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Introduction To Probability Models 10th Pdf 11



Our aim was to investigate in a joint cohort how important role pre-pregnancy obesity of the mother plays in the likelihood of developing isolated gestational hypertension (GH) and preeclampsia (PE), compared to the role of other risk factors. Our analysis was based on the measurement of several statistical indicators, in the evaluation of multivariate probability models. In order to broaden the assessment of the quality of the prediction of potential GH and PE risk markers, in addition to AUC, we used two newer coefficients: Integrated Discrimination Improvement (IDI) and Net Reclassification Improvement (NRI). The IDI measures the mean change in disease probability when a new marker is added to the model. The NRI, on the other hand, provides a clinically very favorable interpretation by calculating the percentage of persons in whom the addition of the marker under examination improves or worsens the prediction (classification). Missing data were treated as an additional category, and each analysis was based on the same dataset [23,24,25]. We have not found a similar study in the literature.




introduction to probability models 10th pdf 11



Subsequently, multi-factor predictive regression models (separately for GH and PE) were built. A small basic regression model was built, which included age and primiparity. Subsequent models were extended, and one additional (tested) variable was added to the base model. Three prediction indexes were used to assess the improvement in prediction (change in disease probability) in the subsequent extended multivariate models (compared to the base model): Integrated Discrimination Improvement (IDI), Net Reclassification Improvement (NRI), and area under receiver operating characteristic curve (AUC under ROC curve) of the basic and extended model. For each of the three indicators, 95% confidence intervals were calculated, and their statistical significance (p-value) was checked. High and statistically significant values obtained for the difference of AUC and for IDI and NRI prove good predictive ability of the variable added to the basic regression model [23,24,25].


AUC is a known prediction factor in regression models; the greater the difference between the AUC of the extended model and the AUC of the base model, the greater the improvement in the prediction when a new variable is added to the model. The IDI index shows the difference between the value of the mean change in the predicted probability between the group of sick women and the group of healthy women. The NRI index focuses on the reclassification table describing the number of women in whom an upward or downward shift in the disease probability value occurred after a new factor had been added to the model.


Importantly, we assessed multivariate prediction models to investigate the importance of pre-pregnancy obesity/overweight, and not to confirm that the greater number of predictors increases the prediction. Our analysis has several advantages over the widely used odds ratio calculations or AUC analysis. IDI determines the mean change in disease probability due to the addition of a new potential marker to the model. NRI gives a clinically very favorable interpretation by providing the percentage of people in whom the addition of the marker under study improves or worsens the prediction (classification). By summing up the marker hierarchy obtained in the AUC, IDI, and NRI examination, we established the final predictor hierarchy taking into consideration many mathematical results.


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