On the use of historical estimates.

The use of historical, i.e., already existing, estimates in current studies is common in a wide variety of application areas. Nevertheless, despite their routine use, the uncertainty associated with historical estimates is rarely properly accounted for in the analysis. In this communication, we review common practices and then provide a mathematical formulation and a principled frequentist methodology for addressing the problem of drawing inferences in the presence of historical estimates. Three distinct variants are investigated in detail; the corresponding limiting distributions are found and compared. The design of future studies, given historical data, is also explored and relations with a variety of other well-studied statistical problems discussed.

Structural zeros in high-dimensional data with applications to microbiome studies.

This paper is motivated by the recent interest in the analysis of high-dimensional microbiome data. A key feature of these data is the presence of "structural zeros" which are microbes missing from an observation vector due to an underlying biological process and not due to error in measurement. Typical notions of missingness are unable to model these structural zeros. We define a general framework which allows for structural zeros in the model and propose methods of estimating sparse high-dimensional covariance and precision matrices under this setup. We establish error bounds in the spectral and Frobenius norms for the proposed estimators and empirically verify them with a simulation study. The proposed methodology is illustrated by applying it to the global gut microbiome data of Yatsunenko and others (2012. Human gut microbiome viewed across age and geography. Nature 486, 222-227). Using our methodology we classify subjects according to the geographical location on the basis of their gut microbiome.

Newborn readmissions and virtual primary care delivery: a population-based case-control study.

BACKGROUND: Early post-discharge assessments for newborns are recommended. Virtual care has become more prevalent during the pandemic, providing an opportunity to better understand its impact on the quality of post-discharge newborn care. The objective of this study was to understand whether primary care visit modality (in-person vs. virtual) is associated with early newborn hospital readmissions and emergency department (ED) visits. METHODS: We conducted a population-based, case-control study using linked health administrative databases between September 1, 2020 and March 31, 2022 in Ontario, Canada. We compared the modality of primary care visits among cases (hospital readmission within 14 days of life) and controls (newborns without a readmission), matched on infant sex, gestational age, and maternal parity. We included an alternative definition of cases as a composite of either a newborn hospital readmission or emergency department (ED) visit or in-hospital death within the first 14 days of life. Conditional logistic regression models were used to model odds ratios (ORs), comparing those exposed to a virtual visit versus in-person visit, adjusting for infant birth weight, birth hospitalization length of stay, neighbourhood level material deprivation, rurality and presence of active maternal comorbidities. RESULTS: Among 73,324 eligible newborns, 2,220 experienced a hospital readmission within 14 days of life and were matched to 8,880 controls. Jaundice was the primary reason for readmission (75% of readmissions). Compared to newborns who were seen in-person post-discharge, newborns who were seen virtually had higher odds of hospital readmission (adjusted odds ratio [aOR] 1.41 (95% CI 1.09, 1.83); the magnitude of effect was not different using the composite outcome (aOR 1.35, 95% CI 1.05, 1.75). CONCLUSIONS: Newborns who receive a virtual post-discharge visit are more likely than those who receive an in-person visit to require hospital readmission.

Testing for the multivariate stochastic order among ordered experimental groups with application to dose-response studies.

The comparison of two or more ordered experimental groups based on multivariate data is common in a variety of applications such as toxicology, clinical trials and drug development, to name just a few. In this article, we develop a nonparametric methodology for analyzing such data. In particular we propose a global K sample nonparametric test for order among vector valued outcomes. The testing procedure can also be used in a post-hoc fashion to answer questions about the ordering of subgroups and/or single outcomes within any subset of experimental groups. Such a methodology does not currently exist. In contrast with standard methodology such as multivariate analysis of variance (MANOVA), and its nonparametric analogues, we do not assume that the groups differ only by a location parameter or that the components of the response vector have the same marginal distributions between and across groups, that is, we allow for the shape of the distribution to change across groups. We emphasize that our test compares the outcome distributions, not just their mean tendencies, and explicitly incorporates and exploits the order constraints. Consequently it is more powerful than the existing unordered tests. The methodology is illustrated using genotoxicity data where the effect of hydrogen peroxide exposure on damage to DNA is evaluated using a comet assay.

The linear stochastic order and directed inference for multivariate ordered distributions.

Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two sided alternatives they may not be ideal for testing for order between two groups. In this article we introduce the notion of the linear stochastic order and investigate its properties. Statistical theory and methodology are developed to both estimate the direction which best separates two arbitrary ordered distributions and to test for order between the two groups. The new methodology generalizes Roy's classical largest root test to the nonparametric setting and is applicable to random vectors with discrete and/or continuous components. The proposed methodology is illustrated using data obtained from a 90-day pre-chronic rodent cancer bioassay study conducted by the National Toxicology Program (NTP).

