Canadian COVID-19 host genetics cohort replicates known severity associations.

The HostSeq initiative recruited 10,059 Canadians infected with SARS-CoV-2 between March 2020 and March 2023, obtained clinical information on their disease experience and whole genome sequenced (WGS) their DNA. We analyzed the WGS data for genetic contributors to severe COVID-19 (considering 3,499 hospitalized cases and 4,975 non-hospitalized after quality control). We investigated the evidence for replication of loci reported by the International Host Genetics Initiative (HGI); analyzed the X chromosome; conducted rare variant gene-based analysis and polygenic risk score testing. Population stratification was adjusted for using meta-analysis across ancestry groups. We replicated two loci identified by the HGI for COVID-19 severity: the LZTFL1/SLC6A20 locus on chromosome 3 and the FOXP4 locus on chromosome 6 (the latter with a variant significant at P < 5E-8). We found novel significant associations with MRAS and WDR89 in gene-based analyses, and constructed a polygenic risk score that explained 1.01% of the variance in severe COVID-19. This study provides independent evidence confirming the robustness of previously identified COVID-19 severity loci by the HGI and identifies novel genes for further investigation.

Statistical and Scientific Considerations Concerning the Interpretation, Replicability, and Transportability of Research Findings.

To advance scientific understanding of disease processes and related intervention effects, study results should be free from bias and replicable. More broadly, investigators seek results that are transportable, that is, applicable to a perceived study population as well as in other environments and populations. We review fundamental statistical issues that arise in the analysis of observational data from disease cohorts and other sources and discuss how these issues affect the transportability and replicability of research results. Much of the literature focuses on estimating average exposure or intervention effects at the population level, but we argue for more nuanced analyses of conditional effects that reflect the complexity of disease processes.

Estimands in clinical trials of complex disease processes.

Clinical trials with random assignment of treatment provide evidence about causal effects of an experimental treatment compared to standard care. However, when disease processes involve multiple types of possibly semi-competing events, specification of target estimands and causal inferences can be challenging. Intercurrent events such as study withdrawal, the introduction of rescue medication, and death further complicate matters. There has been much discussion about these issues in recent years, but guidance remains ambiguous. Some recommended approaches are formulated in terms of hypothetical settings that have little bearing in the real world. We discuss issues in formulating estimands, beginning with intercurrent events in the context of a linear model and then move on to more complex disease history processes amenable to multistate modeling. We elucidate the meaning of estimands implicit in some recommended approaches for dealing with intercurrent events and highlight the disconnect between estimands formulated in terms of potential outcomes and the real world.

Multistate models as a framework for estimand specification in clinical trials of complex processes.

Intensity-based multistate models provide a useful framework for characterizing disease processes, the introduction of interventions, loss to followup, and other complications arising in the conduct of randomized trials studying complex life history processes. Within this framework we discuss the issues involved in the specification of estimands and show the limiting values of common estimators of marginal process features based on cumulative incidence function regression models. When intercurrent events arise we stress the need to carefully define the target estimand and the importance of avoiding targets of inference that are not interpretable in the real world. This has implications for analyses, but also the design of clinical trials where protocols may help in the interpretation of estimands based on marginal features.

Independence conditions and the analysis of life history studies with intermittent observation.

Multistate models provide a powerful framework for the analysis of life history processes when the goal is to characterize transition intensities, transition probabilities, state occupancy probabilities, and covariate effects thereon. Data on such processes are often only available at random visit times occurring over a finite period. We formulate a joint multistate model for the life history process, the recurrent visit process, and a random loss to follow-up time at which the visit process terminates. This joint model is helpful when discussing the independence conditions necessary to justify the use of standard likelihoods involving the life history model alone and provides a basis for analyses that accommodate dependence. We consider settings with disease-driven visits and routinely scheduled visits and develop likelihoods that accommodate partial information on the types of visits. Simulation studies suggest that suitably constructed joint models can yield consistent estimates of parameters of interest even under dependent visit processes, providing the models are correctly specified; identifiability and estimability issues are also discussed. An application is given to a cohort of individuals attending a rheumatology clinic where interest lies in progression of joint damage.

