of these test procedures. A discussion on advantages and disadvantages of the proposed test procedures based on the GOR versus those based on Wald’s tests under the normal random effects proportional odds model is provided. The data taken as a part of a crossover trial studying the effects of low and high doses of an analgesic versus a placebo for the relief of pain in primary dysmenorrhea over the first two periods are applied to illustrate the use of these test procedures.

Abstract: Missing covariate data occurs often in regression analysis, which frequently arises in the health and social sciences as well as in survey sampling. We study methods for the analysis of a nonignorable covariate-missing data problem in an assumed conditional mean function when some covariates are completely observed but other covariates are missing for some subjects. We adopt the semiparametric perspective of Bartlett et al. (Improving upon the efficiency of complete case analysis when covariates are MNAR. Biostatistics 2014;15:719–30) on regression analyses with nonignorable missing covariates, in which they have introduced the use of two working models, the working probability model of missingness and the working conditional score model. In this paper, we study an empirical likelihood approach to nonignorable covariate-missing data problems with the objective of effectively utilizing the two working models in the analysis of covariate-missing data. We propose a unified approach to constructing a system of unbiased estimating equations, where there are more equations than unknown parameters of interest. One useful feature of these unbiased estimating equations is that they naturally incorporate the incomplete data into the data analysis, making it possible to seek efficient estimation of the parameter of interest even when the working regression function is not specified to be the optimal regression function. We apply the general methodology of empirical likelihood to optimally combine these unbiased estimating equations. We propose three maximum empirical likelihood estimators of the underlying regression parameters and compare their efficiencies with other existing competitors. We present a simulation study to compare the finite-sample performance of various methods with respect to bias, efficiency, and robustness to model misspecification. The proposed empirical likelihood method is also illustrated by an analysis of a data set from the US National Health and Nutrition Examination Survey (NHANES).

Motivated by an HIV example, we consider how to compare and combine treatment selection markers, which are essential to the notion of precision medicine. The current literature on precision medicine is focused on evaluating and optimizing treatment regimes, which can be obtained by dichotomizing treatment selection markers. In practice, treatment decisions are based not only on efficacy but also on safety, cost and individual preference, making it difficult to choose a single cutoff value for all patients in all settings. It is therefore desirable to have a statistical framework for comparing and combining treatment selection markers without dichotomization. We provide such a framework based on a quantitative concordance measure, which quantifies the extent to which higher marker values are predictive of larger treatment effects. For a given marker, the proposed concordance measure can be estimated from clinical trial data using a U-statistic, which can incorporate auxiliary covariate information through an augmentation term. For combining multiple markers, we propose to maximize the estimated concordance measure among a specified family of combination markers. A cross-validation procedure can be used to remove any re-substitution bias in assessing the quality of an optimized combination marker. The proposed methodology is applied to the HIV example and evaluated in simulation studies.

Recurrent events are often encountered in medical follow up studies. In addition, such recurrences have other quantities associated with them that are of considerable interest, for instance medical costs of the repeated hospitalizations and tumor size in cancer recurrences. These processes can be viewed as point processes, i.e. processes with arbitrary positive jump at each recurrence. An analysis of the mean function for such point processes have been proposed in the literature. However, such point processes are often skewed, leading to median as a more appropriate measure than the mean. Furthermore, the analysis of recurrent event data is often complicated by the presence of death. We propose a semiparametric model for assessing the effect of covariates on the quantiles of the point processes. We investigate both the finite sample as well as the large sample properties of the proposed estimators. We conclude with a real data analysis of the medical cost associated with the treatment of ovarian cancer.

Conditioning on a shared outcome of two variables can alter the association between these variables, possibly adding a bias component when estimating effects. In particular, if two causes are marginally independent, they might be dependent in strata of their common effect. Explanations of the phenomenon, however, do not explicitly state when dependence will be created and have been largely informal. We prove that two, marginally independent, causes will be dependent in a particular stratum of their shared outcome if and only if they modify each other’s effects, on a probability ratio scale, on that value of the outcome variable. Using our result, we also qualify the claim that such causes will “almost certainly” be dependent in at least one stratum of the outcome: dependence must be created in one stratum of a binary outcome, and independence can be maintained in every stratum of a trinary outcome.

Statistical analysis of high-dimensional data has been attracting more and more attention due to the abundance of such data in various fields such as genetic studies or genomics and the existence of many interesting topics. Among them, one is the identification of a gene or genes that have significant effects on the occurrence of or are significantly related to a certain disease. In this paper, we will discuss such a problem that can be formulated as a group test or testing a group of variables or coefficients when one faces right-censored failure time response variable. For the problem, we develop a corrected variance reduced partial profiling (CVRPP) linear regression model and a likelihood ratio test procedure when the failure time of interest follows the additive hazards model. The numerical study suggests that the proposed method works well in practical situations and gives better performance than the existing one. An illustrative example is provided.

Physicians and patients may choose a certain treatment only if it is predicted to have a large effect for the profile of that patient. We consider randomized controlled trials in which the clinical goal is to identify as many patients as possible that can highly benefit from the treatment. This is challenging with large numbers of covariate profiles, first, because the theoretical, exact method is not feasible, and, second, because usual model-based methods typically give incorrect results. Better, more recent methods use a two-stage approach, where a first stage estimates a working model to produce a scalar predictor of the treatment effect for each covariate profile; and a second stage estimates empirically a high-benefit group based on the first-stage predictor. The problem with these methods is that each of the two stages is usually agnostic about the role of the other one in addressing the clinical goal. We propose a method that characterizes highly benefited patients by linking model estimation directly to the particular clinical goal. It is shown that the new method has the following two key properties in comparison with existing approaches: first, the meaning of the solution with regard to the clinical goal is the same, and second, the value of the solution is the best that can be achieved when using the working model as a predictor, even if that model is incorrect. In the Citalopram for Agitation in Alzheimer’s Disease (CitAD) randomized controlled trial, the new method identifies substantially larger groups of highly benefited patients, many of whom are missed by the standard method.