Sample size calculations for designing clinical proteomic profiling studies using mass spectrometry

In cancer clinical proteomics, MALDI and SELDI profiling are used to search for biomarkers of potentially curable early-stage disease. A given number of samples must be analysed in order to detect clinically relevant differences between cancers and controls, with adequate statistical power. From clinical proteomic profiling studies, expression data for each peak (protein or peptide) from two or more clinically defined groups of subjects are typically available. Typically, both exposure and confounder information on each subject are also available, and usually the samples are not from randomized subjects. Moreover, the data is usually available in replicate. At the design stage, however, covariates are not typically available and are often ignored in sample size calculations. This leads to the use of insufficient numbers of samples and reduced power when there are imbalances in the numbers of subjects between different phenotypic groups. A method is proposed for accommodating information on covariates, data imbalances and design-characteristics, such as the technical replication and the observational nature of these studies, in sample size calculations. It assumes knowledge of a joint distribution for the protein expression values and the covariates. When discretized covariates are considered, the effect of the covariates enters the calculations as a function of the proportions of subjects with specific attributes. This makes it relatively straightforward (even when pilot data on subject covariates is unavailable) to specify and to adjust for the effect of the expected heterogeneities. The new method suggests certain experimental designs which lead to the use of a smaller number of samples when planning a study. Analysis of data from the proteomic profiling of colorectal cancer reveals that fewer samples are needed when a study is balanced than when it is unbalanced, and when the IMAC30 chip-type is used. The method is implemented in the clippda package and is available in R at: http://www.bioconductor.org/help/bioc-views/release/bioc/html/clippda.html.     

One-step targeted maximum likelihood estimation for time-to-event outcomes

Researchers in observational survival analysis are interested in not only estimating survival curve nonparametrically but also having statistical inference for the parameter. We consider right-censored failure time data where we observe n independent and identically distributed observations of a vector random variable consisting of baseline covariates, a binary treatment at baseline, a survival time subject to right censoring, and the censoring indicator. We assume the baseline covariates are allowed to affect the treatment and censoring so that an estimator that ignores covariate information would be inconsistent. The goal is to use these data to estimate the counterfactual average survival curve of the population if all subjects are assigned the same treatment at baseline. Existing observational survival analysis methods do not result in monotone survival curve estimators, which is undesirable and may lose efficiency by not constraining the shape of the estimator using the prior knowledge of the estimand. In this paper, we present a one-step Targeted Maximum Likelihood Estimator (TMLE) for estimating the counterfactual average survival curve. We show that this new TMLE can be executed via recursion in small local updates. We demonstrate the finite sample performance of this one-step TMLE in simulations and an application to a monoclonal gammopathy data.     

Novel two-phase sampling designs for studying binary outcomes

In biomedical cohort studies for assessing the association between an outcome variable and a set of covariates, usually, some covariates can only be measured on a subgroup of study subjects. An important design question is—which subjects to select into the subgroup to increase statistical efficiency. When the outcome is binary, one may adopt a case-control sampling design or a balanced case-control design where cases and controls are further matched on a small number of complete discrete covariates. While the latter achieves success in estimating odds ratio (OR) parameters for the matching covariates, similar two-phase design options have not been explored for the remaining covariates, especially the incompletely collected ones. This is of great importance in studies where the covariates of interest cannot be completely collected. To this end, assuming that an external model is available to relate the outcome and complete covariates, we propose a novel sampling scheme that oversamples cases and controls with worse goodness-of-fit based on the external model and further matches them on complete covariates similarly to the balanced design. We develop a pseudolikelihood method for estimating OR parameters. Through simulation studies and explorations in a real-cohort study, we find that our design generally leads to reduced asymptotic variances of the OR estimates and the reduction for the matching covariates is comparable to that of the balanced design.     

The effect of miss-specified baseline characteristics on inference for longitudinal trends in linear mixed models

The main advantage of longitudinal studies is that they can distinguish changes over time within individuals (longitudinal effects) from differences among subjects at the start of the study (baseline characteristics, cross-sectional effects). Often, especially in observational studies, longitudinal trends are studied after correction for many potentially important baseline differences between subjects. We show that, in the context of linear mixed models, inference for longitudinal trends is in general biased if a wrong model for the baseline characteristics is used. However, we will argue that this bias is small in most practical situations and completely vanishes in the special case of a growth curve model for complete balanced data. In the latter case, inference for longitudinal trends is completely independent of additional baseline covariates that might have been omitted from the model.     

