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F E Harrell

Publications and source records attributed to F E Harrell.

At least 19 recordsLinked to original sources
PubMed2004

Penalized maximum likelihood estimation to directly adjust diagnostic and prognostic prediction models for overoptimism: a clinical example.

BACKGROUND AND OBJECTIVE: There is growing interest in developing prediction models. The accuracy of such models when applied in new patient samples is commonly lower than estimated from the development sample. This may be because of differences between the samples and/or because the developed model was overfitted (too optimistic). Various methods, including bootstrapping techniques exist for afterwards shrinking the regression coefficients and the model's discrimination and calibration for overoptimism. Penalized maximum likelihood estimation (PMLE) is a more rigorous method because adjustment for overfitting is directly built into the model development, instead of relying on shrinkage afterwards. PMLE has been described mainly in the statistical literature and is rarely applied to empirical data. Using empirical data, we illustrate the use of PMLE to develop a prediction model. METHODS: The accuracy of the final PMLE model will be contrasted with the final models derived by ordinary stepwise logistic regression without and with shrinkage afterwards. The potential advantages and disadvantages of PMLE over the other two strategies are discussed. RESULTS: PMLE leads to smaller prediction errors, provides for model reduction to a user-defined degree, and may differently shrink each predictor for overoptimism without sacrificing much discriminative accuracy of the model. CONCLUSION: PMLE is an easily applicable and promising method to directly adjust clinical prediction models for overoptimism.

Bias↗
PubMed2001

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.

Aged↗
PubMed2001

Joint testing of mortality and a non-fatal outcome in clinical trials.

The following procedures are proposed for clinical trials of potentially lethal diseases with a non-fatal primary outcome: (i) comparison of treatments on worst-rank scores combining mortality and the non-fatal outcome; (ii) testing first for mortality differences, and then for differences on the worst-rank scoring if there is no significant evidence for mortality differences. Power and control of type I error rate while testing mortality and worst-rank scores by Bonferroni or closed testing procedures are compared. Used together these procedures improve power to detect treatments with favourable effects on both mortality and the designated non-fatal outcome, while reducing the likelihood of declaring that a treatment benefits patients when undetected adverse effects on mortality are present.

Bias↗
PubMed2001

BJ: an S-Plus program to fit linear regression models to censored data using the Buckley-James method.

Most researchers are familiar with ordinary multiple regression models, most commonly fitted using the method of least squares. The method of Buckley and James (J. Buckley, I. James, Linear regression with censored data, Biometrika 66 (1979) 429-436.) is an extension of least squares for fitting multiple regression models when the response variable is right-censored as in the analysis of survival time data. The Buckley-James method has been shown to have good statistical properties under usual regularity conditions (T.L. Lai, Z. Ying, Large sample theory of a modified Buckley-James estimator for regression analysis with censored data, Ann. Stat. 19 (1991) 1370-1402.). Nevertheless, even after 20 years of its existence, it is almost never used in practice. We believe that this is mainly due to lack of software and we describe here an S-Plus program that through its inclusion in a public domain function library fully exploits the power of the S-Plus programming environment. This environment provides multiple facilities for model specification, diagnostics, statistical inference, and graphical depiction of the model fit.

Data Interpretation, Statistical↗
PubMed2001

Internal validation of predictive models: efficiency of some procedures for logistic regression analysis.

The performance of a predictive model is overestimated when simply determined on the sample of subjects that was used to construct the model. Several internal validation methods are available that aim to provide a more accurate estimate of model performance in new subjects. We evaluated several variants of split-sample, cross-validation and bootstrapping methods with a logistic regression model that included eight predictors for 30-day mortality after an acute myocardial infarction. Random samples with a size between n = 572 and n = 9165 were drawn from a large data set (GUSTO-I; n = 40,830; 2851 deaths) to reflect modeling in data sets with between 5 and 80 events per variable. Independent performance was determined on the remaining subjects. Performance measures included discriminative ability, calibration and overall accuracy. We found that split-sample analyses gave overly pessimistic estimates of performance, with large variability. Cross-validation on 10% of the sample had low bias and low variability, but was not suitable for all performance measures. Internal validity could best be estimated with bootstrapping, which provided stable estimates with low bias. We conclude that split-sample validation is inefficient, and recommend bootstrapping for estimation of internal validity of a predictive logistic regression model.

