Use of predictive models to identify patients who are likely to benefit from refraction at a follow-up visit after cataract surgery.

PURPOSE: To develop predictive models to identify cataract surgery patients who are more likely to benefit from refraction at a four-week postoperative exam. METHODS: In this retrospective study, we used data of all 86,776 cataract surgeries performed in 2015 at a large tertiary-care eye hospital in India. The outcome variable was a binary indicator of whether the difference between corrected distance visual acuity and uncorrected visual acuity at the four-week postoperative exam was at least two lines on the Snellen chart. We examined the following statistical models: logistic regression, decision tree, pruned decision tree, random forest, weighted k-nearest neighbor, and a neural network. Predictor variables included in each model were patient sex and age, source eye (left or right), preoperative visual acuity, first-day postoperative visual acuity, intraoperative and immediate postoperative complications, and combined surgeries. We compared the predictive performance of models and assessed their clinical impact in test samples. RESULTS: All models demonstrated predictive accuracy better than chance based on area under the receiver operating characteristic curve. In a targeting exercise with a fixed intervention budget, we found that gains from predictive models in identifying patients who would benefit from refraction ranged from 7.8% (increase from 1500 to 1617 patients) to 74% (increase from 250 to 435 patients). CONCLUSION: The use of predictive statistical models to identify patients who are likely to benefit from refraction at follow-up can improve the economic efficiency of interventions. Simpler models like logistic regression perform almost as well as more complex machine-learning models, but are easier to implement.

Mean centering, multicollinearity, and moderators in multiple regression: The reconciliation redux.

In this article, we attempt to clarify our statements regarding the effects of mean centering. In a multiple regression with predictors A, B, and A × B (where A × B serves as an interaction term), mean centering A and B prior to computing the product term can clarify the regression coefficients (which is good) and the overall model fit R2 will remain undisturbed (which is also good).

Mean centering helps alleviate "micro" but not "macro" multicollinearity.

There seems to be confusion among researchers regarding whether it is good practice to center variables at their means prior to calculating a product term to estimate an interaction in a multiple regression model. Many researchers use mean centered variables because they believe it's the thing to do or because reviewers ask them to, without quite understanding why. Adding to the confusion is the fact that there is also a perspective in the literature that mean centering does not reduce multicollinearity. In this article, we clarify the issues and reconcile the discrepancy. We distinguish between "micro" and "macro" definitions of multicollinearity and show how both sides of such a debate can be correct. To do so, we use proofs, an illustrative dataset, and a Monte Carlo simulation to show the precise effects of mean centering on both individual correlation coefficients as well as overall model indices. We hope to contribute to the literature by clarifying the issues, reconciling the two perspectives, and quelling the current confusion regarding whether and how mean centering can be a useful practice.