A Robust Method for Estimating Optimal Treatment Regimes

Summary A treatment regime is a rule that assigns a treatment, among a set of possible treatments, to a patient as a function of his/her observed characteristics, hence “personalizing” treatment to the patient. The goal is to identify the optimal treatment regime that, if followed by the entire population of patients, would lead to the best outcome on average. Given data from a clinical trial or observational study, for a single treatment decision, the optimal regime can be found by assuming a regression model for the expected outcome conditional on treatment and covariates, where, for a given set of covariates, the optimal treatment is the one that yields the most favorable expected outcome. However, treatment assignment via such a regime is suspect if the regression model is incorrectly specified. Recognizing that, even if misspecified, such a regression model defines a class of regimes, we instead consider finding the optimal regime within such a class by finding the regime that optimizes an estimator of overall population mean outcome. To take into account possible confounding in an observational study and to increase precision, we use a doubly robust augmented inverse probability weighted estimator for this purpose. Simulations and application to data from a breast cancer clinical trial demonstrate the performance of the method.     

Propensity score matching with time-dependent covariates

In observational studies with a time-dependent treatment and time-dependent covariates, it is desirable to balance the distribution of the covariates at every time point. A time-dependent propensity score based on the Cox proportional hazards model is proposed and used in risk set matching. Matching on this propensity score is shown to achieve a balanced distribution of the covariates in both treated and control groups. Optimal matching with various designs is conducted and compared in a study of a surgical treatment, cystoscopy and hydrodistention, given in response to a chronic bladder disease, interstitial cystitis. Simulation studies also suggest that the statistical analysis after matching outperforms the analysis without matching in terms of both point and interval estimations.     

A randomization-based causal inference framework for uncovering environmental exposure effects on human gut microbiota

Statistical analysis of microbial genomic data within epidemiological cohort studies holds the promise to assess the influence of environmental exposures on both the host and the host-associated microbiome. However, the observational character of prospective cohort data and the intricate characteristics of microbiome data make it challenging to discover causal associations between environment and microbiome. Here, we introduce a causal inference framework based on the Rubin Causal Model that can help scientists to investigate such environment-host microbiome relationships, to capitalize on existing, possibly powerful, test statistics, and test plausible sharp null hypotheses. Using data from the German KORA cohort study, we illustrate our framework by designing two hypothetical randomized experiments with interventions of (i) air pollution reduction and (ii) smoking prevention. We study the effects of these interventions on the human gut microbiome by testing shifts in microbial diversity, changes in individual microbial abundances, and microbial network wiring between groups of matched subjects via randomization-based inference. In the smoking prevention scenario, we identify a small interconnected group of taxa worth further scrutiny, including Christensenellaceae and Ruminococcaceae genera, that have been previously associated with blood metabolite changes. These findings demonstrate that our framework may uncover potentially causal links between environmental exposure and the gut microbiome from observational data. We anticipate the present statistical framework to be a good starting point for further discoveries on the role of the gut microbiome in environmental health.     

Voice pitch predicts electability,but does not signal leadership ability

Voice pitch, the perceived “highness” or “lowness” of a voice, influences how humans perceive and treat each other in various ways. One example is the selection of leaders. A growing number of studies, both experimental and observational, show that individuals with lower-pitched voices are more likely to win elected office. This leads to the yet untested question of whether individuals with lower voices are actually better leaders. That is, is voice pitch a reliable signal of leadership ability? Here we address this question with an observational study of the vocal pitch and leadership ability of elected officials, and an experiment where subjects were asked to respond to persuasive political policy statements made by speakers with different pitched voices. Both studies lead to the same conclusion: voice pitch does not correlate with leadership ability.     

Sensitivity analysis for m-estimates, tests, and confidence intervals in matched observational studies

Huber's m-estimates use an estimating equation in which observations are permitted a controlled level of influence. The family of m-estimates includes least squares and maximum likelihood, but typical applications give extreme observations limited weight. Maritz proposed methods of exact and approximate permutation inference for m-tests, confidence intervals, and estimators, which can be derived from random assignment of paired subjects to treatment or control. In contrast, in observational studies, where treatments are not randomly assigned, subjects matched for observed covariates may differ in terms of unobserved covariates, so differing outcomes may not be treatment effects. In observational studies, a method of sensitivity analysis is developed for m-tests, m-intervals, and m-estimates: it shows the extent to which inferences would be altered by biases of various magnitudes due to nonrandom treatment assignment. The method is developed for both matched pairs, with one treated subject matched to one control, and for matched sets, with one treated subject matched to one or more controls. The method is illustrated using two studies: (i) a paired study of damage to DNA from exposure to chromium and nickel and (ii) a study with one or two matched controls comparing side effects of two drug regimes to treat tuberculosis. The approach yields sensitivity analyses for: (i) m-tests with Huber's weight function and other robust weight functions, (ii) the permutational t-test which uses the observations directly, and (iii) various other procedures such as the sign test, Noether's test, and the permutation distribution of the efficient score test for a location family of distributions. Permutation inference with covariance adjustment is briefly discussed.     

