Optimal design for epidemiological studies subject to designed missingness

Auxiliary variable-enriched biomarker-stratified design

Clinical trials in the era of precision medicine require assessment of biomarkers to identify appropriate subgroups of patients for targeted therapy. In a biomarker-stratified design (BSD), biomarkers are measured on all patients and used as stratification variables. However, such a trial can be both inefficient and costly, especially when the prevalence of the subgroup of primary interest is low and the cost of assessing the biomarkers is high. Efficiency can be improved and costs reduced by using enriched biomarker-stratified designs, in which patients of primary interest, typically the biomarker-positive patients, are oversampled. We consider a special type of enrichment design, an auxiliary variable-enriched design (AEBSD), in which enrichment is based on some inexpensive auxiliary variable that is positively correlated with the true biomarker. The proposed AEBSD reduces the total cost of the trial compared with a standard BSD when the prevalence rate of true biomarker positivity is small and the positive predictive value (PPV) of the auxiliary biomarker is larger than the prevalence rate. In addition, for an AEBSD, we can immediately randomize the patients selected in the screening process without waiting for the result of the true biomarker test, reducing the treatment waiting time. We propose an adaptive Bayesian method to adjust the assumed PPV while the trial is ongoing. Numerical studies and an example illustrate the approach. An R package is available.

Optimal design for longitudinal studies to estimate pubertal height growth in individuals

BACKGROUND

The SITAR model expresses individual pubertal height growth in terms of mean size, peak height velocity (PHV) and age at PHV.

AIM

To use SITAR to identify the optimal time interval between measurements to summarise individual pubertal height growth.

SUBJECTS AND METHODS

Heights in 3172 boys aged 9-19 years from Christ's Hospital School measured on 128 679 occasions (a median of 42 heights per boy) were analysed using the SITAR (SuperImposition by Translation And Rotation) mixed effects growth curve model, which estimates a mean curve and three subject-specific random effects. Separate models were fitted to sub-sets of the data with measurement intervals of 2, 3, 4, 6, 12 and 24 months, and the different models were compared.

RESULTS

The models for intervals 2-12 months gave effectively identical results for the residual standard deviation (0.8 cm), mean spline curve (6 degrees of freedom) and random effects (correlations >0.9), showing there is no benefit in measuring height more often than annually. The model for 2-year intervals fitted slightly less well, but needed just four-to-five measurements per individual.

CONCLUSIONS

Height during puberty needs to be measured only annually and, with slightly lower precision, just four biennial measurements can be sufficient.

On Enrichment Strategies for Biomarker Stratified Clinical Trials

In the era of precision medicine, drugs are increasingly developed to target subgroups of patients with certain biomarkers. In large all-comer trials using a biomarker stratified design, the cost of treating and following patients for clinical outcomes may be prohibitive. With a fixed number of randomized patients, the efficiency of testing certain treatments parameters, including the treatment effect among biomarker-positive patients and the interaction between treatment and biomarker, can be improved by increasing the proportion of biomarker positives on study, especially when the prevalence rate of biomarker positives is low in the underlying patient population. When the cost of assessing the true biomarker is prohibitive, one can further improve the study efficiency by oversampling biomarker positives with a cheaper auxiliary variable or a surrogate biomarker that correlates with the true biomarker. To improve efficiency and reduce cost, we can adopt an enrichment strategy for both scenarios by concentrating on testing and treating patient subgroups that contain more information about specific treatment parameters of primary interest to the investigators. In the first scenario, an enriched biomarker stratified design enriches the cohort of randomized patients by directly oversampling the relevant patients with the true biomarker, while in the second scenario, an auxiliary-variable-enriched biomarker stratified design enriches the randomized cohort based on an inexpensive auxiliary variable, thereby avoiding testing the true biomarker on all screened patients and reducing treatment waiting time. For both designs, we discuss how to choose the optimal enrichment proportion when testing a single hypothesis or two hypotheses simultaneously. At a requisite power, we compare the two new designs with the BSD design in terms of the number of randomized patients and the cost of trial under scenarios mimicking real biomarker stratified trials. The new designs are illustrated with hypothetical examples for designing biomarker-driven cancer trials.

