Tumour heterogeneity in the clinic.

Recent therapeutic advances in oncology have been driven by the identification of tumour genotype variations between patients, called interpatient heterogeneity, that predict the response of patients to targeted treatments. Subpopulations of cancer cells with unique genomes in the same patient may exist across different geographical regions of a tumour or evolve over time, called intratumour heterogeneity. Sequencing technologies can be used to characterize intratumour heterogeneity at diagnosis, monitor clonal dynamics during treatment and identify the emergence of clinical resistance during disease progression. Genetic interpatient and intratumour heterogeneity can pose challenges for the design of clinical trials that use these data.

Genome-wide association study of three-dimensional facial morphology identifies a variant in PAX3 associated with nasion position.

Craniofacial morphology is highly heritable, but little is known about which genetic variants influence normal facial variation in the general population. We aimed to identify genetic variants associated with normal facial variation in a population-based cohort of 15-year-olds from the Avon Longitudinal Study of Parents and Children. 3D high-resolution images were obtained with two laser scanners, these were merged and aligned, and 22 landmarks were identified and their x, y, and z coordinates used to generate 54 3D distances reflecting facial features. 14 principal components (PCs) were also generated from the landmark locations. We carried out genome-wide association analyses of these distances and PCs in 2,185 adolescents and attempted to replicate any significant associations in a further 1,622 participants. In the discovery analysis no associations were observed with the PCs, but we identified four associations with the distances, and one of these, the association between rs7559271 in PAX3 and the nasion to midendocanthion distance (n-men), was replicated (p = 4 × 10(-7)). In a combined analysis, each G allele of rs7559271 was associated with an increase in n-men distance of 0.39 mm (p = 4 × 10(-16)), explaining 1.3% of the variance. Independent associations were observed in both the z (nasion prominence) and y (nasion height) dimensions (p = 9 × 10(-9) and p = 9 × 10(-10), respectively), suggesting that the locus primarily influences growth in the yz plane. Rare variants in PAX3 are known to cause Waardenburg syndrome, which involves deafness, pigmentary abnormalities, and facial characteristics including a broad nasal bridge. Our findings show that common variants within this gene also influence normal craniofacial development.

Sieve estimation in semiparametric modeling of longitudinal data with informative observation times.

Analyzing irregularly spaced longitudinal data often involves modeling possibly correlated response and observation processes. In this article, we propose a new class of semiparametric mean models that allows for the interaction between the observation history and covariates, leaving patterns of the observation process to be arbitrary. For inference on the regression parameters and the baseline mean function, a spline-based least squares estimation approach is proposed. The consistency, rate of convergence, and asymptotic normality of the proposed estimators are established. Our new approach is different from the usual approaches relying on the model specification of the observation scheme, and it can be easily used for predicting the longitudinal response. Simulation studies demonstrate that the proposed inference procedure performs well and is more robust. The analyses of bladder tumor data and medical cost data are presented to illustrate the proposed method.

Fast forward selection for generalized estimating equations with a large number of predictor variables.

We propose a new variable selection criterion designed for use with forward selection algorithms; the score information criterion (SIC). The proposed criterion is based on score statistics which incorporate correlated response data. The main advantage of the SIC is that it is much faster to compute than existing model selection criteria when the number of predictor variables added to a model is large, this is because SIC can be computed for all candidate models without actually fitting them. A second advantage is that it incorporates the correlation between variables into its quasi-likelihood, leading to more desirable properties than competing selection criteria. Consistency and prediction properties are shown for the SIC. We conduct simulation studies to evaluate the selection and prediction performances, and compare these, as well as computational times, with some well-known variable selection criteria. We apply the SIC on a real data set collected on arthropods by considering variable selection on a large number of interactions terms consisting of species traits and environmental covariates.

Likelihood-based analysis of longitudinal data from outcome-related sampling designs.