A novel performance scoring quantification framework for stress test set-ups.

Stress tests, e.g., the cardiac stress test, are standard clinical screening tools aimed to unmask clinical pathology. As such stress tests indirectly measure physiological reserves. The term reserve has been developed to account for the dis-junction, often observed, between pathology and clinical manifestation. It describes a physiological capacity that is utilized in demanding situations. However, developing a new and reliable stress test based screening tool is complex, prolonged, and relies extensively on domain knowledge. We propose a novel distributional-free machine-learning framework, the Stress Test Performance Scoring (STEPS) framework, to model expected performance in a stress test. A performance scoring function is trained with measures taken during the performance in a given task while exploiting information regarding the stress test set-up and subjects' medical state. Multiple ways of aggregating performance scores at different stress levels are suggested and are examined with an extensive simulation study. When applied to a real-world data example, an AUC of 84.35[95%CI: 70.68 - 95.13] was obtained for the STEPS framework to distinguish subjects with neurodegeneration from controls. In summary, STEPS improved screening by exploiting existing domain knowledge and state-of-the-art clinical measures. The STEPS framework can ease and speed up the production of new stress tests.

Constrained inference in mixed-effects models for longitudinal data with application to hearing loss.

In medical studies, endpoints are often measured for each patient longitudinally. The mixed-effects model has been a useful tool for the analysis of such data. There are situations in which the parameters of the model are subject to some restrictions or constraints. For example, in hearing loss studies, we expect hearing to deteriorate with time. This means that hearing thresholds which reflect hearing acuity will, on average, increase over time. Therefore, the regression coefficients associated with the mean effect of time on hearing ability will be constrained. Such constraints should be accounted for in the analysis. We propose maximum likelihood estimation procedures, based on the expectation-conditional maximization either algorithm, to estimate the parameters of the model while accounting for the constraints on them. The proposed methods improve, in terms of mean square error, on the unconstrained estimators. In some settings, the improvement may be substantial. Hypotheses testing procedures that incorporate the constraints are developed. Specifically, likelihood ratio, Wald, and score tests are proposed and investigated. Their empirical significance levels and power are studied using simulations. It is shown that incorporating the constraints improves the mean squared error of the estimates and the power of the tests. These improvements may be substantial. The methodology is used to analyze a hearing loss study.

Order-restricted inference for multivariate longitudinal data with applications to the natural history of hearing loss.

Multivariate outcomes are often measured longitudinally. For example, in hearing loss studies, hearing thresholds for each subject are measured repeatedly over time at several frequencies. Thus, each patient is associated with a multivariate longitudinal outcome. The multivariate mixed-effects model is a useful tool for the analysis of such data. There are situations in which the parameters of the model are subject to some restrictions or constraints. For example, it is known that hearing thresholds, at every frequency, increase with age. Moreover, this age-related threshold elevation is monotone in frequency, that is, the higher the frequency, the higher, on average, is the rate of threshold elevation. This means that there is a natural ordering among the different frequencies in the rate of hearing loss. In practice, this amounts to imposing a set of constraints on the different frequencies' regression coefficients modeling the mean effect of time and age at entry to the study on hearing thresholds. The aforementioned constraints should be accounted for in the analysis. The result is a multivariate longitudinal model with restricted parameters. We propose estimation and testing procedures for such models. We show that ignoring the constraints may lead to misleading inferences regarding the direction and the magnitude of various effects. Moreover, simulations show that incorporating the constraints substantially improves the mean squared error of the estimates and the power of the tests. We used this methodology to analyze a real hearing loss study.

Order-restricted semiparametric inference for the power bias model.

The power bias model, a generalization of length-biased sampling, is introduced and investigated in detail. In particular, attention is focused on order-restricted inference. We show that the power bias model is an example of the density ratio model, or in other words, it is a semiparametric model that is specified by assuming that the ratio of several unknown probability density functions has a parametric form. Estimation and testing procedures under constraints are developed in detail. It is shown that the power bias model can be used for testing for, or against, the likelihood ratio ordering among multiple populations without resorting to any parametric assumptions. Examples and real data analysis demonstrate the usefulness of this approach.

Minimum-norm estimation for binormal receiver operating characteristic (ROC) curves.

The receiver operating characteristic (ROC) curve is often used to assess the usefulness of a diagnostic test. We present a new method to estimate the parameters of a popular semi-parametric ROC model, called the binormal model. Our method is based on minimization of the functional distance between two estimators of an unknown transformation postulated by the model, and has a simple, closed-form solution. We study the asymptotics of our estimators, show via simulation that they compare favorably with existing estimators, and illustrate how covariates may be incorporated into the norm minimization framework.

The association of dropout and outcome in trials of antipsychotic medication and its implications for dealing with missing data.