Clustered restricted mean survival time regression

For multicenter randomized trials or multilevel observational studies, the Cox regression model has long been the primary approach to study the effects of covariates on time-to-event outcomes. A critical assumption of the Cox model is the proportionality of the hazard functions for modeled covariates, violations of which can result in ambiguous interpretations of the hazard ratio estimates. To address this issue, the restricted mean survival time (RMST), defined as the mean survival time up to a fixed time in a target population, has been recommended as a model-free target parameter. In this article, we generalize the RMST regression model to clustered data by directly modeling the RMST as a continuous function of restriction times with covariates while properly accounting for within-cluster correlations to achieve valid inference. The proposed method estimates regression coefficients via weighted generalized estimating equations, coupled with a cluster-robust sandwich variance estimator to achieve asymptotically valid inference with a sufficient number of clusters. In small-sample scenarios where a limited number of clusters are available, however, the proposed sandwich variance estimator can exhibit negative bias in capturing the variability of regression coefficient estimates. To overcome this limitation, we further propose and examine bias-corrected sandwich variance estimators to reduce the negative bias of the cluster-robust sandwich variance estimator. We study the finite-sample operating characteristics of proposed methods through simulations and reanalyze two multicenter randomized trials.     

Explained and unexplained regional variation in Canadian obesity prevalence

The objective of our study was to examine sociodemographic and behavioral variables underlying the geographic variation of obesity in Canada. We aimed to quantify the share of regional variation in average BMI attributable to commonly cited determinants of obesity and the remaining share, which is attributable to the idiosyncrasies of the regional environment ("regional effects"). Using data from the Canadian Community Health Survey (CCHS) (2004), ordinary least squares (OLS) regression, and Blinder-Oaxaca decomposition to decompose the difference in mean BMI between regions, we quantify two parts of the difference: a share explained by different levels of the covariates and a share explained by those covariates having different effects on BMI in the different regions, using the Atlantic provinces as the reference group. We observed that some differences (e.g., average BMI for males in Quebec compared to the Atlantic provinces) are mostly explained by the different levels of socio-demographic and behavioral covariates, while others (e.g., average BMI for females in Quebec compared to the Atlantic provinces) are mostly explained by the different effects of the covariates on BMI. In the latter scenario, even if covariates were made to be identical in the different regions, the difference in average BMI would persist. Thus, targeting covariates in different regions through plans like physical activity or nutrition policy, income equalization, or education subsidies will have ambiguous effects for addressing disparate obesity levels, being plausible policy options in some regions but less so in others. Future research and policy would benefit from identifying these region-specific attributes that have local implications for BMI.     

Estimating treatment effects from a randomized clinical trial in the presence of a secondary treatment

In randomized clinical trials involving survival time, a challenge that arises frequently, for example, in cancer studies (Manegold, Symanowski, Gatzemeier, Reck, von Pawel, Kortsik, Nackaerts, Lianes and Vogelzang, 2005. Second-line (post-study) chemotherapy received by patients treated in the phase III trial of pemetrexed plus cisplatin versus cisplatin alone in malignant pleural mesothelioma. Annals of Oncology 16, 923--927), is that subjects may initiate secondary treatments during the follow-up. The marginal structural Cox model and the method of inverse probability of treatment weighting (IPTW) have been proposed, originally for observational studies, to make causal inference on time-dependent treatments. In this paper, we adopt the marginal structural Cox model and propose an inferential method that improves the efficiency of the usual IPTW method by tailoring it to the setting of randomized clinical trials. The improvement in efficiency does not depend on any additional assumptions other than those required by the IPTW method, which is achieved by exploiting the knowledge that the study treatment is independent of baseline covariates due to randomization. The finite-sample performance of the proposed method is demonstrated via simulations and by application to data from a cancer clinical trial.     

Conditional and unconditional categorical regression models with missing covariates

We consider methods for analyzing categorical regression models when some covariates (Z) are completely observed but other covariates (X) are missing for some subjects. When data on X are missing at random (i.e., when the probability that X is observed does not depend on the value of X itself), we present a likelihood approach for the observed data that allows the same nuisance parameters to be eliminated in a conditional analysis as when data are complete. An example of a matched case-control study is used to demonstrate our approach.     

