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Under the setting of a case-cohort design, covariate values are ascertained for a smaller subgroup of the original study cohort which typically is a representative sample from a population. Individuals with a specific event outcome are selected to the second stage study group as cases and an additional subsample is selected to act as a control group. We carry out analysis of such a design using conditional likelihood where the likelihood expression is conditioned on the ascertainment to the second stage study group. Such likelihood expression involves the probability of ascertainment which need to be expressed in terms of the model parameters. We present examples of conditional likelihoods for models for categorical response and time-to-event response. We show that the conditional likelihood inference leads to valid estimation of population parameters. Our application considers joint estimation of haplotype-event association parameters and population haplotype frequencies based on SNP genotype data collected under a case-cohort design.

Characterizing the genetic correlates to complex diseases requires consideration of a large number of potentially informative biological markers. In addition, attention to alignment of alleles within or across chromosomal pairs, commonly referred to as phase, may be essential for uncovering true biological associations. In the context of population based association studies, phase is generally unobservable. Preservation of type-1 error in a setting with multiple testing presents a further analytical challenge. This manuscript combines a likelihood-based approach to handling missing-ness in phase with a resampling method to adjust for multiple testing. Through simulations we demonstrate preservation of the family-wise error rate and reasonable power for detecting associations. The method is applied to a cohort of 626 HIV-1 infected individuals receiving highly active anti-retroviral therapies, to ascertain potential genetic contributions to abnormalities in lipid profiles. The haplotypic effects of 2 genes, hepatic lipase (HL) and endothelial lipase (EL), on high-density lipoprotein cholesterol (HDL-C) are tested.

Marginal structural models (MSM) are an important class of models in causal inference. Given a longitudinal data structure observed on a sample of n independent and identically distributed experimental units, MSM model the counterfactual outcome distribution corresponding with a static treatment intervention, conditional on user-supplied baseline covariates. Identification of a static treatment regimen-specific outcome distribution based on observational data requires, beyond the standard sequential randomization assumption, the assumption that each experimental unit has positive probability of following the static treatment regimen. The latter assumption is called the experimental treatment assignment (ETA) assumption, and is parameter-specific. In many studies the ETA is violated because some of the static treatment interventions to be compared cannot be followed by all experimental units, due either to baseline characteristics or to the occurrence of certain events over time. For example, the development of adverse effects or contraindications can force a subject to stop an assigned treatment regimen.In this article we propose causal effect models for a user-supplied set of realistic individualized treatment rules. Realistic individualized treatment rules are defined as treatment rules which always map into the set of possible treatment options. Thus, causal effect models for realistic treatment rules do not rely on the ETA assumption and are fully identifiable from the data. Further, these models can be chosen to generalize marginal structural models for static treatment interventions. The estimating function methodology of Robins and Rotnitzky (1992) (analogue to its application in Murphy, et. al. (2001) for a single treatment rule) provides us with the corresponding locally efficient double robust inverse probability of treatment weighted estimator.In addition, we define causal effect models for “intention-to-treat” regimens. The proposed intention-to-treat interventions enforce a static intervention until the time point at which the next treatment does not belong to the set of possible treatment options, at which point the intervention is stopped. We provide locally efficient estimators of such intention-to-treat causal effects.

We consider random design nonparametric regression when the response variable is subject to right censoring. Following the work of Fan and Gijbels (1994), a common approach to this problem is to apply what has been termed a censoring unbiased transformation to the data to obtain surrogate responses, and then enter these surrogate responses with covariate data into standard smoothing algorithms. Existing censoring unbiased transformations generally depend on either the conditional survival function of the response of interest, or that of the censoring variable. We show that a mapping introduced in another statistical context is in fact a censoring unbiased transformation with a beneficial double robustness property, in that it can be used for nonparametric regression if either of these two conditional distributions are estimated accurately. Advantages of using this transformation for smoothing are illustrated in simulations and on the Stanford heart transplant data.