Aged↗
PubMed2001

Using full probability models to compute probabilities of actual interest to decision makers.

The objective of this paper is to illustrate the advantages of the Bayesian approach in quantifying, presenting, and reporting scientific evidence and in assisting decision making. Three basic components in the Bayesian framework are the prior distribution, likelihood function, and posterior distribution. The prior distribution describes analysts' belief a priori, the likelihood function captures how data modify the prior knowledge; and the posterior distribution synthesizes both prior and likelihood information. The Bayesian approach treats the parameters of interest as random variables, uses the entire posterior distribution to quantify the evidence, and reports evidence in a "probabilistic" manner. Two clinical examples are used to demonstrate the value of the Bayesian approach to decision makers. Using either an uninformative or a skeptical prior distribution, these examples show that the Bayesian methods allow calculations of probabilities that are usually of more interest to decision makers, e.g., the probability that treatment A is similar to treatment B, the probability that treatment A is at least 5% better than treatment B, and the probability that treatment A is not within the "similarity region" of treatment B, etc. In addition, the Bayesian approach can deal with multiple endpoints more easily than the classic approach. For example, if decision makers wish to examine mortality and cost jointly, the Bayesian method can report the probability that a treatment achieves at least 2% mortality reduction and less than $20,000 increase in costs. In conclusion, probabilities computed from the Bayesian approach provide more relevant information to decision makers and are easier to interpret.

Arterial Occlusive Diseases↗
PubMed2001

Characteristics of adult primary care patients as predictors of future health services charges.

BACKGROUND: Utilization risk assessment is potentially useful for allocation of health care resources, but precise measurement is difficult. OBJECTIVE: Test the hypotheses that health-related quality of life (HRQOL), severity of illness, and diagnoses at a single primary care visit are comparable case-mix predictors of future 1-year charges in all clinical settings within a large health system, and that these predictors are more accurate in combination than alone. RESEARCH DESIGN: Longitudinal observational study in which subjects' characteristics were measured at baseline, and their outpatient clinic visits and charges and their inpatient hospital days and charges were tracked for 1 year. SUBJECTS: Adult primary care patients. MEASURES: Duke Health Profile for HRQOL, Duke Severity of Illness Checklist for severity of illness, and Johns Hopkins Ambulatory Care Groups for diagnostic groups classification. RESULTS: Of 1,202 patients, 84.4% had follow up in the primary care clinic, 63.2% in subspecialty clinics, 14.8% in the emergency room, and 9.6% in the hospital. Of $6,290,775 total charges, $779,037 (12.2%) was for follow-up primary care. The highest accuracy was found for predicting primary care charges, where R2 for predictors ranged from 0.083 for medical record auditor-reported severity of illness to 0.107 for HRQOL. When predictors were combined, the highest R2 of 0.125 was found for the combination of HRQOL and diagnostic groups. CONCLUSIONS: Baseline HRQOL, severity of illness, and diagnoses were comparable predictors of 1-year health services charges in all clinical sites but most predictive for primary care charges, and were more accurate in combination than alone.

Adult↗
PubMed2000

Prognostic modelling with logistic regression analysis: a comparison of selection and estimation methods in small data sets.

Logistic regression analysis may well be used to develop a prognostic model for a dichotomous outcome. Especially when limited data are available, it is difficult to determine an appropriate selection of covariables for inclusion in such models. Also, predictions may be improved by applying some sort of shrinkage in the estimation of regression coefficients. In this study we compare the performance of several selection and shrinkage methods in small data sets of patients with acute myocardial infarction, where we aim to predict 30-day mortality. Selection methods included backward stepwise selection with significance levels alpha of 0.01, 0.05, 0. 157 (the AIC criterion) or 0.50, and the use of qualitative external information on the sign of regression coefficients in the model. Estimation methods included standard maximum likelihood, the use of a linear shrinkage factor, penalized maximum likelihood, the Lasso, or quantitative external information on univariable regression coefficients. We found that stepwise selection with a low alpha (for example, 0.05) led to a relatively poor model performance, when evaluated on independent data. Substantially better performance was obtained with full models with a limited number of important predictors, where regression coefficients were reduced with any of the shrinkage methods. Incorporation of external information for selection and estimation improved the stability and quality of the prognostic models. We therefore recommend shrinkage methods in full models including prespecified predictors and incorporation of external information, when prognostic models are constructed in small data sets.

