Kerry L. Lee

Multivariable regression models are powerful tools that are used frequently in studies of clinical outcomes. These models can use a mixture of categorical and continuous variables and can handle partially observed (censored) responses. However, uncritical application of modelling techniques can result in models that poorly fit the dataset at hand, or, even more likely, inaccurately predict outcomes on new subjects. One must know how to measure qualities of a model's fit in order to avoid poorly fitted or overfitted models. Measurement of predictive accuracy can be difficult for survival time data in the presence of censoring. We discuss an easily interpretable index of predictive discrimination as well as methods for assessing calibration of predicted survival probabilities. Both types of predictive accuracy should be unbiasedly validated using bootstrapping or cross-validation, before using predictions in a new data series. We discuss some of the hazards of poorly fitted and overfitted regression models and present one modelling strategy that avoids many of the problems discussed. The methods described are applicable to all regression models, but are particularly needed for binary, ordinal, and time-to-event outcomes. Methods are illustrated with a survival analysis in prostate cancer using Cox regression.

BACKGROUND: Sudden death from cardiac causes remains a leading cause of death among patients with congestive heart failure (CHF). Treatment with amiodarone or an implantable cardioverter-defibrillator (ICD) has been proposed to improve the prognosis in such patients. METHODS: We randomly assigned 2521 patients with New York Heart Association (NYHA) class II or III CHF and a left ventricular ejection fraction (LVEF) of 35 percent or less to conventional therapy for CHF plus placebo (847 patients), conventional therapy plus amiodarone (845 patients), or conventional therapy plus a conservatively programmed, shock-only, single-lead ICD (829 patients). Placebo and amiodarone were administered in a double-blind fashion. The primary end point was death from any cause. RESULTS: The median LVEF in patients was 25 percent; 70 percent were in NYHA class II, and 30 percent were in class III CHF. The cause of CHF was ischemic in 52 percent and nonischemic in 48 percent. The median follow-up was 45.5 months. There were 244 deaths (29 percent) in the placebo group, 240 (28 percent) in the amiodarone group, and 182 (22 percent) in the ICD group. As compared with placebo, amiodarone was associated with a similar risk of death (hazard ratio, 1.06; 97.5 percent confidence interval, 0.86 to 1.30; P=0.53) and ICD therapy was associated with a decreased risk of death of 23 percent (0.77; 97.5 percent confidence interval, 0.62 to 0.96; P=0.007) and an absolute decrease in mortality of 7.2 percentage points after five years in the overall population. Results did not vary according to either ischemic or nonischemic causes of CHF, but they did vary according to the NYHA class. CONCLUSIONS: In patients with NYHA class II or III CHF and LVEF of 35 percent or less, amiodarone has no favorable effect on survival, whereas single-lead, shock-only ICD therapy reduces overall mortality by 23 percent.

BACKGROUND: Empirical antiarrhythmic therapy has not reduced mortality among patients with coronary artery disease and asymptomatic ventricular arrhythmias. Previous studies have suggested that antiarrhythmic therapy guided by electrophysiologic testing might reduce the risk of sudden death. METHODS: We conducted a randomized, controlled trial to test the hypothesis that electrophysiologically guided antiarrhythmic therapy would reduce the risk of sudden death among patients with coronary artery disease, a left ventricular ejection fraction of 40 percent or less, and asymptomatic, unsustained ventricular tachycardia. Patients in whom sustained ventricular tachyarrhythmias were induced by programmed stimulation were randomly assigned to receive either antiarrhythmic therapy, including drugs and implantable defibrillators, as indicated by the results of electrophysiologic testing, or no antiarrhythmic therapy. Angiotensin-converting-enzyme inhibitors and beta-adrenergic-blocking agents were administered if the patients could tolerate them. RESULTS: A total of 704 patients with inducible, sustained ventricular tachyarrhythmias were randomly assigned to treatment groups. Five-year Kaplan-Meier estimates of the incidence of the primary end point of cardiac arrest or death from arrhythmia were 25 percent among those receiving electrophysiologically guided therapy and 32 percent among the patients assigned to no antiarrhythmic therapy (relative risk, 0.73; 95 percent confidence interval, 0.53 to 0.99), representing a reduction in risk of 27 percent). The five-year estimates of overall mortality were 42 percent and 48 percent, respectively (relative risk, 0.80; 95 percent confidence interval, 0.64 to 1.01). The risk of cardiac arrest or death from arrhythmia among the patients who received treatment with defibrillators was significantly lower than that among the patients discharged without receiving defibrillator treatment (relative risk, 0.24; 95 percent confidence interval, 0.13 to 0.45; P<0.001). Neither the rate of cardiac arrest or death from arrhythmia nor the overall mortality rate was lower among the patients assigned to electrophysiologically guided therapy and treated with antiarrhythmic drugs than among the patients assigned to no antiarrhythmic therapy. CONCLUSIONS: Electrophysiologically guided antiarrhythmic therapy with implantable defibrillators, but not with antiarrhythmic drugs, reduces the risk of sudden death in high-risk patients with coronary disease.

Regression models such as the Cox proportional hazards model have had increasing use in modelling and estimating the prognosis of patients with a variety of diseases. Many applications involve a large number of variables to be modelled using a relatively small patient sample. Problems of overfitting and of identifying important covariates are exacerbated in analysing prognosis because the accuracy of a model is more a function of the number of events than of the sample size. We used a general index of predictive discrimination to measure the ability of a model developed on training samples of varying sizes to predict survival in an independent test sample of patients suspected of having coronary artery disease. We compared three methods of model fitting: (1) standard 'step-up' variable selection, (2) incomplete principal components regression, and (3) Cox model regression after developing clinical indices from variable clusters. We found regression using principal components to offer superior predictions in the test sample, whereas regression using indices offers easily interpretable models nearly as good as the principal components models. Standard variable selection has a number of deficiencies.

Background— Dual-chamber (DDDR) pacing preserves AV synchrony and may reduce heart failure (HF) and atrial fibrillation (AF) compared with ventricular (VVIR) pacing in sinus node dysfunction (SND). However, DDDR pacing often results in prolonged QRS durations (QRSd) as the result of right ventricular stimulation, and ventricular desynchronization may result. The effect of pacing-induced ventricular desynchronization in patients with normal baseline QRSd is unknown. Methods and Results— Baseline QRSd was obtained from 12-lead ECGs before pacemaker implantation in MOST, a 2010-patient, 6-year, randomized trial of DDDR versus VVIR pacing in SND. Cumulative percent ventricular paced (Cum%VP) was determined from stored pacemaker data. Baseline QRSd &lt;120 ms was observed in 1339 patients (707 DDDR, 632 VVIR). Cum%VP was greater in DDDR versus VVIR (90% versus 58%, P =0.001). Cox models demonstrated that the time-dependent covariate Cum%VP was a strong predictor of HF hospitalization in DDDR (hazard ratio [HR], 2.99 [95% CI, 1.15 to 7.75] for Cum%VP &gt;40%) and VVIR (HR 2.56 [95% CI, 1.48 to 4.43] for Cum%VP &gt;80%). The risk of AF increased linearly with Cum%VP from 0% to 85% in both groups (DDDR, HR 1.36 [95% CI, 1.09, 1.69]; VVIR, HR 1.21 [95% CI 1.02, 1.43], for each 25% increase in Cum%VP). Model results were unaffected by adjustment for known baseline predictors of HF hospitalization and AF. Conclusions— Ventricular desynchronization imposed by ventricular pacing even when AV synchrony is preserved increases the risk of HF hospitalization and AF in SND with normal baseline QRSd.