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Abstract Background The aggregation of a series of N-of-1 trials presents an innovative and efficient study design, as an alternative to traditional randomized clinical trials. Challenges for the statistical analysis arise when there is carry-over or complex dependencies of the treatment effect of interest. Methods In this study, we evaluate and compare methods for the analysis of aggregated N-of-1 trials in different scenarios with carry-over and complex dependencies of treatment effects on covariates. For this, we simulate data of a series of N-of-1 trials for Chronic Nonspecific Low Back Pain based on assumed causal relationships parameterized by directed acyclic graphs. In addition to existing statistical methods such as regression models, Bayesian Networks, and G-estimation, we introduce a carry-over adjusted parametric model (COAPM). Results The results show that all evaluated existing models have a good performance when there is no carry-over and no treatment dependence. When there is carry-over, COAPM yields unbiased and more efficient estimates while all other methods show some bias in the estimation. When there is known treatment dependence, all approaches that are capable to model it yield unbiased estimates. Finally, the efficiency of all methods decreases slightly when there are missing values, and the bias in the estimates can also increase. Conclusions This study presents a systematic evaluation of existing and novel approaches for the statistical analysis of a series of N-of-1 trials. We derive practical recommendations which methods may be best in which scenarios.

Abstract Background Machine learning models promise to support diagnostic predictions, but may not perform well in new settings. Selecting the best model for a new setting without available data is challenging. We aimed to investigate the transportability by calibration and discrimination of prediction models for cognitive impairment in simulated external settings with different distributions of demographic and clinical characteristics. Methods We mapped and quantified relationships between variables associated with cognitive impairment using causal graphs, structural equation models, and data from the ADNI study. These estimates were then used to generate datasets and evaluate prediction models with different sets of predictors. We measured transportability to external settings under guided interventions on age, APOE ε4, and tau-protein, using performance differences between internal and external settings measured by calibration metrics and area under the receiver operating curve (AUC). Results Calibration differences indicated that models predicting with causes of the outcome were more transportable than those predicting with consequences. AUC differences indicated inconsistent trends of transportability between the different external settings. Models predicting with consequences tended to show higher AUC in the external settings compared to internal settings, while models predicting with parents or all variables showed similar AUC. Conclusions We demonstrated with a practical prediction task example that predicting with causes of the outcome results in better transportability compared to anti-causal predictions when considering calibration differences. We conclude that calibration performance is crucial when assessing model transportability to external settings.

Abstract Background In epidemiology, causal inference and prediction modeling methodologies have been historically distinct. Directed Acyclic Graphs (DAGs) are used to model a priori causal assumptions and inform variable selection strategies for causal questions. Although tools originally designed for prediction are finding applications in causal inference, the counterpart has remained largely unexplored. The aim of this theoretical and simulation-based study is to assess the potential benefit of using DAGs in clinical risk prediction modeling. Methods We explore how incorporating knowledge about the underlying causal structure can provide insights about the transportability of diagnostic clinical risk prediction models to different settings. We further probe whether causal knowledge can be used to improve predictor selection in clinical risk prediction models. Results A single-predictor model in the causal direction is likely to have better transportability than one in the anticausal direction in some scenarios. We empirically show that the Markov Blanket, the set of variables including the parents, children, and parents of the children of the outcome node in a DAG, is the optimal set of predictors for that outcome. Conclusions Our findings provide a theoretical basis for the intuition that a diagnostic clinical risk prediction model including causes as predictors is likely to be more transportable. Furthermore, using DAGs to identify Markov Blanket variables may be a useful, efficient strategy to select predictors in clinical risk prediction models if strong knowledge of the underlying causal structure exists or can be learned.