Regression models in clinical studies: determining relationships between predictors and response.

Multiple regression models are increasingly being applied to clinical studies. Such models are powerful analytic tools that yield valid statistical inferences and make reliable predictions if various assumptions are satisfied. Two types of assumptions made by regression models concern the distribution of the response variable and the nature or shape of the relationship between the predictors and the response. This paper addresses the latter assumption by applying a direct and flexible approach, cubic spline functions, to two widely used models: the logistic regression model for binary responses and the Cox proportional hazards regression model for survival time data.

Clinical judgment and therapeutic decision making.

Clinical decision making is under increased scrutiny due to concerns about the cost and quality of medical care. Variability in physician decision making is common, in part because of deficiencies in the knowledge base, but also due to the difference in physicians' approaches to clinical problem solving. Evaluation of patient prognosis is a critical factor in the selection of therapy, and careful attention to methodology is essential to provide reliable information. Randomized controlled clinical trials provide the most solid basis for the establishment of broad therapeutic principles. Because randomized studies cannot be performed to address every question, observational studies will continue to play a complementary role in the evaluation of therapy. Randomized studies in progress, meta analyses of existing data, and increased use of administrative and collaborative clinical data bases will improve the knowledge base for decision making in the future.

Comparison of predictions based on observational data with the results of randomized controlled clinical trials of coronary artery bypass surgery.

Clinical decisions are most secure when based on findings from several large randomized clinical trials, but relevant randomized trial data are often unavailable. Analyses using clinical data bases might provide useful information if statistical methods can adequately correct for the lack of randomization. To test this approach, the findings of the three major randomized trials of coronary bypass surgery were compared with predictions of multivariable statistical models derived from observations in the Duke Cardiovascular Disease Databank. Clinical characteristics of patients at Duke University Medical Center who met eligibility requirements for each major randomized trial were used in the models to predict 5 year survival rates expected for medical and surgical therapy in each randomized trial. Model predictions agreed well with randomized trial results and were within the 95% confidence limits of the observed survival rates in 24 (92%) of 26 clinical subgroups. The overall correlation between predicted and observed survival rates was good (Spearman coefficient 0.73, p less than 0.0001). These results suggest that carefully performed analyses of observational data can complement the results of randomized trials.

Importance of clinical measures of ischemia in the prognosis of patients with documented coronary artery disease.

To examine the value of clinical measures of ischemia for stratifying prognosis, 5,886 consecutive patients who had symptomatic significant (greater than or equal to 75% stenosis) coronary artery disease were studied. Using the Cox regression model in a randomly selected half of the patients, the prognostically independent clinical variables were weighted and arranged into a simple angina score: angina score = angina course X (1 + daily angina frequency) + ST-T changes, where angina course was equal to 3 if unstable or variant angina was present, 2 if the patient's angina was progressive with nocturnal episodes, 1 if it was progressive without nocturnal symptoms and 0 if it was stable; 6 points were added for the presence of "ischemic" ST-T changes. This angina score was then validated in an independent patient sample. The score was a more powerful predictor of prognosis than was any individual anginal descriptor. Furthermore, the angina score added significant independent prognostic information to the patient's age, sex, coronary anatomy and left ventricular function. Patients with three vessel disease and a normal ventricle (n = 1,233) had a 2 year infarction-free survival rate of 90% with an angina score of 0 and a 68% survival rate with an angina score greater than or equal to 9. With an ejection fraction less than 50% and three vessel disease (n = 1,116), the corresponding infarction-free survival figures were 76 and 56%.(ABSTRACT TRUNCATED AT 250 WORDS)

Prognostic value of the simplified Selvester QRS score in patients with coronary artery disease.

