Optimal designs to select individuals for genotyping conditional on observed binary or survival outcomes and non-genetic covariates

Two-phase sample selection strategies for design and analysis in post-genome-wide association fine-mapping studies

Post-GWAS analysis, in many cases, focuses on fine-mapping targeted genetic regions discovered at GWAS-stage; that is, the aim is to pinpoint potential causal variants and susceptibility genes for complex traits and disease outcomes using next-generation sequencing (NGS) technologies. Large-scale GWAS cohorts are necessary to identify target regions given the typically modest genetic effect sizes. In this context, two-phase sampling design and analysis is a cost-reduction technique that utilizes data collected during phase 1 GWAS to select an informative subsample for phase 2 sequencing. The main goal is to make inference for genetic variants measured via NGS by efficiently combining data from phases 1 and 2. We propose two approaches for selecting a phase 2 design under a budget constraint. The first method identifies sampling fractions that select a phase 2 design yielding an asymptotic variance covariance matrix with certain optimal characteristics, for example, smallest trace, via Lagrange multipliers (LM). The second relies on a genetic algorithm (GA) with a defined fitness function to identify exactly a phase 2 subsample. We perform comprehensive simulation studies to evaluate the empirical properties of the proposed designs for a genetic association study of a quantitative trait. We compare our methods against two ranked designs: residual-dependent sampling and a recently identified optimal design. Our findings demonstrate that the proposed designs, GA in particular, can render competitive power in combined phase 1 and 2 analysis compared with alternative designs while preserving type 1 error control. These results are especially evident under the more practical scenario where design values need to be defined a priori and are subject to misspecification. We illustrate the proposed methods in a study of triglyceride levels in the North Finland Birth Cohort of 1966. R code to reproduce our results is available at github.com/egosv/TwoPhase_postGWAS.

Principles of Experimental Design for Big Data Analysis

Big Datasets are endemic, but are often notoriously difficult to analyse because of their size, heterogeneity and quality. The purpose of this paper is to open a discourse on the potential for modern decision theoretic optimal experimental design methods, which by their very nature have traditionally been applied prospectively, to improve the analysis of Big Data through retrospective designed sampling in order to answer particular questions of interest. By appealing to a range of examples, it is suggested that this perspective on Big Data modelling and analysis has the potential for wide generality and advantageous inferential and computational properties. We highlight current hurdles and open research questions surrounding efficient computational optimisation in using retrospective designs, and in part this paper is a call to the optimisation and experimental design communities to work together in the field of Big Data analysis.

How many longitudinal covariate measurements are needed for risk prediction?

OBJECTIVE

In epidemiologic follow-up studies, many key covariates, such as smoking, use of medication, blood pressure, and cholesterol, are time varying. Because of practical and financial limitations, time-varying covariates cannot be measured continuously, but only at certain prespecified time points. We study how the number of these longitudinal measurements can be chosen cost-efficiently by evaluating the usefulness of the measurements for risk prediction.

STUDY DESIGN AND SETTING

The usefulness is addressed by measuring the improvement in model discrimination between models using different amounts of longitudinal information. We use simulated follow-up data and the data from the Finnish East-West study, a follow-up study, with eight longitudinal covariate measurements carried out between 1959 and 1999.

RESULTS

In a simulation study, we show how the variability and the hazard ratio of a time-varying covariate are connected to the importance of remeasurements. In the East-West study, it is seen that for older people, the risk predictions obtained using only every other measurement are almost equivalent to the predictions obtained using all eight measurements.

CONCLUSION

Decisions about the study design have significant effects on the costs. The cost-efficiency can be improved by applying the measures of model discrimination to data from previous studies and simulations.

Optimal selection of individuals for repeated covariate measurements in follow-up studies

Repeated covariate measurements bring important information on the time-varying risk factors in long epidemiological follow-up studies. However, due to budget limitations, it may be possible to carry out the repeated measurements only for a subset of the cohort. We study cost-efficient alternatives for the simple random sampling in the selection of the individuals to be remeasured. The proposed selection criteria are based on forms of the D-optimality. The selection methods are compared with the simulation studies and illustrated with the data from the East-West study carried out in Finland from 1959 to 1999. The results indicate that cost savings can be achieved if the selection is focused on the individuals with high expected risk of the event and, on the other hand, on those with extreme covariate values in the previous measurements.

The value of reusing prior nested case-control data in new studies with different outcome

Many epidemiological studies use a nested case-control (NCC) design to reduce cost while maintaining study power. However, because of the incidence density sampling used, reusing data from NCC studies for analysis of secondary outcomes is not straightforward. Recent methodological developments have opened the possibility for prior NCC data to be used to complement controls in a current study, thereby improving study efficiency. However, practical guidelines on the effectiveness of prior data relative to newly sampled subjects and the potential power gains are still lacking. Using simulated cohorts, we show in this paper how the efficiency of NCC studies that use a mixture of prior and newly sampled subjects depends on the number of newly sampled controls and prior subjects as well as the overlap in the distributions of the matching variables. We explore the feasibility and efficiency of a current study that gathers no controls, relying instead on prior data. Using the concept of effective number of controls, we show how researchers can assess the potential power gains from reusing prior data. We apply the method to analyses of anorexia and contralateral breast cancer in the Swedish population and show how power calculations can be done using publicly available software. This work has important applications in genetic and molecular epidemiology to make optimal use of costly exposure measurements.

Optimal designs for epidemiologic longitudinal studies with binary outcomes

Alternating presence and absence of a medical condition in human subjects is often modelled as an outcome of underlying process dynamics. Longitudinal studies provide important insights into research questions involving such dynamics. This article concerns optimal designs for studies in which the dynamics are modelled as a binary continuous-time Markov process. Either one or both the transition rate parameters in the model are to be estimated with maximum precision from a sequence of observations made at discrete times on a number of subjects. The design questions concern the choice of time interval between observations, the initial state of each subject and the choice between number of subjects versus repeated observations per subject. Sequential designs are considered due to dependence of the designs on the model parameters. The optimal time spacing can be approximated by the reciprocal of the sum of the two rates. The initial distribution of the study subjects should be taken into account when relatively few repeated samples per subject are to be collected. A study with a reasonably large size should be designed in more than one phase because there are then enough observations to be spent in the first phase to revise the time spacing for the subsequent phases.