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Sample size and power determination in joint modeling of longitudinal and survival data.

ABSTRACT: Owing to the rapid development of biomarkers in clinical trials, joint modeling of longitudinal and survival data has gained its popularity in the recent years because it reduces bias and provides improvements of efficiency in the assessment of treatment effects and other prognostic factors. Although much effort has been put into inferential methods in joint modeling, such as estimation and hypothesis testing, design aspects have not been formally considered. Statistical design, such as sample size and power calculations, is a crucial first step in clinical trials. In this paper, we derive a closed-form sample size formula for estimating the effect of the longitudinal process in joint modeling, and extend Schoenfeld's sample size formula to the joint modeling setting for estimating the overall treatment effect. The sample size formula we develop is quite general, allowing for p-degree polynomial trajectories. The robustness of our model is demonstrated in simulation studies with linear and quadratic trajectories. We discuss the impact of the within-subject variability on power and data collection strategies, such as spacing and frequency of repeated measurements, in order to maximize the power. When the within-subject variability is large, different data collection strategies can influence the power of the study in a significant way. Optimal frequency of repeated measurements also depends on the nature of the trajectory with higher polynomial trajectories and larger measurement error requiring more frequent measurements.

SUBMITTER: Chen LM

PROVIDER: S-EPMC3278672 | biostudies-other | 2011 Aug

REPOSITORIES: biostudies-other

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Sample size and power determination in joint modeling of longitudinal and survival data.

Chen Liddy M LM Ibrahim Joseph G JG Chu Haitao H

Statistics in medicine 20110517 18

Owing to the rapid development of biomarkers in clinical trials, joint modeling of longitudinal and survival data has gained its popularity in the recent years because it reduces bias and provides improvements of efficiency in the assessment of treatment effects and other prognostic factors. Although much effort has been put into inferential methods in joint modeling, such as estimation and hypothesis testing, design aspects have not been formally considered. Statistical design, such as sample s ...[more]

PMID: 21590793

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Project description:BACKGROUND:Joint modeling is appropriate when one wants to predict the time to an event with covariates that are measured longitudinally and are related to the event. An underlying random effects structure links the survival and longitudinal submodels and allows for individual-specific predictions. Multiple time-varying and time-invariant covariates can be included to potentially increase prediction accuracy. The goal of this study was to estimate a multivariate joint model on several longitudinal observational studies of Huntington's disease, examine external validity performance, and compute individual-specific predictions for characterizing disease progression. Emphasis was on the survival submodel for predicting the hazard of motor diagnosis. METHODS:Data from four observational studies was analyzed: Enroll-HD, PREDICT-HD, REGISTRY, and Track-HD. A Bayesian approach to estimation was adopted, and external validation was performed using a time-varying AUC measure. Individual-specific cumulative hazard predictions were computed based on a simulation approach. The cumulative hazard was used for computing predicted age of motor onset and also for a deviance residual indicating the discrepancy between observed diagnosis status and model-based status. RESULTS:The joint model trained in a single study had very good performance in discriminating among diagnosed and pre-diagnosed participants in the remaining test studies, with the 5-year mean AUC?=?.83 (range .77-.90), and the 10-year mean AUC?=?.86 (range .82-.92). Graphical analysis of the predicted age of motor diagnosis showed an expected strong relationship with the trinucleotide expansion that causes Huntington's disease. Graphical analysis of the deviance-type residual revealed there were individuals who converted to a diagnosis despite having relatively low model-based risk, others who had not yet converted despite having relatively high risk, and the majority falling between the two extremes. CONCLUSIONS:Joint modeling is an improvement over traditional survival modeling because it considers all the longitudinal observations of covariates that are predictive of an event. Predictions from joint models can have greater accuracy because they are tailored to account for individual variability. These predictions can provide relatively accurate characterizations of individual disease progression, which might be important in the timing of interventions, determining the qualification for appropriate clinical trials, and general genotypic analysis.

Project description:BackgroundWith the increasing number of expression profiling technologies, researchers today are confronted with choosing the technology that has sufficient power with minimal sample size, in order to reduce cost and time. These depend on data variability, partly determined by sample type, preparation and processing. Objective measures that help experimental design, given own pilot data, are thus fundamental.ResultsRelative power and sample size analysis were performed on two distinct data sets. The first set consisted of Affymetrix array data derived from a nutrigenomics experiment in which weak, intermediate and strong PPARalpha agonists were administered to wild-type and PPARalpha-null mice. Our analysis confirms the hierarchy of PPARalpha-activating compounds previously reported and the general idea that larger effect sizes positively contribute to the average power of the experiment. A simulation experiment was performed that mimicked the effect sizes seen in the first data set. The relative power was predicted but the estimates were slightly conservative. The second, more challenging, data set describes a microarray platform comparison study using hippocampal deltaC-doublecortin-like kinase transgenic mice that were compared to wild-type mice, which was combined with results from Solexa/Illumina deep sequencing runs. As expected, the choice of technology greatly influences the performance of the experiment. Solexa/Illumina deep sequencing has the highest overall power followed by the microarray platforms Agilent and Affymetrix. Interestingly, Solexa/Illumina deep sequencing displays comparable power across all intensity ranges, in contrast with microarray platforms that have decreased power in the low intensity range due to background noise. This means that deep sequencing technology is especially more powerful in detecting differences in the low intensity range, compared to microarray platforms.ConclusionPower and sample size analysis based on pilot data give valuable information on the performance of the experiment and can thereby guide further decisions on experimental design. Solexa/Illumina deep sequencing is the technology of choice if interest lies in genes expressed in the low-intensity range. Researchers can get guidance on experimental design using our approach on their own pilot data implemented as a BioConductor package, SSPA http://bioconductor.org/packages/release/bioc/html/SSPA.html.

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Sample size and power determination in joint modeling of longitudinal and survival data.

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Sample size and power determination in joint modeling of longitudinal and survival data.

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