The relation of the simplified Selvester QRS scoring system for the estimation of myocardial infarct size to survival was studied in 1,915 nonsurgically treated patients with documented coronary artery disease. Electrocardiograms (ECGs) were scored according to a simplified 29 point QRS scoring system. Using Cox model analyses, QRS scores were found to provide strong prognostic information by themselves (p less than 0.0001). Higher QRS scores were associated with lower survival rates. Patients with a score of 0 had a 1 year survival rate of 95% and a 5 year survival rate of 88%; patients with a score of 10 or more had survival rates of 81 and 52%, respectively, at the same intervals. Directly compared with the presence or absence of Q waves on the ECG, QRS scores provided greater prognostic information (p less than 0.001). When compared with 13 individual factors previously shown to provide the greatest independent prognostic information, the QRS score was the third most powerful individual prognostic factor. It did not contribute independent prognostic information in combination with the whole group, but did provide independent information in combination with the six most predictive factors. Its prognostic information overlapped mostly with clinical factors related to heart failure, and combined best with clinical factors related to the severity of ongoing myocardial ischemia. Because it is inexpensive and simple and maximizes the prognostic information from the ECG, the simplified Selvester QRS scoring system can be a useful clinical descriptor for practitioners and clinical investigators.

Cardiac rupture, mortality and the timing of thrombolytic therapy: a meta-analysis.

This study examined the relation between the risk of cardiac rupture and the timing of thrombolytic therapy for acute myocardial infarction. To test the hypothesis that cardiac rupture is prevented by early thrombolytic therapy but is promoted by late treatment, randomized controlled trials of thrombolytic agents for myocardial infarction were pooled. A logistic regression model including 58 cases of cardiac rupture among 1,638 patients from four trials showed that the odds ratio (treated/control) of cardiac rupture was directly correlated with time to treatment (p = 0.01); at 7 h, the odds ratio was 0.4 (95% confidence limits 0.17 to 0.93); at 11 h, it was 0.93 (0.53 to 1.60) and at 17 h, it was 3.21 (1.10 to 10.1). Analysis of data from the Gruppo Italiano per lo Studio della Streptochinasi nell'Infarto Miocardico (GISSI) trial independently confirmed the relation between time to thrombolytic therapy and risk of cardiac rupture (p = 0.03). Analysis of 4,692 deaths in 44,346 patients demonstrated that the odds ratio of death was also directly correlated with time to treatment (p = 0.006); at 3 h, the odds ratio for death was 0.72 (0.67 to 0.77); at 14 h, it was 0.88 (0.77 to 1.00) and at 21 h, it was 1 (0.82 to 1.37). Thrombolytic therapy early after acute myocardial infarction improves survival and decreases the risk of cardiac rupture. Late administration of thrombolytic therapy also appears to improve survival but may increase the risk of cardiac rupture.

Comparison of survival of amiodarone-treated patients with coronary artery disease and malignant ventricular arrhythmias with that of a control group with coronary artery disease.

Although amiodarone is effective in the treatment of ventricular arrhythmias, it is associated with serious toxic effects. In addition, the prognosis of patients with malignant ventricular arrhythmias and coronary artery disease treated with amiodarone remains poor. The survival of 54 consecutive patients with angiographically documented coronary artery disease and symptomatic ventricular tachycardia or ventricular fibrillation treated with amiodarone was compared with that of 5,125 medically treated patients with coronary artery disease. The amiodarone group was older, with worse left ventricular function and more peripheral and cerebrovascular disease. The 1 year survival probability was 0.73 for the amiodarone group and 0.94 for the control coronary artery disease group. At 2 years of follow-up, the survival probabilities were 0.60 and 0.90 for the amiodarone and the control group, respectively. When the survival curves were adjusted for group differences in baseline prognostic characteristics (integrated as a previously published hazard score), there was no difference in the prognosis of the two groups. These findings suggest that treatment with amiodarone of malignant ventricular arrhythmias associated with coronary artery disease maintains patients on an underlying survival curve determined by the degree of myocardial dysfunction, clinical characteristics and coronary anatomy, and that amiodarone does not have a deleterious effect on survival.

Painless exercise ST deviation on the treadmill: long-term prognosis.