OBJECTIVE: The extent to which noncompletion of a clinical trial relates to outcomes has implications for choosing the most appropriate method for contending with missing data due to dropout. We examined whether dropout relates to outcome in clinical trials of antipsychotic medication. METHODS: Data from 5 large clinical trials of schizophrenia (n=3483) were examined separately. Patients were aggregated into groups based on their final study visit. Group mean Positive and Negative Syndrome Scale (PANSS) total scores for each visit were computed and graphed. Change from baseline to end point for each group was computed and examined using ANCOVA. Cox regression modeling was used to examine baseline PANSS total and change as predictors of time to dropout. RESULTS: In all 5 trials there was a statistically significantly relationship between time in trial and improvement. The longer the patients remained in the trial the more that they improved, with trial completers showing the most improvement at each time point. Higher baseline PANSS scores and symptom deterioration indicated by increased PANSS preceding the final study visit prior to dropout corresponded significantly with a greater likelihood of dropout. CONCLUSIONS: Dropout in clinical trials of antipsychotic medications corresponds with efficacy outcomes, the dynamics of symptom change and baseline symptom severity. Therefore, methods for statistical analysis should examine both efficacy and dropout and cannot assume that missing data due to dropout are completely at random.

A composite approach that includes dropout rates when analyzing efficacy data in clinical trials of antipsychotic medications.

BACKGROUND: Often, outcomes in clinical trials of antipsychotic medications are examined using last observation carried forward (LOCF). One limitation of LOCF and other common approaches is that they overlook the meaning underpinning trial completion and noncompletion. Noncompletion often relates to lack of drug tolerability. Because long-term treatment is often indicated, noncompletion is an important outcome. An alternative approach is to test the composite hypothesis of the difference between (a) completion rates and (b) efficacy of complete cases. Studies to date have not applied this relatively new method. OBJECTIVE: To illustrate the composite approach, we applied it to a systematic review of studies and compared the results with the reported LOCF analysis. METHODS: A systematic search of the Schizophrenia Module of the Cochrane Library and Medline was conducted that identified 127 relevant randomized clinical trials of antipsychotic medications conducted since 1995. Extracted from study reports were the P values of a difference in dropout and the P value of a difference in improvement among complete cases. These P values were combined using standard approaches. RESULTS: We identified 11 trials with 5339 participants that provided the necessary information to adequately apply the composite approach. In 2 trials, (18.2%) in which the LOCF results were not significant, the composite results were significant. CONCLUSIONS: The composite approach was more sensitive to change than LOCF and conceptually answers a more relevant question. It is likely that applying the composite approach would change how results of many trials are interpreted.

Testing for inequality constraints in singular models by trimming or winsorizing the variance matrix.

There are many applications in which a statistic follows, at least asymptotically, a normal distribution with a singular or nearly singular variance matrix. A classic example occurs in linear regression models under multicollinearity but there are many more such examples. There is well-developed theory for testing linear equality constraints when the alternative is two-sided and the variance matrix is either singular or non-singular. In recent years there is considerable, and growing, interest in developing methods for situations in which the estimated variance matrix is nearly singular. However, there is no corresponding methodology for addressing one-sided, i.e., constrained or ordered alternatives. In this paper we develop a unified framework for analyzing such problems. Our approach may be viewed as the trimming or winsorizing of the eigenvalues of the corresponding variance matrix. The proposed methodology is applicable to a wide range of scientific problems and to a variety of statistical models in which inequality constraints arise. We illustrate the methodology using data from a gene expression microarray experiment obtained from the NIEHS' Fibroid Growth Study.

Analysis of Microbiome Data in the Presence of Excess Zeros.

Motivation: An important feature of microbiome count data is the presence of a large number of zeros. A common strategy to handle these excess zeros is to add a small number called pseudo-count (e.g., 1). Other strategies include using various probability models to model the excess zero counts. Although adding a pseudo-count is simple and widely used, as demonstrated in this paper, it is not ideal. On the other hand, methods that model excess zeros using a probability model often make an implicit assumption that all zeros can be explained by a common probability models. As described in this article, this is not always recommended as there are potentially three types/sources of zeros in a microbiome data. The purpose of this paper is to develop a simple methodology to identify and accomodate three different types of zeros and to test hypotheses regarding the relative abundance of taxa in two or more experimental groups. Another major contribution of this paper is to perform constrained (directional or ordered) inference when there are more than two ordered experimental groups (e.g., subjects ordered by diet or age groups or environmental exposure groups). As far as we know this is the first paper that addresses such problems in the analysis of microbiome data. Results: Using extensive simulation studies, we demonstrate that the proposed methodology not only controls the false discovery rate at a desired level of significance while competing well in terms of power with DESeq2, a popular procedure derived from RNASeq literature. As expected, the method using pseudo-counts tends to be very conservative and the classical t-test that ignores the underlying simplex structure in the data has an inflated FDR.

