Effective sample size: A measure of individual uncertainty in predictions.

Clinical prediction models are estimated using a sample of limited size from the target population, leading to uncertainty in predictions, even when the model is correctly specified. Generally, not all patient profiles are observed uniformly in model development. As a result, sampling uncertainty varies between individual patients' predictions.

Landmarking 2.0: Bridging the gap between joint models and landmarking.

The problem of dynamic prediction with time-dependent covariates, given by biomarkers, repeatedly measured over time, has received much attention over the last decades. Two contrasting approaches have become in widespread use. The first is joint modeling, which attempts to jointly model the longitudinal markers and the event time.

Analysis of time-to-event for observational studies: Guidance to the use of intensity models.

This paper provides guidance for researchers with some mathematical background on the conduct of time-to-event analysis in observational studies based on intensity (hazard) models. Discussions of basic concepts like time axis, event definition and censoring are given. Hazard models are introduced, with special emphasis on the Cox proportional hazards regression model.

Prediction meets causal inference: the role of treatment in clinical prediction models.

In this paper we study approaches for dealing with treatment when developing a clinical prediction model. Analogous to the estimand framework recently proposed by the European Medicines Agency for clinical trials, we propose a 'predictimand' framework of different questions that may be of interest when predicting risk in relation to treatment started after baseline. We provide a formal definition of the estimands matching these questions, give examples of settings in which each is useful and discuss appropriate estimators including their assumptions.

On the relation between the cause-specific hazard and the subdistribution rate for competing risks data: The Fine-Gray model revisited.

The Fine-Gray proportional subdistribution hazards model has been puzzling many people since its introduction. The main reason for the uneasy feeling is that the approach considers individuals still at risk for an event of cause 1 after they fell victim to the competing risk of cause 2. The subdistribution hazard and the extended risk sets, where subjects who failed of the competing risk remain in the risk set, are generally perceived as unnatural .

Assessment of heterogeneity in an individual participant data meta-analysis of prediction models: An overview and illustration.

Clinical prediction models aim to provide estimates of absolute risk for a diagnostic or prognostic endpoint. Such models may be derived from data from various studies in the context of a meta-analysis. We describe and propose approaches for assessing heterogeneity in predictor effects and predictions arising from models based on data from different sources.

Understanding Landmarking and Its Relation with Time-Dependent Cox Regression.

Time-dependent Cox regression and landmarking are the two most commonly used approaches for the analysis of time-dependent covariates in time-to-event data. The estimated effect of the time-dependent covariate in a landmarking analysis is based on the value of the time-dependent covariate at the landmark time point, after which the time-dependent covariate may change value. In this note we derive expressions for the (time-varying) regression coefficient of the time-dependent covariate in the landmark analysis, in terms of the regression coefficient and baseline hazard of the time-dependent Cox regression.

Testing interaction between treatment and high-dimensional covariates in randomized clinical trials.

In this paper, we considered different methods to test the interaction between treatment and a potentially large number (p) of covariates in randomized clinical trials. The simplest approach was to fit univariate (marginal) models and to combine the univariate statistics or p-values (e.g.

Dynamic frailty models based on compound birth-death processes.

Frailty models are used in survival analysis to model unobserved heterogeneity. They accommodate such heterogeneity by the inclusion of a random term, the frailty, which is assumed to multiply the hazard of a subject (individual frailty) or the hazards of all subjects in a cluster (shared frailty). Typically, the frailty term is assumed to be constant over time.

The role of empirical Bayes methodology as a leading principle in modern medical statistics.

This paper reviews and discusses the role of Empirical Bayes methodology in medical statistics in the last 50 years. It gives some background on the origin of the empirical Bayes approach and its link with the famous Stein estimator. The paper describes the application in four important areas in medical statistics: disease mapping, health care monitoring, meta-analysis, and multiple testing.

From model building to validation and back: a plea for robustness.

This paper is the written version of the President's invited lecture speaker at the International Society for Clinical Biostatistics conference in Munich in 2013. The paper takes the stand of clinician and patient who are in need of a reliable prognostic model for the planning of treatment and patient care during the follow-up after the initial treatment. The paper discusses (i) the need for grouping of data; (ii) the lack of robustness of the Cox model; (iii) the robust approach to repeated measures; and (iv) the robust handling of time-dependent covariates (biomarkers) in dynamic survival analysis.

Comparison of stopped Cox regression with direct methods such as pseudo-values and binomial regression.