To evaluate the clinical correlates and long-term prognostic significance of silent ischemia during exercise, 1,698 consecutive symptomatic patients with coronary artery disease who had both treadmill testing and cardiac catheterization were studied. These patients were classified into three groups: Group 1 = patients with no exercise ST deviation (n = 856), Group 2 = patients with painless exercise ST deviation (n = 242) and Group 3 = patients with both angina and ST segment deviation during exercise (n = 600). Patients with exercise angina had a history of a longer and more aggressive anginal course (with a greater frequency of angina, with nocturnal episodes and/or progressive symptom pattern) and more severe coronary artery disease (almost two-thirds had three vessel disease). The 5 year survival rate among the patients with painless ST deviation was similar to that of patients without ST deviation (86% and 88%, respectively) and was significantly better than that of patients with both symptoms and ST deviation (5 year survival rate 73% in patients with exercise-limiting angina). Similar trends were obtained in subgroups defined by the amount of coronary artery disease present. In the total study group of 1,698 patients, silent ischemia on the treadmill was not a benign finding (average annual mortality rate 2.8%) but, compared with symptomatic ischemia, did indicate a subgroup of patients with coronary artery disease who had a less aggressive anginal course, less coronary artery disease and a better prognosis. Thus, silent ischemia during exercise testing in patients with symptomatic coronary artery disease represents an intermediate risk response in the spectrum of exercise-induced ischemia.

Prognostic value of dobutamine stress technetium-99m-sestamibi single-photon emission computed tomography myocardial perfusion imaging: stratification of a high-risk population.

OBJECTIVES: This work was undertaken to define the intrinsic cardiac risk of the patient population referred for dobutamine stress perfusion imaging and to determine whether dobutamine technetium-99m ((99m)Tc)-sestamibi single-photon emission computed tomography (SPECT) imaging is capable of risk stratification in this population. BACKGROUND: In animal models, dobutamine attenuates the myocardial uptake of (99m)Tc-sestamibi resulting in underestimation of coronary stenoses. Therefore, we hypothesized that the prognostic value of dobutamine stress (99m)Tc-sestamibi SPECT myocardial perfusion imaging might be impaired, owing to reduced detection of coronary stenoses. METHODS: We reviewed the clinical outcome of 308 patients (166 women, 142 men) who underwent dobutamine stress SPECT (99m)Tc-sestamibi imaging at our institution from September 1992 through December 1996. RESULTS: During an average follow-up of 1.9 +/- 1.1 years, there were 33 hard cardiac events (18 myocardial infarctions [MI] and 15 cardiac deaths) corresponding to an annual cardiac event rate of 5.8%/year, which is significantly higher than the event rate for patients referred for exercise SPECT imaging at our institution (2.2%/year). Event rates were higher after an abnormal dobutamine (99m)Tc-sestamibi SPECT study (10.0%/year) than after a normal study (2.3%/year) (p < 0.01), even after adjusting for clinical variables. In the subgroup (n = 29) with dobutamine-induced ST-segment depression and abnormal SPECT imaging, the prognosis was poor, with annual cardiac death and nonfatal MI rates of 7.9% and 13.2%, respectively. CONCLUSIONS: Patients referred for dobutamine perfusion imaging are a high-risk population, and dobutamine stress (99m)Tc-sestamibi SPECT imaging is capable of risk stratification in these patients.

Prognostic value of ventricular arrhythmias associated with treadmill exercise testing in patients studied with cardiac catheterization for suspected ischemic heart disease.

The prognostic information provided by ventricular arrhythmias associated with treadmill exercise testing was evaluated in 1,293 consecutive nonsurgically treated patients undergoing an exercise test within 6 weeks of cardiac catheterization. The 236 patients with simple ventricular arrhythmias (at least one premature ventricular complex, but without paired complexes or ventricular tachycardia) had a higher prevalence of significant coronary artery disease (57 versus 44%), three vessel disease (31 versus 17%) and abnormal left ventricular function (43 versus 24%) than did patients without ventricular arrhythmias. Patients with paired complexes or ventricular tachycardia had an even higher prevalence of significant coronary artery disease (75%), three vessel disease (39%) and abnormal left ventricular function (54%). In the 620 patients with significant coronary artery disease, patients with paired complexes or ventricular tachycardia had a lower 3 year survival rate (75%) than did patients with simple ventricular arrhythmias (83%) and patients with no ventricular arrhythmias (90%). Ventricular arrhythmias were found to add independent prognostic information to the noninvasive evaluation, including history, physical examination, chest roentgenogram, electrocardiogram and other exercise test variables (p = 0.03). Ventricular arrhythmias made no independent contribution once the cardiac catheterization data were known. In patients without significant coronary artery disease, no relation between ventricular arrhythmias and survival was found.

