ABSTRACT Large observational datasets, including those derived from electronic health records, are a valuable resource for medical research but are often affected by missingness, measurement error, and misclassification. Two‐phase sampling with generalized raking (GR) estimation is an efficient and robust approach to statistical inference in such settings. In this approach, variables that are unavailable or measured with error in a large Phase 1 cohort are obtained with higher‐quality measurements in a Phase 2 subsample. Previous research has studied optimal Phase 2 sampling designs for inverse‐probability‐weighted (IPW) estimators in nonadaptive, multiparameter settings, and for GR estimators in single‐parameter settings. In this work, we extend these results by deriving optimal adaptive, multiwave sampling designs for IPW and GR estimators when multiple parameters are of interest. We propose several practical allocation strategies, examine the design choices that arise when implementing them, and evaluate their performance through extensive simulations and an example using data from people living with HIV attending the Vanderbilt Comprehensive Care Clinic (VCCC). Our results show that independently optimizing allocation for each parameter improves efficiency over traditional case‐control sampling. We also derive an integer‐valued, A‐optimal allocation method that typically outperforms independent optimization. Notably, we find that optimal designs for GR can differ substantially from those for IPW, and that this distinction can meaningfully affect estimator efficiency in the multiple‐parameter setting. These findings offer practical guidance for future two‐phase studies involving incomplete or error‐prone data.
ABSTRACT Statistical prediction models for binary outcomes are becoming increasingly popular. One significant challenge is calibrating these models to suit the characteristics of a target population that is structurally different from the original population. Calibration is especially challenging when there is no training data available from the target population. To address this problem, we propose a novel calibration method, SimCal, which uses synthetic data generated from the model development data in conjunction with marginal statistics from the calibration cohort. We show that expert judgment modeling (EJM) may be used for calibration if cross‐sectional data from the target population are available comprising expert judgments about the potential outcome and the covariates. We describe three alternative calibration approaches when calibration data are lacking: similarity‐binning averaging (SBA), adaptive calibration of predictions (ACP), and Elkan calibration. In a simulation study, we compare SBA, ACP, Elkan calibration, and SimCal. R code for applying these methods is provided from the re‐analysis of data on coronary artery disease. We illustrate all 5 calibration approaches with a real data set for predicting functional outcome after stroke and all approaches but EJM in the re‐analysis of the Cleveland Clinic data. None of the approaches performed convincingly well in all situations. SimCal performed well when model parameters were correctly specified. EJM failed on the stroke data. Further research is urgently required for calibration in the absence of calibration data.
ABSTRACT Time‐to‐event analyses on individual patient data are commonly performed with Cox or Poisson regression. The statistical power of epidemiological findings from such analyses is often sufficient when a large amount of data is analyzed, especially when studying rare outcomes or rare exposures. The increase of sample size can be achieved by co‐analyzing data collected from different cohorts and hosted at different locations. For co‐analyzing data located at different centers, the common options are either (i) to physically transfer and pool the data into a single dataset and analyze them jointly or (ii) to conduct a two‐step meta‐analysis where a separate analysis is done at each center and the center‐specific results are then pooled and combined into a single estimate. DataSHIELD offers a third option where individual patient data from different locations are analyzed in a federated manner without transporting any data. In this paper, we describe how a federated Poisson regression can be conducted on time‐to‐event data using this infrastructure, providing relevant estimates.
ABSTRACT Mendelian randomization (MR) studies increasingly rely on summary statistics from genome‐wide association studies (GWASs). However, current summary‐data methods treat marginal GWAS effect estimates as independent across instrumental single‐nucleotide polymorphisms (SNPs), which holds only when the SNPs have no effect. Without imposing this independence assumption, we derive expressions for the two‐stage least squares (TSLS), two‐sample TSLS (TSTSLS), and generalized method‐of‐moments estimators together with their variance estimators using only GWAS summary statistics, assuming the instrumental SNPs are in linkage equilibrium. We show that the widely used inverse‐variance weighted (IVW) estimator is generally not equivalent to either TSLS or TSTSLS, contrary to a common claim in the MR literature. We further demonstrate that the conventional IVW standard error is generally inconsistent and provide a consistent alternative. Extensive simulations confirm the theoretical results and reveal that Wald confidence intervals based on summary statistics can be anti‐conservative. An application to publicly available GWAS summary statistics on body mass index and systolic blood pressure illustrates the practical implications of the proposed methodology.
ABSTRACT In the absence of censoring, locally estimated scatterplot smoothing (LOESS) is a powerful tool to estimate the relationship between a continuous covariate and the probability of an event and is often used to visually assess calibration of prognostic models. Since follow‐up in prognostic studies is often incomplete, we aimed to study the extension of LOESS to right‐censored data. In line with other work, we first obtained inverse‐probability‐of‐censoring (IPC) weights through Kaplan–Meier estimation. When censoring varied by covariate levels, we used Cox regression with a spline function of the covariate to obtain IPC weights. We then applied LOESS to the weighted event indicators to estimate the relationship between the covariate and the probability of an event within a specific time horizon. We illustrated the application of LOESS for censored data (LOESScd) using patients with complex coronary artery disease. We used the LOESScd to estimate the association between continuous predictors and the probability of death within 10 years. LOESScd estimates closely followed grouped Kaplan–Meier estimates, especially in case of weak smoothing. Covariate‐dependent IPC weights improved LOESScd when censoring varied by covariate levels. We then examined the finite‐sample behavior of LOESScd in simulations motivated by four typical prognostic model validation scenarios. In 2000 samples of 1800 patients, bias was limited and coverage was close to nominal. In conclusion, LOESScd is a promising estimator of the relationship of a continuous covariate with the probability of an event in the presence of right‐censoring. LOESScd is especially useful for estimating calibration curves when validating prognostic models.