As a generalization of the accelerated failure time models, we consider parametric models of lifetime Y, where the conditional mean E(Y|X;beta) can depend nonlinearly on the covariates X and some parameters beta. The error distribution can be heteroscedastic and dependent on X. With observed data subject to right censoring, we propose regression analysis for beta based on Kaplan-Meier estimates of the means over several regions of X. Consistency and asymptotic distributional properties of the estimators are established under general conditions. A resulting estimator of beta is shown to be the sum of two possibly dependent asymptotic normal quantities, based on which conservative confidence intervals and tests are derived. Simulation studies are conducted to investigate the performance of the proposed estimator and to compare it with Buckley-Jame's method. To illustrate the methodology, we study an example with kidney transplant data, where a nonlinear relationship called "mixtures-of-experts", proposed in the neural networks literature, is used to model the relationship between the survival time and the age of the patients.

Consider a longitudinal observational or controlled study in which one collects chronological data over time on a random sample of subjects. The time-dependent process one observes on each subject contains time-dependent covariates, time-dependent treatment actions, and an outcome process or single final outcome of interest. A statically optimal individualized treatment rule (as introduced in van der Laan et. al. (2005), Petersen et. al. (2007)) is a treatment rule which at any point in time conditions on a user-supplied subset of the past, computes the future static treatment regimen that maximizes a (conditional) mean future outcome of interest, and applies the first treatment action of the latter regimen. In particular, Petersen et. al. (2007) clarified that, in order to be statically optimal, an individualized treatment rule should not depend on the observed treatment mechanism. Petersen et. al. (2007) further developed estimators of statically optimal individualized treatment rules based on a past capturing all confounding of past treatment history on outcome. In practice, however, one typically wishes to find individualized treatment rules responding to a user-supplied subset of the complete observed history, which may not be sufficient to capture all confounding. The current article provides an important advance on Petersen et. al. (2007) by developing locally efficient double robust estimators of statically optimal individualized treatment rules responding to such a user-supplied subset of the past. However, failure to capture all confounding comes at a price; the static optimality of the resulting rules becomes origin-specific. We explain origin-specific static optimality, and discuss the practical importance of the proposed methodology. We further present the results of a data analysis in which we estimate a statically optimal rule for switching antiretroviral therapy among patients infected with resistant HIV virus.

The objective of this work is to introduce a new method called the Survivorship Instantaneous Log-odds Ratios (SILOR); to illustrate the creation of SILOR from empirical bivariate survival functions; to also derive standard errors of estimation; to compare results with those derived from logistic regression. Hip fracture, AGE and BMI from the Third National Health and Nutritional Examination Survey (NHANES III) were used to calculate empirical survival functions for the adverse health outcome (AHO) and non-AHO. A stable copula was used to create a parametric bivariate survival function, that was fitted to the empirical bivariate survival function. The bivariate survival function had SILOR contours which are not constant. The proposed method has better advantages than logistic regression by following two reasons. The comparison deals with (i) the shapes of the survival surfaces, S(X1, X2), and (ii) the isobols of the log-odds ratios. When using logistic regression the survival surface is either a hyper plane or at most a conic section. Our approach preserves the shape of the survival surface in two dimensions, and the isobols are observed in every detail instead of being overly smoothed by a regression with no more than a second degree polynomial. The present method is straightforward, and it captures all but random variability of the data.

In individuals infected with human immunodeficiency virus (HIV), distributions of quantitative HIV RNA measurements may be highly left-censored due to values falling below assay detection limits (DL). It is of the interest to find the relationship between plasma and semen viral loads. To address this type of problem, we developed an empirical goodness-of-fit test to check the Clayton model assumption for bivariate truncated data. We also used truncated tau to estimate the dependence parameter in the Clayton model for this type of data. It turns out that the proposed methodology works for both truncated and fixed left censored bivariate data. The proposed test procedure is demonstrated using an HIV data set, and statistical inference is drawn based on corresponding test result.

Child growth is characterised by increases in height, and increases in maturational status. Functional data analysis provides a tool to separate these two sources of variation (registration) and differentiates between the variation in maturational tempo (temporal, or “phase” variation) and the variation in height (amplitude variation). We extended this concept by combining Principal Component Analysis (PCA) and the Maximum Likelihood Principle. Longitudinal data on height were obtained from two large growth studies from Lublin, Poland, and Zurich, Switzerland, with altogether 361 children. Variation in amplitude monotonically rises with age; variation in phase peaks during puberty. During mid-puberty, phase variation is large and explains up to 40 percent of total height variance in girls, and up to 50 percent in boys. Eight amplitude and 4 phase components appeared biologically significant. The largest amplitude component explained 91% of the amplitude variance and is characterised by an almost horizontal pattern. The largest phase component explained 66% (boys) and 63% (girls) of phase variance, rises throughout childhood and reaches up to 0.85 years in adolescent boys, and up to 0.75 years in adolescent girls. Phase components significantly correlated with the clinical signs of puberty. The combination of PCA and the Maximum Likelihood Principle provides a new, powerful and automatic tool for growth modelling that includes estimates of future growth, adult stature and developmental tempo. Preliminary results indicate that this approach can be used for automatised screening purposes.