Clinical experience and predicting survival in coronary disease.

To study the accuracy with which long-term prognosis can be predicted in patients with coronary artery disease, prognostic predictions obtained from a large, diverse sample of practicing cardiologists were compared with predictions from a multivariable statistical model. Test samples of 10 patients each were selected from a large series of medically treated patients with significant coronary disease. Using detailed clinical summaries, 49 cardiologists each predicted the probability of 3-year survival and infarction-free survival for 10 patients. Cox regression models, developed using patients who were not in the test samples, were also used to predict corresponding outcome probabilities for each test patient. Overall, the model estimates of prognosis were significantly better than the doctors' predictions. The rank correlation of model predictions with 3-year survival was 0.60, compared with 0.52 for the physicians. Model predictions added significant prognostic information to the doctors' predictions, whereas the converse was not true. Where predictions were made by multiple doctors, the inter-physician variability was substantial. Neither practice characteristics nor extent of clinical experience significantly affected the physicians' predictive accuracy. In coronary artery disease, statistical models developed from carefully collected data can provide prognostic predictions that are more accurate than predictions of experienced clinicians made from detailed case summaries.

Effect of aging on the sensitivity of growth hormone secretion to insulin-like growth factor-I negative feedback.

To determine the effect of aging on the suppression of GH secretion by insulin-like growth factor (IGF)-I, we studied 11 healthy young adults (6 men, 5 women, mean +/- SD: 25.2 +/- 4.6 yr old; body mass index 23.7 +/- 1.8 kg/m2) and 11 older adults (6 men, 5 women, 69.5 +/- 5.8 yr old; body mass index 24.2 +/- 2.5 kg/m2). Saline (control) or recombinant human IGF-I (rhIGF-I) (2 h baseline then, in sequence, 2.5 h each of 1, 3, and 10 micrograms/kg.h) was infused iv during the last 9.5 h of a 40.5-h fast; serum glucose was clamped within 15% of baseline. Baseline serum GH concentrations (mean +/- SE: 3.3 +/- 0.7 vs. 1.9 +/- 0.5 micrograms/L, P = 0.02) and total IGF-I concentrations (219 +/- 15 vs. 103 +/- 19 micrograms/L, P < 0.01) were higher in the younger subjects. In both age groups, GH concentrations were significantly decreased by 3 and 10 micrograms/kg.h, but not by 1 microgram/kg.h rhIGF-I. The absolute decrease in GH concentrations was greater in young than in older subjects during the 3 and 10 micrograms/kg.h rhIGF-I infusion periods, but both young and older subjects suppressed to a similar GH level during the last hour of the rhIGF-I infusion (0.78 +/- 0.24 microgram/L and 0.61 +/- 0.16 microgram/L, respectively). The older subjects had a greater increase above baseline in serum concentrations of both total (306 +/- 24 vs. 244 +/- 14 micrograms/L, P = 0.04) and free IGF-I (8.5 +/- 1.4 vs. 4.2 +/- 0.6 micrograms/L, P = 0.01) than the young subjects during rhIGF-I infusion, and their GH suppression expressed in relation to increases in both total and free serum IGF-I concentrations was significantly less than in the young subjects. We conclude that the ability of exogenous rhIGF-I to suppress serum GH concentrations declines with increasing age. This suggests that increased sensitivity to endogenous IGF-I negative feedback is not a cause of the decline in GH secretion that occurs with aging.

Pirmenol kinetics and effective oral dose.