Investigators commonly gather longitudinal data to assess changes in responses over time and to relate these changes to within-subject changes in predictors. With rare or expensive outcomes such as uncommon diseases and costly radiologic measurements, outcome-dependent, and more generally outcome-related, sampling plans can improve estimation efficiency and reduce cost. Longitudinal follow up of subjects gathered in an initial outcome-related sample can then be used to study the trajectories of responses over time and to assess the association of changes in predictors within subjects with change in response. In this article, we develop two likelihood-based approaches for fitting generalized linear mixed models (GLMMs) to longitudinal data from a wide variety of outcome-related sampling designs. The first is an extension of the semi-parametric maximum likelihood approach developed in Neuhaus, Scott and Wild (2002, Biometrika 89, 23-37) and Neuhaus, Scott and Wild (2006, Biometrics 62, 488-494) and applies quite generally. The second approach is an adaptation of standard conditional likelihood methods and is limited to random intercept models with a canonical link. Data from a study of attention deficit hyperactivity disorder in children motivates the work and illustrates the findings.

Semiparametric analysis of linear transformation models with covariate measurement errors.

We take a semiparametric approach in fitting a linear transformation model to a right censored data when predictive variables are subject to measurement errors. We construct consistent estimating equations when repeated measurements of a surrogate of the unobserved true predictor are available. The proposed approach applies under minimal assumptions on the distributions of the true covariate or the measurement errors. We derive the asymptotic properties of the estimator and illustrate the characteristics of the estimator in finite sample performance via simulation studies. We apply the method to analyze an AIDS clinical trial data set that motivated the work.

Modeling the impact of hepatitis C viral clearance on end-stage liver disease in an HIV co-infected cohort with targeted maximum likelihood estimation.

Despite modern effective HIV treatment, hepatitis C virus (HCV) co-infection is associated with a high risk of progression to end-stage liver disease (ESLD) which has emerged as the primary cause of death in this population. Clinical interest lies in determining the impact of clearance of HCV on risk for ESLD. In this case study, we examine whether HCV clearance affects risk of ESLD using data from the multicenter Canadian Co-infection Cohort Study. Complications in this survival analysis arise from the time-dependent nature of the data, the presence of baseline confounders, loss to follow-up, and confounders that change over time, all of which can obscure the causal effect of interest. Additional challenges included non-censoring variable missingness and event sparsity. In order to efficiently estimate the ESLD-free survival probabilities under a specific history of HCV clearance, we demonstrate the double-robust and semiparametric efficient method of Targeted Maximum Likelihood Estimation (TMLE). Marginal structural models (MSM) can be used to model the effect of viral clearance (expressed as a hazard ratio) on ESLD-free survival and we demonstrate a way to estimate the parameters of a logistic model for the hazard function with TMLE. We show the theoretical derivation of the efficient influence curves for the parameters of two different MSMs and how they can be used to produce variance approximations for parameter estimates. Finally, the data analysis evaluating the impact of HCV on ESLD was undertaken using multiple imputations to account for the non-monotone missing data.

Fully Bayesian inference under ignorable missingness in the presence of auxiliary covariates.

In order to make a missing at random (MAR) or ignorability assumption realistic, auxiliary covariates are often required. However, the auxiliary covariates are not desired in the model for inference. Typical multiple imputation approaches do not assume that the imputation model marginalizes to the inference model. This has been termed "uncongenial" [Meng (1994, Statistical Science 9, 538-558)]. In order to make the two models congenial (or compatible), we would rather not assume a parametric model for the marginal distribution of the auxiliary covariates, but we typically do not have enough data to estimate the joint distribution well non-parametrically. In addition, when the imputation model uses a non-linear link function (e.g., the logistic link for a binary response), the marginalization over the auxiliary covariates to derive the inference model typically results in a difficult to interpret form for the effect of covariates. In this article, we propose a fully Bayesian approach to ensure that the models are compatible for incomplete longitudinal data by embedding an interpretable inference model within an imputation model and that also addresses the two complications described above. We evaluate the approach via simulations and implement it on a recent clinical trial.

Data generation for the Cox proportional hazards model with time-dependent covariates: a method for medical researchers.

The proliferation of longitudinal studies has increased the importance of statistical methods for time-to-event data that can incorporate time-dependent covariates. The Cox proportional hazards model is one such method that is widely used. As more extensions of the Cox model with time-dependent covariates are developed, simulations studies will grow in importance as well. An essential starting point for simulation studies of time-to-event models is the ability to produce simulated survival times from a known data generating process. This paper develops a method for the generation of survival times that follow a Cox proportional hazards model with time-dependent covariates. The method presented relies on a simple transformation of random variables generated according to a truncated piecewise exponential distribution and allows practitioners great flexibility and control over both the number of time-dependent covariates and the number of time periods in the duration of follow-up measurement. Within this framework, an additional argument is suggested that allows researchers to generate time-to-event data in which covariates change at integer-valued steps of the time scale. The purpose of this approach is to produce data for simulation experiments that mimic the types of data structures applied that researchers encounter when using longitudinal biomedical data. Validity is assessed in a set of simulation experiments, and results indicate that the proposed procedure performs well in producing data that conform to the assumptions of the Cox proportional hazards model.