Analyses of individual disease-exposure data within a population are useful when exposure of interest varies sufficiently within the population. When the within-population variance of exposure is limited, however, power of the individual-data analysis is reduced. In such situations, aggregated-data analyses of disease data across populations, with a sample of individual exposure data from each population, can be powerful in estimating the exposure effect if between-population variation of exposure is large. In this paper, we consider a new analytical framework that is a combination of the individual- and aggregated-data analyses, based on an estimating equation approach. The proposed analysis utilizes strengths from individual data and aggregated data in the estimation of the exposure effect of interest, depending on which of the exposure variations (within- versus between-population) dominates. Simulation studies under various different scenarios were performed to show the strengths of the proposed approach in the estimation of the exposure effects of interest.

We present a reformulation of the Benjamini-Hochberg method that is useful in 'large-scale' multiple testing problems based on discrete test statistics and derive its basic asymptotic (as the number of hypotheses tends to infinity) properties, subsuming earlier results. A set of gene expression data is used to illustrate the workings of the method in a multiple testing problem based on Kolmogorov-Smirnov and Mann-Whitney statistics.

Understanding the genetic underpinnings to complex diseases requires consideration of sophisticated analytical methods designed to uncover intricate associations across multiple predictor variables. At the same time, knowledge of whether single nucleotide polymorphisms within a gene are on the same (in cis) or on different (in trans) chromosomal copies, may provide crucial information about measures of disease progression. In association studies of unrelated individuals, allelic phase is generally unobservable, generating an additional analytical challenge. In this manuscript, we describe a novel approach that combines multiple imputation and random forests for this high-dimensional, unobservable data setting. An application to a cohort of HIV-1 infected individuals receiving anti-retroviral therapies is presented. A simulation study is also presented to characterize method performance.

Mortality rate ratios and the associated proportional hazards models have been used to summarize the effect of Alzheimer's disease on longevity. However, the mortality rate ratios vary by age and therefore do not provide a simple parsimonious summary of the effect of the disease on lifespan. Instead, we propose a new parameter that is defined by an additive multistate model. The proposed multistate model accounts for different stages of disease progression. The underlying assumption of the model is that the effect of disease on mortality is to add a constant amount to death rates once the disease progresses from an early to late stage. We explored the properties of the proposed model; in particular the behavior of the mortality rate ratio and median survival that is induced by the model. We combined information from several data sources to estimate the parameter in our model. We found that the effect of Alzheimer's disease on longevity is to increase the absolute annual risk of death by about 8% once a person progressed to late stage disease. Most importantly, we find that this additive effect is the same regardless of the patients' age or gender. Thus, the proposed additive multi-state model provides a parsimonious and clinically interpretable description of the effects of Alzheimer's disease on mortality.

Observational studies of prescription medications and other medical interventions based on administrative data are increasingly used to inform regulatory and clinical decision making. The validity of such studies is often questioned, however, because the available data may not contain measurements of important prognostic variables that guide treatment decisions. Recently, approaches to this problem have been proposed that use instrumental variables (IV) defined at the level of an individual health care provider or aggregation of providers. Implicitly, these approaches attempt to estimate causal effects by using differences in medical practice patterns as a quasi-experiment. Although preference-based IV methods may usefully complement standard statistical approaches, they make assumptions that are unfamiliar to most biomedical researchers and therefore the validity of such an analysis can be hard to evaluate. Here, we describe a simple framework based on a single unobserved dichotomous variable that can be used to explore how violations of IV assumptions and treatment effect heterogeneity may bias the standard IV estimator with respect to the average treatment effect in the population. This framework suggests various ways to anticipate the likely direction of bias using both empirical data and commonly available subject matter knowledge, such as whether medications or medical procedures tend to be overused, underused, or often misused. This approach is described in the context of a study comparing the gastrointestinal bleeding risk attributable to different non-steroidal anti-inflammatory drugs.