Order restricted inference for multivariate binary data with application to toxicology.

In many applications researchers collect multivariate binary response data under two or more, naturally ordered, experimental conditions. In such situations one is often interested in using all binary outcomes simultaneously to detect an ordering among the experimental conditions. To make such comparisons we develop a general methodology for testing for the multivariate stochastic order between K ≥ 2 multivariate binary distributions. The proposed test uses order restricted estimators which, according to our simulation study, are more efficient than the unrestricted estimators in terms of mean squared error. The power of the proposed test was compared with several alternative tests. These included procedures which combine individual univariate tests for order, such as union intersection tests and a Bonferroni based test. We also compared the proposed test with unrestricted Hotelling's T(2) type test. Our simulations suggest that the proposed method competes well with these alternatives. The gain in power is often substantial. The proposed methodology is illustrated by applying it to a two-year rodent cancer bioassay data obtained from the US National Toxicology Program (NTP). Supplemental materials are available online.

Analysis of Correlated Gene Expression Data on Ordered Categories.

A bootstrap based methodology is introduced for analyzing repeated measures/longitudinal microarray gene expression data over ordered categories. The proposed non-parametric procedure uses order-restricted inference to compare gene expressions among ordered experimental conditions. The null distribution for determining significance is derived by suitably bootstrapping the residuals. The procedure addresses two potential sources of correlation in the data, namely, (a) correlations among genes within a chip ("intra-chip" correlation), and (b) correlation within subject due to repeated/longitudinal measurements ("temporal" correlation). To make the procedure computationally efficient, the adaptive bootstrap methodology of Guo and Peddada (2008) is implemented such that the resulting procedure controls the false discovery rate (FDR) at the desired nominal level.

Dropout rates in randomized clinical trials of antipsychotics: a meta-analysis comparing first- and second-generation drugs and an examination of the role of trial design features.

Dropout is often used as an outcome measure in clinical trials of antipsychotic medication. Previous research is inconclusive regarding (a) differences in dropout rates between first- and second-generation antipsychotic medications and (b) how trial design features reduce dropout. Meta-analysis of randomized controlled trials (RCTs) of antipsychotic medication was conducted to compare dropout rates for first- and second-generation antipsychotic drugs and to examine how a broad range of design features effect dropout. Ninety-three RCTs that met inclusion criteria were located (n = 26 686). Meta-analytic random effects models showed that dropout was higher for first- than second-generation drugs (odds ratio = 1.49, 95% confidence interval: 1.31-1.66). This advantage persisted after removing study arms with excessively high dosages, in flexible dose studies, studies of patients with symptom exacerbation, nonresponder patients, inpatients, and outpatients. Mixed effects models for meta-analysis were used to identify design features that effected dropout and develop formulae to derive expected dropout rates based on trial design features, and these assigned a pivotal role to duration. Collectively, dropout rates are lower for second- than first-generation antipsychotic drugs and appear to be partly explained by trial design features thus providing direction for future trial design.

Overdiagnosis in early detection programs.

Overdiagnosis refers to the situation where a screening exam detects a disease that would have otherwise been undetected in a person's lifetime. The disease would have not have been diagnosed because the individual would have died of other causes prior to its clinical onset. Although the probability of overdiagnosis is an important quantity for understanding early detection programs it has not been rigorously studied. We analyze an idealized early detection program and derive the mathematical expression for the probability of overdiagnosis. The results are studied numerically for prostate cancer and applied to a variety of screening schedules. Our investigation indicates that the probability of overdiagnosis is remarkably high.

The theory of case-control studies for early detection programs.

Although case-control studies are widely used for evaluating the benefit of early detection programs, the theoretical basis underlying this application has not been well developed. In this paper the properties of chronic disease case-control studies for evaluating early detection programs are investigated. An idealized case-control study is analyzed and the theoretical expression for the odds ratio associated with the benefit of screening is derived. The odds ratio is related to the natural history of disease and the screening program. Our results indicate that case-control studies result in odds ratios that are surprisingly close to unity and consequently have low power.

Combined association, segregation and aggregation analysis on case-control family data.

Recently genetic epidemiologists have begun using case-control family study designs to investigate the role of genetic and environmental risk factors in disease etiology. The objective of these studies is to assess the association of environmental factors with the disease trait; to characterize the disease genes using segregation analysis; and to quantify the residual familial aggregation after controlling for environmental and genetic factors. Typically these objectives are achieved by conducting separate studies and analysis. This paper describes an estimating equation based approach for a combined association, segregation and aggregation analysis on data from case-control family studies. Simulations indicate that the method performs well in a variety of settings. The method is illustrated using simulated family history data made available to participants in a recent Genetic Analysis Workshop.