Marker-dependent observation and carry-forward of internal covariates in Cox regression.

Studies of chronic disease often involve modeling the relationship between marker processes and disease onset or progression. The Cox regression model is perhaps the most common and convenient approach to analysis in this setting. In most cohort studies, however, biospecimens and biomarker values are only measured intermittently (e.g. at clinic visits) so Cox models often treat biomarker values as fixed at their most recently observed values, until they are updated at the next visit. We consider the implications of this convention on the limiting values of regression coefficient estimators when the marker values themselves impact the intensity for clinic visits. A joint multistate model is described for the marker-failure-visit process which can be fitted to mitigate this bias and an expectation-maximization algorithm is developed. An application to data from a registry of patients with psoriatic arthritis is given for illustration.

Score tests for scale effects, with application to genomic analysis.

Tests for variance or scale effects due to covariates are used in many areas and recently, in genomic and genetic association studies. We study score tests based on location-scale models with arbitrary error distributions that allow incorporation of additional adjustment covariates. Tests based on Gaussian and Laplacian double generalized linear models are examined in some detail. Numerical properties of the tests under Gaussian and other error distributions are examined. Our results show that the use of model-based asymptotic distributions with score tests for scale effects does not control type 1 error well in many settings of practical relevance. We consider simple statistics based on permutation distribution approximations, which correspond to well-known statistics derived by another approach. They are shown to give good type 1 error control under different error distributions and under covariate distribution imbalance. The methods are illustrated through a differential gene expression analysis involving breast cancer tumor samples.

Improving estimation efficiency for regression with MNAR covariates.

For regression with covariates missing not at random where the missingness depends on the missing covariate values, complete-case (CC) analysis leads to consistent estimation when the missingness is independent of the response given all covariates, but it may not have the desired level of efficiency. We propose a general empirical likelihood framework to improve estimation efficiency over the CC analysis. We expand on methods in Bartlett et al. (2014, Biostatistics 15, 719-730) and Xie and Zhang (2017, Int J Biostat 13, 1-20) that improve efficiency by modeling the missingness probability conditional on the response and fully observed covariates by allowing the possibility of modeling other data distribution-related quantities. We also give guidelines on what quantities to model and demonstrate that our proposal has the potential to yield smaller biases than existing methods when the missingness probability model is incorrect. Simulation studies are presented, as well as an application to data collected from the US National Health and Nutrition Examination Survey.

A new perspective on loss to follow-up in failure time and life history studies.

A framework is proposed for the joint modeling of life history and loss to follow-up (LTF) processes in cohort studies. This framework provides a basis for discussing independence conditions for LTF and censoring and examining the implications of dependent LTF. We consider failure time and more general life history processes. The joint models are based on multistate processes with expanded state spaces encompassing both the life history and LTF processes. Tracing studies are discussed as a means of investigating the presence of dependent censoring and providing valid estimates of transition intensities and state occupancy probabilities. Simulation studies and an illustration based on a cohort of individuals with systemic lupus erythematosus demonstrate the usefulness and properties of the proposed methods.

Nonparametric analysis of dependently interval-censored failure time data.

Failure time studies based on observational cohorts often have to deal with irregular intermittent observation of individuals, which produces interval-censored failure times. When the observation times depend on factors related to a person's failure time, the failure times may be dependently interval censored. Inverse-intensity-of-visit weighting methods have been developed for irregularly observed longitudinal or repeated measures data and recently extended to parametric failure time analysis. This article develops nonparametric estimation of failure time distributions using weighted generalized estimating equations and monotone smoothing techniques. Simulations are conducted for examination of the finite sample performance of proposed estimators. This research is motivated in part by the Toronto Psoriatic Arthritis Cohort Study, and the proposed methodology is applied to this study.