Time-dependent classification accuracy curve under marker-dependent sampling

Evaluating the classification accuracy of a candidate biomarker signaling the onset of disease or disease status is essential for medical decision making. A good biomarker would accurately identify the patients who are likely to progress or die at a particular time in the future or who are in urgent need for active treatments. To assess the performance of a candidate biomarker, the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) are commonly used. In many cases, the standard simple random sampling (SRS) design used for biomarker validation studies is costly and inefficient. In order to improve the efficiency and reduce the cost of biomarker validation, marker-dependent sampling (MDS) may be used. In a MDS design, the selection of patients to assess true survival time is dependent on the result of a biomarker assay. In this article, we introduce a nonparametric estimator for time-dependent AUC under a MDS design. The consistency and the asymptotic normality of the proposed estimator is established. Simulation shows the unbiasedness of the proposed estimator and a significant efficiency gain of the MDS design over the SRS design.

Statistical Design Features of the Healthy Communities Study

The Healthy Communities Study is designed to assess relationships between characteristics of community programs and policies targeting childhood obesity and children's BMI, diet, and physical activity. The study involved a complex data collection protocol implemented over a 2-year period (2013-2015) across a diverse sample of 130 communities, defined as public high school catchment areas. The protocol involved baseline assessment within each community that included in-person or telephone interviews regarding community programs and policies and in-home collection of BMI, nutritional, and physical activity outcomes from a sample of up to 81 children enrolled in kindergarten through eighth grade in public schools. The protocol also involved medical record reviews to establish a longitudinal trajectory of BMI for an estimated 70% of participating children. Staged sampling was used to collect less detailed measures of physical activity and nutrition across the entire sample of children, with a subset assessed using more costly, burdensome, and detailed measures. Data from the Healthy Community Study will be analyzed using both cross-sectional and longitudinal models that account for the complex design and correct for measurement error and bias using a likelihood-based Markov-chain Monte Carlo methodology. This methods paper provides insights into the complex design features of the Healthy Communities Study and may serve as an example for future large-scale studies that assess the relationship between community-based programs and policies and health outcomes of community residents.

Item selection via Bayesian IRT models

With reference to a questionnaire that aimed to assess the quality of life for dysarthric speakers, we investigate the usefulness of a model-based procedure for reducing the number of items. We propose a mixed cumulative logit model, which is known in the psychometrics literature as the graded response model: responses to different items are modelled as a function of individual latent traits and as a function of item characteristics, such as their difficulty and their discrimination power. We jointly model the discrimination and the difficulty parameters by using a k-component mixture of normal distributions. Mixture components correspond to disjoint groups of items. Items that belong to the same groups can be considered equivalent in terms of both difficulty and discrimination power. According to decision criteria, we select a subset of items such that the reduced questionnaire is able to provide the same information that the complete questionnaire provides. The model is estimated by using a Bayesian approach, and the choice of the number of mixture components is justified according to information criteria. We illustrate the proposed approach on the basis of data that are collected for 104 dysarthric patients by local health authorities in Lecce and in Milan.

Improving cost-effectiveness of epidemiological studies via designed missingness strategies

Modern epidemiological studies face opportunities and challenges posed by an ever-expanding capacity to measure a wide range of environmental exposures, along with sophisticated biomarkers of exposure and response at the individual level. The challenge of deciding what to measure is further complicated for longitudinal studies, where logistical and cost constraints preclude the collection of all possible measurements on all participants at every follow-up time. This is true for the National Children's Study (NCS), a large-scale longitudinal study that will enroll women both prior to conception and during pregnancy and collect information on their environment, their pregnancies, and their children's development through early adulthood-with a goal of assessing key exposure/outcome relationships among a cohort of approximately 100 000 children. The success of the NCS will significantly depend on the accurate, yet cost-effective, characterization of environmental exposures thought to be related to the health outcomes of interest. The purpose of this paper is to explore the use of cost saving, yet valid and adequately powered statistical approaches for gathering exposure information within epidemiological cohort studies. The proposed approach involves the collection of detailed exposure assessment information on a specially selected subset of the study population, and collection of less-costly, and presumably less-detailed and less-burdensome, surrogate measures across the entire cohort. We show that large-scale efficiency in costs and burden may be achieved without making substantive sacrifices on the ability to draw reliable inferences concerning the relationship between exposure and health outcome. Several detailed scenarios are provided that document how the targeted sub-sampling design strategy can benefit large cohort studies like the NCS, as well as other more focused environmental epidemiologic studies.