Identifying disease-associated biomarker network features through conditional graphical model

Biomarkers are often organized into networks, in which the strengths of network connections vary across subjects depending on subject-specific covariates (eg, genetic variants). Variation of network connections, as subject-specific feature variables, has been found to predict disease clinical outcome. In this work, we develop a two-stage method to estimate biomarker networks that account for heterogeneity among subjects and evaluate network's association with disease clinical outcome. In the first stage, we propose a conditional Gaussian graphical model with mean and precision matrix depending on covariates to obtain covariate-dependent networks with connection strengths varying across subjects while assuming homogeneous network structure. In the second stage, we evaluate clinical utility of network measures (connection strengths) estimated from the first stage. The second-stage analysis provides the relative predictive power of between-region network measures on clinical impairment in the context of regional biomarkers and existing disease risk factors. We assess the performance of proposed method by extensive simulation studies and application to a Huntington's disease (HD) study to investigate the effect of HD causal gene on the rate of change in motor symptom through affecting brain subcortical and cortical gray matter atrophy connections. We show that cortical network connections and subcortical volumes, but not subcortical connections are identified to be predictive of clinical motor function deterioration. We validate these findings in an independent HD study. Lastly, highly similar patterns seen in the gray matter connections and a previous white matter connectivity study suggest a shared biological mechanism for HD and support the hypothesis that white matter loss is a direct result of neuronal loss as opposed to the loss of myelin or dysmyelination.     

A reduced mathematical model of the acute inflammatory response: I. Derivation of model and analysis of anti-inflammation

The acute inflammatory response, triggered by a variety of biological or physical stresses on an organism, is a delicate system of checks and balances that, although aimed at promoting healing and restoring homeostasis, can result in undesired and occasionally lethal physiological responses. In this work, we derive a reduced conceptual model for the acute inflammatory response to infection, built up from consideration of direct interactions of fundamental effectors. We harness this model to explore the importance of dynamic anti-inflammation in promoting resolution of infection and homeostasis. Further, we offer a clinical correlation between model predictions and potential therapeutic interventions based on modulation of immunity by anti-inflammatory agents.     

Revenue management for outpatient appointments: joint capacity control and overbooking with class-dependent no-shows

Outpatient appointment scheduling balances efficiency with access to healthcare services, yet appointment no-shows, cancellations, and delay are significant barriers to effective healthcare delivery. Patients with longer appointment delay often waste appointments more frequently, prompting a need for greater flexibility in appointment allocation. We present a joint capacity control and overbooking model where a clinic maximizes profits by controlling bookings from two sequential patient classes with different no-show rates. When booking advance requests, the clinic must balance high no-show probability with the probability of subsequent requests at lower waste rates. We show the optimal policy is computationally intensive to derive; therefore, we develop bounds and approximations which we compare via numerical study with the optimal policy as well as policies from practice and previous literature. We find the optimal policy increases profits 17.8% over first-come-first-serve allocation. We develop a simple policy which performs 0.3% below optimal on average. While pure open access can achieve optimality, it performs 23.0% below optimal on average.     

Differential measurement errors in zero-truncated regression models for count data

Measurement errors in covariates may result in biased estimates in regression analysis. Most methods to correct this bias assume nondifferential measurement errors-i.e., that measurement errors are independent of the response variable. However, in regression models for zero-truncated count data, the number of error-prone covariate measurements for a given observational unit can equal its response count, implying a situation of differential measurement errors. To address this challenge, we develop a modified conditional score approach to achieve consistent estimation. The proposed method represents a novel technique, with efficiency gains achieved by augmenting random errors, and performs well in a simulation study. The method is demonstrated in an ecology application.     

Heavy-Metal Balances, Part II: Management of Cadmium, Copper, Lead, and Zinc in European Agro-Ecosystems

The aim of sustainable heavy-metal management in agroecosystems is to ensure that the soil continues to fulfill its functions: in agricultural production, in environmental processes such as the cycling of elements, and as a habitat of numerous organisms. To understand and manage heavy-metal flows effectively, a consistent approach to modeling the flows is needed within the particular agro-system under study. General aspects of heavy-metal balance studies in agro-ecosystems were described in part I of this study. In this article (part II), several European studies of heavy-metal balances at varying spatial scales and in a variety of agro-ecosystems are reviewed. Sectoral studies at the national and international levels provide information for economic analyses and generic regulations; however, policies implemented at these levels often ignore farm characteristics and individual management options. Field-scale and farm-gate balances give farmers specific feedback on effective options for better heavy-metal management. Heavy-metal balances could be incorporated in an environmental management system of certified farms. In this way, farm certification may well serve as a basis from which to develop policy to address environmental issues in agriculture.     

Mean residual life cure models for right-censored data with and without length-biased sampling

We propose a semiparametric mean residual life mixture cure model for right-censored survival data with a cured fraction. The model employs the proportional mean residual life model to describe the effects of covariates on the mean residual time of uncured subjects and the logistic regression model to describe the effects of covariates on the cure rate. We develop estimating equations to estimate the proposed cure model for the right-censored data with and without length-biased sampling, the latter is often found in prevalent cohort studies. In particular, we propose two estimating equations to estimate the effects of covariates in the cure rate and a method to combine them to improve the estimation efficiency. The consistency and asymptotic normality of the proposed estimates are established. The finite sample performance of the estimates is confirmed with simulations. The proposed estimation methods are applied to a clinical trial study on melanoma and a prevalent cohort study on early-onset type 2 diabetes mellitus.