Age Factors↗
PubMed2000

Power calculation for clinical trials when the outcome is a composite ranking of survival and a nonfatal outcome.

In a clinical trial in which mortality occurs and a nonfatal outcome is measured after a fixed duration of follow-up, composite rank scores in which deaths (ranked by survival time) are scored below ranks for the nonfatal outcome have been proposed to test for treatment efficacy. This report derives formulae for calculating power for such a rank test under the conservative assumption that the treatment has a beneficial effect on the nonfatal outcome but no effect on mortality.

Clinical Trials as Topic↗
PubMed2000

Ordering an echocardiogram for evaluation of left ventricular function: level of expertise necessary for efficient use.

This prospective study was performed to test the hypothesis that the yield of 2-dimensional echocardiography (2DE) would be higher when it is ordered by a cardiologist than by a noncardiologist. Patients referred for transthoracic 2DE for the evaluation of left ventricular systolic function for the 11-month period between July 10, 1995, and June 10, 1996, were included in the study. Demographic, historical, and clinical findings were recorded. Whether the patient was referred by a cardiologist versus a noncardiologist was used as the predictor variable in a binary logistic regression analysis. To address the possibility that the yield of 2DE may be higher for cardiologists because the prevalence of disease in patients referred to them may be higher (selection bias), the analysis was subjected to a propensity score adjustment. Of 2176 patients referred for 2DE during the study, 1033 were referred for the evaluation of left ventricular function. The test had a positive yield in 52% of patients for cardiologists versus 31% for noncardiologists (chi(2) = 45.5, P <.0001, odds ratio 2.4 [CI = 1. 9-3.1]). This difference remained highly significant even when propensity score risk adjustment was made (chi(2) = 54.2, P <.0001, odds ratio 2.0 [CI = 1.5-2.8]). We conclude that the yield of 2DE is higher for cardiologists compared with noncardiologists and that this result was not related to differences in patient populations examined by the two groups. Thus, more efficient use of 2DE may be achieved if patients are referred to cardiologists rather than directly sent for 2DE.

Aged↗
PubMed2000

Dying with lung cancer or chronic obstructive pulmonary disease: insights from SUPPORT. Study to Understand Prognoses and Preferences for Outcomes and Risks of Treatments.

CONTEXT: Many are calling for patients with advanced chronic obstructive pulmonary disease (COPD) to receive hospice care, but the traditional hospice model may be insufficient. OBJECTIVE: To compare the course of illness and patterns of care for patients with non-small cell lung cancer and severe COPD. DESIGN: Prospective cohort study of seriously ill, hospitalized adults. SETTING: Five teaching hospitals in the United States. PATIENTS: Patients with Stage III or IV non-small cell lung cancer (n = 939) or acute exacerbation of severe COPD (n = 1008). MAIN OUTCOME MEASURES: Patients' preferences for pattern of care and for ventilator use; symptoms; life-sustaining interventions; and survival prognoses. RESULTS: Sixty percent in each group wanted comfort-focused care; 81% with lung cancer and 78% with COPD were extremely unwilling to have mechanical ventilation indefinitely. Severe dyspnea occurred in 32% of patients with lung cancer and 56% of patients with COPD and severe pain in 28 % of patients with lung cancer and 21% of patients with COPD. Patients with COPD who died during index hospitalization were more likely than patients with lung cancer to receive mechanical ventilation (70.4% vs 19.8%), tube feeding (38.7% vs 18.5%), and cardiopulmonary resuscitation (25.2% vs 7.8%). Mechanical ventilation had greater short term effectiveness in patients with COPD, based on survival to hospital discharge (76% vs 38%). Patients with COPD maintained higher median 2-month and 6-month survival prognoses, even days before death. CONCLUSIONS: Hospitalized patients with lung cancer or COPD preferred comfort-focused care, yet dyspnea and pain were problematic in both groups. Patients with COPD were more often treated with life-sustaining interventions, and short-term effectiveness was comparatively better than in patients with lung cancer. In caring for patients with severe COPD, consideration should be given to implementing palliative treatments more aggressively, even while remaining open to provision of life-sustaining interventions.