Estimation of parametric failure time distributions based on interval-censored data with irregular dependent follow-up.

Event history studies based on disease clinic data often face several complications. Specifically, patients may visit the clinic irregularly, and the intermittent observation times could depend on disease-related variables; this can cause a failure time outcome to be dependently interval-censored. We propose a weighted estimating function approach so that dependently interval-censored failure times can be analysed consistently. A so-called inverse-intensity-of-visit weight is employed to adjust for the informative inspection times. Left truncation of failure times can also be easily handled. Additionally, in observational studies, treatment assignments are typically non-randomized and may depend on disease-related variables. An inverse-probability-of-treatment weight is applied to estimating functions to further adjust for measured confounders. Simulation studies are conducted to examine the finite sample performances of the proposed estimators. Finally, the Toronto Psoriatic Arthritis Cohort Study is used for illustration. Copyright © 2017 John Wiley & Sons, Ltd.

Armitage Lecture 2011: the design and analysis of life history studies.

Life history studies collect information on events and other outcomes during people's lifetimes. For example, these may be related to childhood development, education, fertility, health, or employment. Such longitudinal studies have constraints on the selection of study members, the duration and frequency of follow-up, and the accuracy and completeness of information obtained. These constraints, along with factors associated with the definition and measurement of certain outcomes, affect our ability to understand, model, and analyze life history processes. My objective here is to discuss and illustrate some issues associated with the design and analysis of life history studies.

Semiparametric estimation in copula models for bivariate sequential survival times.

Sequentially observed survival times are of interest in many studies but there are difficulties in analyzing such data using nonparametric or semiparametric methods. First, when the duration of followup is limited and the times for a given individual are not independent, induced dependent censoring arises for the second and subsequent survival times. Non-identifiability of the marginal survival distributions for second and later times is another issue, since they are observable only if preceding survival times for an individual are uncensored. In addition, in some studies a significant proportion of individuals may never have the first event. Fully parametric models can deal with these features, but robustness is a concern. We introduce a new approach to address these issues. We model the joint distribution of the successive survival times by using copula functions, and provide semiparametric estimation procedures in which copula parameters are estimated without parametric assumptions on the marginal distributions. This provides more robust estimates and checks on the fit of parametric models. The methodology is applied to a motivating example involving relapse and survival following colon cancer treatment.

Likelihood ratio procedures and tests of fit in parametric and semiparametric copula models with censored data.

Copula models for multivariate lifetimes have become widely used in areas such as biomedicine, finance and insurance. This paper fills some gaps in existing methodology for copula parameters and model assessment. We consider procedures based on likelihood and pseudolikelihood ratio statistics and introduce semiparametric maximum likelihood estimation leading to semiparametric versions. For cases where standard asymptotic approximations do not hold, we propose an efficient simulation technique for obtaining p-values. We apply these methods to tests for a copula model, based on embedding it in a larger copula family. It is shown that the likelihood and pseudolikelihood ratio tests are consistent even when the expanded copula model is misspecified. Power comparisons with two other tests of fit indicate that model expansion provides a convenient, powerful and robust approach. The methods are illustrated on an application concerning the time to loss of vision in the two eyes of an individual.

On testing for infections during epidemics, with application to Covid-19 in Ontario, Canada.

During an epidemic, accurate estimation of the numbers of viral infections in different regions and groups is important for understanding transmission and guiding public health actions. This depends on effective testing strategies that identify a high proportion of infections (that is, provide high ascertainment rates). For the novel coronavirus SARS-CoV-2, ascertainment rates do not appear to be high in most jurisdictions, but quantitative analysis of testing has been limited. We provide statistical models for studying testing and ascertainment rates, and illustrate them on public data on testing and case counts in Ontario, Canada.

Estimation of prediction error for survival models.