By far the most popular model to obtain survival predictions for individual patients is the Cox model. The Cox model does not make any assumptions on the underlying hazard, but it relies heavily on the proportional hazards assumption. The most common ways to circumvent this robustness problem are 1) to categorize patients based on their prognostic risk score and to base predictions on Kaplan-Meier curves for the risk categories, or 2) to include interactions with the covariates and suitable functions of time.

Validation, calibration and refitting of a familial breast cancer model in sisterships: a case study in the Swedish sisters data.

In Sweden, a unique data set has been compiled with breast cancer incidence in all sisterships with at least two sisters born between 1932 and 2001, and the effect of family history has been analyzed by standard epidemiological methods. Such data are ideal to explore the validity of existing models for familial breast cancer. This paper explores the validity of the Jonker model that adds a hypothetical gene to the well-known BRCA1 and BRCA2 genes.

Frailties in multi-state models: Are they identifiable? Do we need them?

The inclusion of latent frailties in survival models can serve two purposes: (1) the modelling of dependence in clustered data, (2) explaining lack of fit of univariate survival models, like deviation from the proportional hazards assumption. Multi-state models are somewhere between univariate data and clustered data. Frailty models can help in understanding the dependence in sequential transitions (like in clustered data) and can be useful in explaining some strange phenomena in the effect of covariates in competing risks models (like in univariate data).

Modelling the effect of baseline risk in meta-analysis: a review from the perspective of errors-in-variables regression.

In meta-analysis of clinical trials, investigating the relationship between the baseline risk and the treatment benefit is often of interest in order to explain the between trials heterogeneity with respect to treatment effect. The relationship is commonly described with a linear model taking into account the fact that the latent baseline risk is estimated from a finite sample and thus subjected to measurement error. Depending on the specific assumption about the latent baseline risks, two different classes of methods can be pursued.

Sensitivity analysis of state-transition models: how to deal with a large number of inputs.

State-transition models are employed to project future prevalence rates of risk factors and diseases within populations. Sensitivity analysis should be performed to assess the reliability of the results but often the number of inputs of the model is so huge, and running the model is so time-consuming, that not all methods of sensitivity analysis are practically available. Screening methods detect which inputs have a major influence on the outputs.

Denial and social and emotional outcomes in lung cancer patients: the protective effect of denial.

Denial is a well-known phenomenon in clinical oncology practice. Yet whether the impact of denial on patient well-being is beneficial or harmful remains unknown. The purpose of the current study is to investigate the relationship between denial and social and emotional outcomes in a large sample of lung cancer patients over an extended time period.

Interleukin-9 polymorphism in infants with respiratory syncytial virus infection: an opposite effect in boys and girls.

The predominance of severe respiratory syncytial virus (RSV) bronchiolitis in boys compared to girls is well known, but its mechanism is not yet understood. This is the first study focusing on gender-specific genetic factors affecting the risk of severe RSV infection using a previously described cohort. We determined 347 single-nucleotide polymorphisms (SNPs) in 470 children hospitalized for RSV infection, their parents, and 1,008 random population controls.

Dealing with heterogeneity between cohorts in genomewide SNP association studies.

In Genomewide association (GWA) studies investigating thousands of SNPs, large sample sizes are needed to obtain a reasonable power after correction for multiple testing. To obtain the necessary sample sizes, data from different populations/cohorts are combined. The problem of pooling evidence across cohorts bears some resemblance with meta-analysis of clinical trials, and in fact classical meta-analytic methodologies from that field are typically used in GWAs.

Vertical modeling: a pattern mixture approach for competing risks modeling.

We study an alternative approach for estimation in the competing risks framework, called vertical modeling. It is motivated by a decomposition of the joint distribution of time and cause of failure. The two elements of this decomposition are (1) the time of failure and (2) the cause of failure condition on time of failure.

Integration of gene ontology pathways with North American Rheumatoid Arthritis Consortium genome-wide association data via linear modeling.

We describe an empirical Bayesian linear model for integration of functional gene annotation data with genome-wide association data. Using case-control study data from the North American Rheumatoid Arthritis Consortium and gene annotation data from the Gene Ontology, we illustrate how the method can be used to prioritize candidate genes for further investigation.

Multivariate random effects meta-analysis of diagnostic tests with multiple thresholds.

Background: Bivariate random effects meta-analysis of diagnostic tests is becoming a well established approach when studies present one two-by-two table or one pair of sensitivity and specificity. When studies present multiple thresholds for test positivity, usually meta-analysts reduce the data to a two-by-two table or take one threshold value at a time and apply the well developed meta-analytic approaches. However, this approach does not fully exploit the data.