We employed a generalised esti-mating equation (GEE) logistic model with an exchangeablewithin-patient correlation structure to account for individualpatients having multiple exacerbations.

Weobserved that an established machine-learning method (GB) narrowlyoutperformed other prediction algorithmsand resulted in a prediction model with ahigh discrimination power (AUC = 0.82),which also showed robust calibration in thevalidation data.

In particular, we comparedlogistic regression (LR), random forest (RF),neural network (NN), and gradient-boosting (GB) methods (20).

For model comparison with machine learning–basedclassification, we selected the following classifiers: decisiontrees [15], random forests [16], k-nearest neighbor clustering[17], linear discriminant analysis, and adaptive boosting [18]

Classification algorithms for this study were selected accordingto previously published studies on COPD such as those of Wanget al [13] and Rahman et al [14].

Adjusted multiple logistic regression models were alsoperformed, including independent variables associated with exac-erbation (P
0.20) in the univariate analysis

First, we analyzedrisk of having frequent exacerbationsduring the first year of follow-up usinglogistic regression

(1) baseline differences between patients with and withouthospitalized exacerbation during follow-up were tested using analysisof variance or Wilcoxon rank-sum test for continuous variables, andx2 test for categorical variables; (2) the incidence (first hospitalizedexacerbation during the prospective follow-up) and recurrence (secondhospitalized exacerbation during the prospective follow-up) of hos-pitalized exacerbations was summarized as a rate per person per year(PPPY), using a sum of individual patient’s person-time in the studyand standardized per year, accompanied by 95% CIs; (3) factors asso-ciated with first hospitalized (and recurrent) exacerbations during the3-year follow-up, were explored using Cox proportional hazards models,adjusted for a wide range of demographics, and clinical and biologicmarkers.

logisticmultivariate regression tests

Time-dependentvariables from hospital discharge were analyzed with Cox logisticregression and Kaplan-Meier statistics.

The mostcommon statistical method was logistic regression (11 out of 25 different statistical methods analysed)followed by Cox regression (10), and correlation analysis between an index (or a multivariable regressionequation) with the outcome (three). Finally, Poisson regression model, negative binomial regression modeland random forest model were each used once.

n most cases, if censoring isnegligible and the follow-up period clearly defined, logistic regres-sion is used; if censoring is significant or time to event is important,then a survival time approach using a Cox proportional Hazardsmodel is preferred. Other more complex model approaches such asmachine learning or competing risk models exist but are beyond thescope of this chapter [18, 19].

To ensure stability of the model coefficients in logistic and Coxregression, an event frequency of at least 10/events per degree offreedom in the model is advised [13]. For example, in a cohort of1000 patients where 100 outcomes have been observed, the pre-diction model should include at most 10 variables. Ratios of lessthan 10 events per variable can result in overfitting of the data,leading to poor generalizability in other patient cohorts. All thesegeneral aspects of study and model specification should bedescribed in the methods to allow assessment of internal validity.

Cox proportional hazards modeling would alsohave been a valid approach for risk estimation, but we choselogistic regression analysis because we considered each exac-erbation within our predefined time frame of 2 years to beof equal importance, regardless of whether this exacerbationoccurred early or late in the follow-up period.

We used logistic regression modeling to estimate the riskof occurrence of COPD exacerbations within the proceeding24 months.

Common classification algorithms for supervisedlearning in the healthcare field include artificialneural networks, 36 decision trees, 37 random forests, 38Bayesian networks, 39 k-nearest neighbors,40 supportvector machines, 41 linear discriminant analysis, 42 k-means clustering 43 and logistic regression. 44

Five different prediction models for the annual exacerba-tion rate were estimated using negative binomial regression2

These methods included logistic regression with multipleregularization methods (lasso, ridge and elastic net), ran-dom forest and gradient boosted trees models (XGBoost).

This set of models(along with support vector machines and neural networks,which were not taken into consideration being more chal-lenging to interpret) are considered gold standard formachine learning classification studies done on tabulardata. Resampling was applied during cross-validation,making sure that only training folds of each cross-valida-tion iteration are affected, and the effect of resampling istested on the non-resampled test fold in each cross-valida-tion iteration.

Our study assumes that the SVM model can achieve acertain prediction effect in predicting the risk of readmis-sion in COPD patients, and the results have certain refer-ence value. Therefore, it is proposed to use SVM to builda 30-day acute exacerbation readmission risk predictionmodel for elderly COPD patients, and evaluate its predic-tion effect, so as to provide a basis for early identificationof patients with high risk of readmission in the future.

First, although ACCEPTshowed good-to-excellent discrimination overalland appears superior to exacerbation history alone,improvement in risk prediction was smaller in thosewith previous history of exacerbations than in thosewithout.

Usinga joint survival–logistic model, this risk tool providesan individualised risk estimate for exacerbations in thesubsequent year and their severity, as well as the rate offuture events.

Use of the ubiquitous proportional hazardsmodel, with time to first exacerbation as the outcome, is acommon mode of inference in contemporary clinical trialsof COPD. While it is robust in estimating treatment effectin randomized controlled trials, this analytical method fallsshort of providing other features, such as background rateof exacerbations or the shape of the incidence function, toenable predictions about the rate and (absolute or relative)duration of time to future events for a given patient. Asmentioned by Cox et al. (11), making such informative pre-dictions has been hindered by the widespread use of semi-parametric proportional hazards models.

In the present work, we used a joint para-metric recurrent-event and logistic regression model toenable full quantification of exacerbation incidence andseverity and their correlation

We used a joint accelerated failure time and logistic modelto characterise rate and severity of exacerbations. We havepreviously published details of this approach elsewhere.14