The propensity score is the probability of treatment assignment conditional on observed baseline characteristics. The propensity score allows one to design and analyze an observational (nonrandomized) study so that it mimics some of the particular characteristics of a randomized controlled trial. In particular, the propensity score is a balancing score: conditional on the propensity score, the distribution of observed baseline covariates will be similar between treated and untreated subjects. I describe 4 different propensity score methods: matching on the propensity score, stratification on the propensity score, inverse probability of treatment weighting using the propensity score, and covariate adjustment using the propensity score. I describe balance diagnostics for examining whether the propensity score model has been adequately specified. Furthermore, I discuss differences between regression-based methods and propensity score-based methods for the analysis of observational data. I describe different causal average treatment effects and their relationship with propensity score analyses.

https://www.tandfonline.com/doi/pdf/10.1080/00273171.2011.568786

An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies

General Strategies.- Regression Models.- Classification Models.- Other Considerations.- Appendix.- References.- Indices.

Applied Predictive Modeling

The TRIPOD (Transparent Reporting of a multivariable prediction model for Individual Prognosis Or Diagnosis) Statement includes a 22-item checklist, which aims to improve the reporting of studies developing, validating, or updating a prediction model, whether for diagnostic or prognostic purposes. The TRIPOD Statement aims to improve the transparency of the reporting of a prediction model study regardless of the study methods used. This explanation and elaboration document describes the rationale; clarifies the meaning of each item; and discusses why transparent reporting is important, with a view to assessing risk of bias and clinical usefulness of the prediction model. Each checklist item of the TRIPOD Statement is explained in detail and accompanied by published examples of good reporting. The document also provides a valuable reference of issues to consider when designing, conducting, and analyzing prediction model studies. To aid the editorial process and help peer reviewers and, ultimately, readers and systematic reviewers of prediction model studies, it is recommended that authors include a completed checklist in their submission. The TRIPOD checklist can also be downloaded from www.tripod-statement.org.

/pdf/transparent-reporting-of-a-multivariable-prediction-model-3n8wy14hp9.pdf

Transparent Reporting of a multivariable prediction model for Individual Prognosis or Diagnosis (TRIPOD): explanation and elaboration.

The performance of prediction models can be assessed using a variety of methods and metrics. Traditional measures for binary and survival outcomes include the Brier score to indicate overall model performance, the concordance (or c) statistic for discriminative ability (or area under the receiver operating characteristic [ROC] curve), and goodness-of-fit statistics for calibration.Several new measures have recently been proposed that can be seen as refinements of discrimination measures, including variants of the c statistic for survival, reclassification tables, net reclassification improvement (NRI), and integrated discrimination improvement (IDI). Moreover, decision-analytic measures have been proposed, including decision curves to plot the net benefit achieved by making decisions based on model predictions.We aimed to define the role of these relatively novel approaches in the evaluation of the performance of prediction models. For illustration, we present a case study of predicting the presence of residual tumor versus benign tissue in patients with testicular cancer (n = 544 for model development, n = 273 for external validation).We suggest that reporting discrimination and calibration will always be important for a prediction model. Decision-analytic measures should be reported if the predictive model is to be used for clinical decisions. Other measures of performance may be warranted in specific applications, such as reclassification metrics to gain insight into the value of adding a novel predictor to an established model.

/pdf/assessing-the-performance-of-prediction-models-a-framework-2soq09lsy5.pdf

Assessing the performance of prediction models: a framework for traditional and novel measures.

Objective To review and appraise the validity and usefulness of published and preprint reports of prediction models for diagnosing coronavirus disease 2019 (covid-19) in patients with suspected infection, for prognosis of patients with covid-19, and for detecting people in the general population at increased risk of covid-19 infection or being admitted to hospital with the disease. Design Living systematic review and critical appraisal by the COVID-PRECISE (Precise Risk Estimation to optimise covid-19 Care for Infected or Suspected patients in diverse sEttings) group. Data sources PubMed and Embase through Ovid, up to 1 July 2020, supplemented with arXiv, medRxiv, and bioRxiv up to 5 May 2020. Study selection Studies that developed or validated a multivariable covid-19 related prediction model. Data extraction At least two authors independently extracted data using the CHARMS (critical appraisal and data extraction for systematic reviews of prediction modelling studies) checklist; risk of bias was assessed using PROBAST (prediction model risk of bias assessment tool). Results 37 421 titles were screened, and 169 studies describing 232 prediction models were included. The review identified seven models for identifying people at risk in the general population; 118 diagnostic models for detecting covid-19 (75 were based on medical imaging, 10 to diagnose disease severity); and 107 prognostic models for predicting mortality risk, progression to severe disease, intensive care unit admission, ventilation, intubation, or length of hospital stay. The most frequent types of predictors included in the covid-19 prediction models are vital signs, age, comorbidities, and image features. Flu-like symptoms are frequently predictive in diagnostic models, while sex, C reactive protein, and lymphocyte counts are frequent prognostic factors. Reported C index estimates from the strongest form of validation available per model ranged from 0.71 to 0.99 in prediction models for the general population, from 0.65 to more than 0.99 in diagnostic models, and from 0.54 to 0.99 in prognostic models. All models were rated at high or unclear risk of bias, mostly because of non-representative selection of control patients, exclusion of patients who had not experienced the event of interest by the end of the study, high risk of model overfitting, and unclear reporting. Many models did not include a description of the target population (n=27, 12%) or care setting (n=75, 32%), and only 11 (5%) were externally validated by a calibration plot. The Jehi diagnostic model and the 4C mortality score were identified as promising models. Conclusion Prediction models for covid-19 are quickly entering the academic literature to support medical decision making at a time when they are urgently needed. This review indicates that almost all pubished prediction models are poorly reported, and at high risk of bias such that their reported predictive performance is probably optimistic. However, we have identified two (one diagnostic and one prognostic) promising models that should soon be validated in multiple cohorts, preferably through collaborative efforts and data sharing to also allow an investigation of the stability and heterogeneity in their performance across populations and settings. Details on all reviewed models are publicly available at https://www.covprecise.org/. Methodological guidance as provided in this paper should be followed because unreliable predictions could cause more harm than benefit in guiding clinical decisions. Finally, prediction model authors should adhere to the TRIPOD (transparent reporting of a multivariable prediction model for individual prognosis or diagnosis) reporting guideline. Systematic review registration Protocol https://osf.io/ehc47/, registration https://osf.io/wy245. Readers’ note This article is a living systematic review that will be updated to reflect emerging evidence. Updates may occur for up to two years from the date of original publication. This version is update 3 of the original article published on 7 April 2020 (BMJ 2020;369:m1328). Previous updates can be found as data supplements (https://www.bmj.com/content/369/bmj.m1328/related#datasupp). When citing this paper please consider adding the update number and date of access for clarity.

https://www.bmj.com/content/bmj/369/bmj.m1328.full.pdf

Prediction models for diagnosis and prognosis of covid-19: systematic review and critical appraisal

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Clinical Prediction Models: A Practical Approach to Development, Validation and Updating

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Clinical Prediction Models: A Practical Approach to Development, Validation and Updating