The oral form of pirmenol has not been administered to man. Pirmenol was given by mouth to eight patients with chronic, stable premature ventricular beats (PVBs) to determine effective dose and kinetics. The patients were evaluated with a dose-ranging protocol following by a double-blind, crossover, placebo-controlled study of doses that were effective during dose ranging. Oral doses of 150 to 250 mg induced at least 90% suppression of PVBs 18 of the 19 times they were administered during both protocols. During the double blind experiment, a single oral dose of pirmenol suppressed 95 +/- 8% PVBs/hr (mean +/- SD) for 3 consecutive hr, while placebo suppressed 4 +/- 42% PVBs/hr (P less than 0.01). a 90% or greater reduction in PVBs persisted for a median of 6 hr (range 1 to 8 hr). The range of plasma pirmenol concentrations associated with an at last 90% reduction in PVBs was 0.7 to 2.0 micrograms/ml. Median half-life (t1/2) was 9.3 hr (range 6.0 to 12.4) with 86.6 +/- 2.4% protein binding and 82.6 +/- 23.6% bioavailability. At peak drug level there was lengthening of the QTc interval (0.036 sec, P less than 0.05), but no change in heart rate, blood pressure, PR interval or QRS duration, or symptoms. In this single-dose study, pirmenol effectively reduced PVBs, has a relatively long t1/2, and was minimally toxic.

Estimating the likelihood of significant coronary artery disease.

Among 23 clinical characteristics examined in 3,627 consecutive, symptomatic patients referred for cardiac catheterization between 1969 and 1979, nine were found to be important for estimating the likelihood a patient had significant coronary artery disease. A model using these characteristics accurately estimated the likelihood of disease when applied prospectively to 1,811 patients referred since 1979 and when used to estimate the prevalence of disease in subgroups reported in the literature. Since accurate estimates of the likelihood of significant disease that are based on clinical characteristics are reproducible, they should be used in interpreting the results of additional noninvasive tests and in quantitating the added diagnostic value.

Estimating the likelihood of severe coronary artery disease.

PURPOSE: To determine which clinical characteristics obtained by a physician during an initial clinical examination are important for estimating the likelihood of severe coronary artery disease, and to determine whether estimates based on these characteristics remain valid when applied prospectively and in different patient groups. PATIENTS AND METHODS: We examined clinical characteristics predictive of severe disease in 6,435 consecutive symptomatic patients referred for suspected coronary artery disease between 1969 and 1983. RESULTS: Eleven of 23 characteristics were important for estimating the likelihood of severe coronary artery disease. A model using these characteristics accurately estimated the likelihood of severe disease in an independent sample of 2,342 patients referred since 1983. The model also accurately estimated the prevalence of severe disease in large series of patients reported in the literature. CONCLUSIONS: These findings suggest that the clinician's initial evaluation can identify patients at high or low risk of anatomically severe coronary artery disease. Cost-conscious quality care is encouraged by identifying patients at higher risk for severe coronary artery disease who are most likely to benefit from further evaluation.

Factors affecting sensitivity and specificity of exercise electrocardiography. Multivariable analysis.

Unlike the predictive value of a diagnostic test, which depends on the prevalence of disease in the population tested, its sensitivity and specificity have been assumed to be constants. This assumption was examined in patients who had both exercise electrocardiography and cardiac catheterization. The effects on sensitivity of factors from clinical history, catheterization, and exercise performance were defined by multivariable logistic regression analysis in 1,401 patients with coronary disease; effects on specificity were defined by a similar analysis in 868 patients without coronary disease. Five factors had significant, independent effects on exercise electrocardiographic sensitivity: maximal exercise heart rate, number of diseased coronary arteries, type of angina, and the patient's age and sex. Only maximal exercise heart rate had a significant, independent effect on exercise electrocardiographic specificity. Thus, the sensitivity and specificity of exercise electrocardiography vary with clinical history, extent of disease, and treadmill performance; the sensitivity and specificity of other diagnostic tests may also vary.

Predicting outcome in coronary disease. Statistical models versus expert clinicians.