When statistical models are used to predict the values of unobserved random variables, loss functions are often used to quantify the accuracy of a prediction. The expected loss over some specified set of occasions is called the prediction error. This paper considers the estimation of prediction error when regression models are used to predict survival times and discusses the use of these estimates. Extending the previous work, we consider both point and confidence interval estimations of prediction error, and allow for variable selection and model misspecification. Different estimators are compared in a simulation study for an absolute relative error loss function, and results indicate that cross-validation procedures typically produce reliable point estimates and confidence intervals, whereas model-based estimates are sensitive to model misspecification. Links between performance measures for point predictors and for predictive distributions of survival times are also discussed. The methodology is illustrated in a medical setting involving survival after treatment for disease.

A copula-based mixed Poisson model for bivariate recurrent events under event-dependent censoring.

In many chronic disease processes subjects are at risk of two or more types of events. We describe a bivariate mixed Poisson model in which a copula function is used to model the association between two gamma distributed random effects. The resulting model is a bivariate negative binomial process in which each type of event arises from a negative binomial process. Methods for parameter estimation are described for parametric and semiparametric models based on an EM algorithm. We also consider the issue of event-dependent censoring based on one type of event, which arises when one event is sufficiently serious that its occurence may influence the decision of whether to withdraw a patient from a study. The asymptotic biases of estimators of rate and mean functions from naive marginal analyses are discussed, as well as associated treatment effects. Because the joint model is fit based on a likelihood, consistent estimates are obtained. Simulation studies are carried out to evaluate the empirical performance of the proposed estimators with independent and event-dependent censoring and applications to a trial of breast cancer patients with skeletal metastases and a study of patients with chronic obstructive pulmonary disease illustrate the approach.

Models and estimation for systems with recurrent events and usage processes.

This paper considers settings where populations of units may experience recurrent events, termed failures for convenience, and where the units are subject to varying levels of usage. We provide joint models for the recurrent events and usage processes, which facilitate analysis of their relationship as well as prediction of failures. Data on usage are often incomplete and we show how to implement maximum likelihood estimation in such cases. Random effects models with linear usage processes and gamma usage processes are considered in some detail. Data on automobile warranty claims are used to illustrate the proposed models and estimation methodology.

Likelihood methods for regression models with expensive variables missing by design.

In some applications involving regression the values of certain variables are missing by design for some individuals. For example, in two-stage studies (Zhao and Lipsitz, 1992), data on "cheaper" variables are collected on a random sample of individuals in stage I, and then "expensive" variables are measured for a subsample of these in stage II. So the "expensive" variables are missing by design at stage I. Both estimating function and likelihood methods have been proposed for cases where either covariates or responses are missing. We extend the semiparametric maximum likelihood (SPML) method for missing covariate problems (e.g. Chen, 2004; Ibrahim et al., 2005; Zhang and Rockette, 2005, 2007) to deal with more general cases where covariates and/or responses are missing by design, and show that profile likelihood ratio tests and interval estimation are easily implemented. Simulation studies are provided to examine the performance of the likelihood methods and to compare their efficiencies with estimating function methods for problems involving (a) a missing covariate and (b) a missing response variable. We illustrate the ease of implementation of SPML and demonstrate its high efficiency.

Insights from mixture cure modeling of molecular markers for prognosis in breast cancer.

With the ultimate aim of improving clinical management of breast cancer, investigators have sought to identify molecular genetic markers that stratify newly diagnosed patients into subtypes differing in short- or long-term prognosis. Conventional survival models can fail to describe adequately the relationship between subtype and disease recurrence, particularly when there is a substantial proportion of long-term disease-free survivors. The observed patterns of disease-free survival in an undifferentiated patient cohort may be explained by an underlying mixture of two subgroups: patients who will remain free of disease in the long term (ie, cured), and those who will experience disease recurrence within their lifetime (ie, susceptible.) In this article, we review the concepts and methods of the mixture cure models and apply them in the analysis of molecular genetic prognostic factors for disease-free survival and time to disease recurrence in a cohort of patients with axillary lymph node-negative breast cancer.