Estimation of the treatment effect in the presence of non-compliance and missing data.

Treatment non-compliance and missing data are common problems in clinical trials. Non-compliance is a broad term including any kind of deviation from the assigned treatment protocol, such as dose modification, treatment discontinuation or switch, often resulting in missing values. Missing values and treatment non-compliance may bias study results. Follow-up of all patients until the planned end of treatment period irrespective of their protocol adherence may provide useful information on the effectiveness of a study drug, taking the actual compliance into account. In this paper, we consider non-compliance as discontinuation of treatment and assume that the endpoint of interest is recorded for some non-complying patients after treatment discontinuation. As a result, the patient's longitudinal profile is dividable into on- and off-treatment observations. Within the framework of depression trials, which usually show a considerably high amount of dropouts, we compare different analysis strategies including both on- and off-treatment observations to gain insight into how the additional use of off-treatment data may affect the trial's outcome. We compare naïve strategies, which simply ignore off-treatment data or treat on- and off-treatment data in the same way, with more complex strategies based on piecewise linear mixed models, which assume different treatment effects for on- and off-treatment data. We show that naïve strategies may considerably overestimate treatment effects. Therefore, it is worthwhile to follow up as many patients as possible until the end of their planned treatment period irrespective of compliance, including all available data in an analysis that accounts for the different treatment conditions.

An analytic method for the placebo-based pattern-mixture model.

Pattern-mixture models provide a general and flexible framework for sensitivity analyses of nonignorable missing data. The placebo-based pattern-mixture model (Little and Yau, Biometrics 1996; 52:1324-1333) treats missing data in a transparent and clinically interpretable manner and has been used as sensitivity analysis for monotone missing data in longitudinal studies. The standard multiple imputation approach (Rubin, Multiple Imputation for Nonresponse in Surveys, 1987) is often used to implement the placebo-based pattern-mixture model. We show that Rubin's variance estimate of the multiple imputation estimator of treatment effect can be overly conservative in this setting. As an alternative to multiple imputation, we derive an analytic expression of the treatment effect for the placebo-based pattern-mixture model and propose a posterior simulation or delta method for the inference about the treatment effect. Simulation studies demonstrate that the proposed methods provide consistent variance estimates and outperform the imputation methods in terms of power for the placebo-based pattern-mixture model. We illustrate the methods using data from a clinical study of major depressive disorders.

A Bayesian approach to joint analysis of multivariate longitudinal data and parametric accelerated failure time.

Impairment caused by Parkinson's disease (PD) is multidimensional (e.g., sensoria, functions, and cognition) and progressive. Its multidimensional nature precludes a single outcome to measure disease progression. Clinical trials of PD use multiple categorical and continuous longitudinal outcomes to assess the treatment effects on overall improvement. A terminal event such as death or dropout can stop the follow-up process. Moreover, the time to the terminal event may be dependent on the multivariate longitudinal measurements. In this article, we consider a joint random-effects model for the correlated outcomes. A multilevel item response theory model is used for the multivariate longitudinal outcomes and a parametric accelerated failure time model is used for the failure time because of the violation of proportional hazard assumption. These two models are linked via random effects. The Bayesian inference via MCMC is implemented in 'BUGS' language. Our proposed method is evaluated by a simulation study and is applied to DATATOP study, a motivating clinical trial to determine if deprenyl slows the progression of PD.

Methods for a longitudinal quantitative outcome with a multivariate Gaussian distribution multi-dimensionally censored by therapeutic intervention.