To study the accuracy with which long-term prognosis can be predicted in patients with coronary artery disease, prognostic predictions from a data-based multivariable statistical model were compared with predictions from senior clinical cardiologists. Test samples of 100 patients each were selected from a large series of medically treated patients with significant coronary disease. Using detailed case summaries, five senior cardiologists each predicted one- and three-year survival and infarct-free survival probabilities for 100 patients. Fifty patients appeared in multiple samples for assessing interphysician variability. Cox regression models, developed using patients not in the test samples, predicted corresponding outcome probabilities for each test patient. Overall, model predictions correlated better with actual patient outcomes than did the doctors' predictions. For three-year survival, rank correlations were 0.61 (model) and 0.49 (doctors). For three-year infarct-free survival predictions, correlations with outcome were 0.48 (model) and 0.29 (doctors). Comparisons by individual doctor revealed Cox model three-year survival predictions were better than those of four of five doctors (model predictions added significant [p less than 0.05] prognostic information to the doctor's predictions, whereas the converse was not true). For infarct-free survival, the Cox model was superior to all five doctors. Where predictions were made by multiple doctors, the interphysician variability was substantial. In coronary artery disease, statistical models developed from carefully collected data can provide prognostic predictions that are more accurate than predictions of experienced clinicians made from detailed case summaries.

'Reactive gliosis' in the medulla oblongata of victims of the sudden infant death syndrome.

A current hypothesis that the sudden infant death syndrome (SIDS) is a sleep apnea syndrome precipitated by defective control of involuntary respiration prompted the present study in which "reactive gliosis" in sections of the medulla oblongata of 45 SIDS victims was quantitated and compared with that in 20 control infants. Six anatomic regions were studied; five are related and one is unrelated to neural control of involuntary respiration. Increased numbers of "reactive" astrocytes were found in the SIDS group when the counts for all regions were combined (P = .04). Counts were also significantly higher in the SIDS victims for each of three regions alone: (1) the hilum of the inferior olivary nucleus (P = .01); (2) a lateral region (P = .02); and (3) the nucleus of the tractus solitarius (P = .03). The region with the greatest statistical difference, the inferior olivary hilum, has no recognized role in the control of involuntary respiration. There were no consistent associations between reactive astrocyte counts and specific clinical, socioeconomic, and pathologic variables. Characterization of the SIDS group whose counts exceeded that of the highest control infant also did not uncover distinguishing features. This study reinforces previous observations that, at least statistically, an abnormality of the brainstem occurs in a group of SIDS victims in contrast to a group of control infants, but also discloses considerable overlap in the numbers of such cells between these two groups.

Natural history of patients with single-vessel disease suitable for percutaneous transluminal coronary angioplasty.

To permit comparison of percutaneous transluminal coronary angioplasty (PTCA) with conventional therapy, the clinical outcome was established in patients who would have been suitable candidates for PTCA but who presented before the technique was available. Coronary angiograms were reviewed of patients who met the following criteria: single-vessel disease with proximal subtotal coronary stenosis, chest pain of at least class II, and cardiac catheterization before 1981. Angiograms were evaluated according to established criteria for PTCA by an experienced angiographer. One hundred ten patients (2.1% of the patient population) were judged suitable for PTCA. Clinical and catheterization findings closely resembled those of patients in the national PTCA registry. Five years after catheterization, 97% of PTCA candidates treated medically were alive and 85% had not had myocardial infarction. Forty-six patients had coronary artery bypass surgery within 6 months of catheterization and 10 other patients had subsequent surgery. Five years after surgery, 91% were alive and 87% had not had myocardial infarction. At 6 months of follow-up, 78% of all patients had improved at least 1 functional class, and 86% of all patients working before catheterization were still employed. Functional capacity was well maintained during long-term follow-up (median 6.5 years, range 1.4 to 12.2). These data indicate that PTCA candidates have an excellent prognosis for survival, a low risk of infarction, and well-maintained functional capacity when revascularization is reserved for those with inadequate control of symptoms by medical therapy.

An improving prognosis over time in medically treated patients with coronary artery disease.

The national mortality rate from coronary heart disease has decreased during the past decade, for reasons that are not yet clear. The mortality rate and the total number of cardiovascular events both decreased during the last 10 years in 1,911 medically treated patients with significant coronary artery disease. This decrease cannot be explained by less sick patients being referred for evaluation. This study suggests that at least part of the decrease in coronary heart disease mortality observed nationally is occurring in patients with established coronary disease.