In longitudinal studies, a quantitative outcome (such as blood pressure) may be altered during follow-up by the administration of a non-randomized, non-trial intervention (such as anti-hypertensive medication) that may seriously bias the study results. Current methods mainly address this issue for cross-sectional studies. For longitudinal data, the current methods are either restricted to a specific longitudinal data structure or are valid only under special circumstances. We propose two new methods for estimation of covariate effects on the underlying (untreated) general longitudinal outcomes: a single imputation method employing a modified expectation-maximization (EM)-type algorithm and a multiple imputation (MI) method utilizing a modified Monte Carlo EM-MI algorithm. Each method can be implemented as one-step, two-step, and full-iteration algorithms. They combine the advantages of the current statistical methods while reducing their restrictive assumptions and generalizing them to realistic scenarios. The proposed methods replace intractable numerical integration of a multi-dimensionally censored MVN posterior distribution with a simplified, sufficiently accurate approximation. It is particularly attractive when outcomes reach a plateau after intervention due to various reasons. Methods are studied via simulation and applied to data from the Diabetes Control and Complications Trial/Epidemiology of Diabetes Interventions and Complications study of treatment for type 1 diabetes. Methods proved to be robust to high dimensions, large amounts of censored data, low within-subject correlation, and when subjects receive non-trial intervention to treat the underlying condition only (with high Y), or for treatment in the majority of subjects (with high Y) in combination with prevention for a small fraction of subjects (with normal Y).

Visualising and modelling changes in categorical variables in longitudinal studies.

BACKGROUND: Graphical techniques can provide visually compelling insights into complex data patterns. In this paper we present a type of lasagne plot showing changes in categorical variables for participants measured at regular intervals over time and propose statistical models to estimate distributions of marginal and transitional probabilities. METHODS: The plot uses stacked bars to show the distribution of categorical variables at each time interval, with different colours to depict different categories and changes in colours showing trajectories of participants over time. The models are based on nominal logistic regression which is appropriate for both ordinal and nominal categorical variables. To illustrate the plots and models we analyse data on smoking status, body mass index (BMI) and physical activity level from a longitudinal study on women's health. To estimate marginal distributions we fit survey wave as an explanatory variable whereas for transitional distributions we fit status of participants (e.g. smoking status) at previous surveys. RESULTS: For the illustrative data the marginal models showed BMI increasing, physical activity decreasing and smoking decreasing linearly over time at the population level. The plots and transition models showed smoking status to be highly predictable for individuals whereas BMI was only moderately predictable and physical activity was virtually unpredictable. Most of the predictive power was obtained from participant status at the previous survey. Predicted probabilities from the models mostly agreed with observed probabilities indicating adequate goodness-of-fit. CONCLUSIONS: The proposed form of lasagne plot provides a simple visual aid to show transitions in categorical variables over time in longitudinal studies. The suggested models complement the plot and allow formal testing and estimation of marginal and transitional distributions. These simple tools can provide valuable insights into categorical data on individuals measured at regular intervals over time.

Challenges and strategies for cohort retention and data collection in an indigenous population: Australian Aboriginal Birth Cohort.

BACKGROUND: Longitudinal prospective birth cohort studies are pivotal to identifying fundamental causes and determinants of disease and health over the life course. There is limited information about the challenges, retention, and collection strategies in the study of Indigenous populations. The aim is to describe the follow-up rates of an Australian Aboriginal Birth Cohort study and how they were achieved. METHODS: Participants were 686 babies enrolled between January 1987 and March 1990, born to a mother recorded in the Delivery Suite Register of the Royal Darwin Hospital (RDH) as a self-identified Aboriginal. The majority of the participants (70%) resided in Northern Territory within rural, remote and very remote Aboriginal communities that maintain traditional connections to their land and culture. The Aboriginal communities are within a sparsely populated (0.2 people/ km2) area of approximately 900,000 km² (347 sq miles), with poor communication and transport infrastructures. Follow-ups collecting biomedical and lifestyle data directly from participants in over 40 locations were conducted at 11.4 years (Wave-2) and 18.2 years (Wave-3), with Wave-4 follow-up currently underway. RESULTS: Follow-ups at 11 and 18 years of age successfully examined 86% and 72% of living participants respectively. Strategies addressing logistic, cultural and ethical challenges are documented. CONCLUSIONS: Satisfactory follow-up rates of a prospective longitudinal Indigenous birth cohort with traditional characteristics are possible while maintaining scientific rigor in a challenging setting. Approaches included flexibility, respect, and transparent communication along with the adoption of culturally sensitive behaviours. This work should inform and assist researchers undertaking or planning similar studies in Indigenous and developing populations.

A 15-year follow-up of first unprovoked seizures: a prospective study of 200 children.

Epilepsy is associated with an extended spectrum of behaviour, psychiatric problems, and learning difficulties. The aim of this study was to establish the natural history of children with first unprovoked seizures. We studied prospectively 200 children under the age of 11 years who attended hospital emergency with a first unprovoked seizure. Demographic variables, personal and family history, neurological examination, EEG, psychiatric, and cognitive and educational profiles were analysed. Patients who developed epilepsy were characterised with respect to: time to relapse, remission rate, duration of epilepsy, neuroimaging, aetiology, epileptic syndrome, and therapeutic regimen. These results were compared to data of patients who had a single seizure over a follow-up period of 15 years. Thirty percent of children who had a first unprovoked seizure developed epilepsy. Partial seizure type was a statistically significant variable for the development of epilepsy. An EEG with epileptic abnormalities proved to be the main risk factor for recurrence. Fifteen years later, the group with epilepsy exhibited a 2.6 greater risk of psychiatric and academic comorbidities, compared to the group without epilepsy.

Application of person-centered analytic methodology in longitudinal research: exemplars from the Women's Health Initiative Clinical Trial data.

Despite the variety of available analytic methods, longitudinal research in nursing has been dominated by use of a variable-centered analytic approach. The purpose of this article is to present the utility of person-centered methodology using a large cohort of American women 65 and older enrolled in the Women's Health Initiative Clinical Trial (N = 19,891). Four distinct trajectories of energy/fatigue scores were identified. Levels of fatigue were closely linked to age, socio-demographic factors, comorbidities, health behaviors, and poor sleep quality. These findings were consistent regardless of the methodological framework. Finally, we demonstrated that energy/fatigue levels predicted future hospitalization in non-disabled elderly. Person-centered methods provide unique opportunities to explore and statistically model the effects of longitudinal heterogeneity within a population.

On computing standard errors for marginal structural Cox models.

In recent decades, marginal structural models have gained popularity for proper adjustment of time-dependent confounders in longitudinal studies through time-dependent weighting. When the marginal model is a Cox model, using current standard statistical software packages was thought to be problematic because they were not developed to compute standard errors in the presence of time-dependent weights. We address this practical modelling issue by extending the standard calculations for Cox models with case weights to time-dependent weights and show that the coxph procedure in R can readily compute asymptotic robust standard errors. Through a simulation study, we show that the robust standard errors are rather conservative, though corresponding confidence intervals have good coverage. A second contribution of this paper is to introduce a Cox score bootstrap procedure to compute the standard errors. We show that this method is efficient and tends to outperform the non-parametric bootstrap in small samples.

The versatility of multi-state models for the analysis of longitudinal data with unobservable features.

Multi-state models provide a convenient statistical framework for a wide variety of medical applications characterized by multiple events and longitudinal data. We illustrate this through four examples. The potential value of the incorporation of unobserved or partially observed states is highlighted. In addition, joint modelling of multiple processes is illustrated with application to potentially informative loss to follow-up, mis-measured or missclassified data and causal inference.

Challenges and solutions during analysis in a longitudinal narrative case study.

AIM: To describe the challenges faced by those performing complex qualitative analysis during a narrative study and to offer solutions. BACKGROUND: Qualitative research requires rigorous analysis. However, novice researchers often struggle to identify appropriately robust analytical procedures that will move them from their transcripts to their final findings. The lack of clear and detailed accounts in the literature that consider narrative analysis and how to address some of the common challenges researchers face add to this problem. DATA SOURCES: A longitudinal narrative case study exploring the personal and familial changes reported by uninjured family members during the first year of another family member's traumatic brain injury. Review methods This is a methodological paper. DISCUSSION: The challenges of analysis included: conceptualising analysis; demonstrating the relationship between the different analytical layers and the final research findings; interpreting the data in a way that reflected the priorities of a narrative approach; and managing large quantities of data. The solutions explored were: the mapping of analytic intentions; aligning analysis and interpretation with the conceptual framework; and the use of matrices to store and manage quotes, codes and reflections. CONCLUSION: Working with qualitative data can be daunting for novice researchers. Ensuring rigorous, transparent, and auditable data analysis procedures can further constrain the interpretive aspect of analysis. Implications for research/practice The solutions offered in this paper should help novice researchers to manage and work with their data, assisting them to develop the confidence to be more intuitive and creative in their research.