Activities of Daily Living↗
PubMed2000

Prediction of survival for older hospitalized patients: the HELP survival model. Hospitalized Elderly Longitudinal Project.

OBJECTIVE: To develop and validate a model estimating the survival time of hospitalized persons aged 80 years and older. DESIGN: A prospective cohort study with mortality follow-up using the National Death Index. SETTING: Four teaching hospitals in the US. PARTICIPANTS: Hospitalized patients enrolled between January 1993 and November 1994 in the Hospitalized Elderly Longitudinal Project (HELP). Patients were excluded if their length of hospital stay was 48 hours or less or if admitted electively for planned surgery. MEASUREMENTS: A log-normal model of survival time up to 711 days was developed with the following variables: patient demographics, disease category, nursing home residence, severity of physiologic imbalance, chart documentation of weight loss, current quality of life, exercise capacity, and functional status. We assessed whether model accuracy could be improved by including symptoms of depression or history of recent fall, serum albumin, physician's subjective estimate of prognosis, and physician and patient preferences for general approach to care. RESULTS: A total of 1266 patients were enrolled over a 10-month period, (median age 84.9, 61% female, 68% with one or more dependency), and 505 (40%) died during an average follow-up of more than 2 years. Important prognostic factors included the Acute Physiology Score of APACHE III collected on the third hospital day, modified Glasgow coma score, major diagnosis (ICU categories together, congestive heart failure, cancer, orthopedic, and all other), age, activities of daily living, exercise capacity, chart documentation of weight loss, and global quality of life. The Somers' Dxy for a model including these factors was 0.48 (equivalent to a receiver-operator curve (ROC) area of 0.74, suggesting good discrimination). Bootstrap estimation indicated good model validation (corrected Dxy of 0.46, ROC of 0.73). A nomogram based on this log-normal model is presented to facilitate calculation of median survival time and 10th and 90th percentile of survival time. A count of geriatric syndromes or comorbidities did not add explanatory power to the model, nor did the hospital of patient recruitment, depression, or the patient preferences for general approach to care. The physician's perception of the patient's preferences and the physician's subjective estimate of the patient's prognosis improved the estimate of survival time significantly. CONCLUSIONS: Accurate estimation of length of life for older hospitalized persons may be calculated using a limited amount of clinical information available from the medical chart plus a brief interview with the patient or surrogate. The accuracy of this model can be improved by including measures of the physician's perception of the patient's preferences for care and the physician's subjective estimate of prognosis.

Activities of Daily Living↗
PubMed2000

Decision-making and outcomes of prolonged ICU stays in seriously ill patients.

BACKGROUND: Despite concern about the high costs and the uncertain benefit of prolonged treatment in the intensive care unit (ICU), there has been little research examining decision-making and outcomes for patients with prolonged ICU stays. OBJECTIVES: To evaluate decision-making and outcomes for seriously ill patients with an ICU stay of at least 14 days. DESIGN: A prospective cohort study. SETTING: Five teaching hospitals. PARTICIPANTS: Seriously ill patients enrolled in the Study To Understand Prognoses and Preferences for Risks and Outcomes of Treatments (SUPPORT). MEASUREMENT: Patients, their surrogate decision-makers, and their physicians were interviewed about prognosis, communication, and goals of medical care. Based on age, diagnoses, comorbid illnesses, and acute physiology data, the SUPPORT Prognostic Model provided estimates of 6-month survival on study days 1, 3, 7, and 14. Hospital costs were estimated from hospital billing data. RESULTS: Of the 9105 patients enrolled in SUPPORT, 1494 (16%) had ICU stays of 14 days or longer. The median length of stay in an ICU was 4 days for the entire SUPPORT cohort and 35 days for patients who were treated in an ICU for 14 days or longer. Median hospital costs were $76,501 for patients who had ICU stays 14 days or longer and $10,916 for patients who did not have long ICU stays. Fifty-five percent of patients with long ICU stays had died by 6 months, and an additional 19% had substantial functional impairment. Among patients with ICU stays of at least 14 days, only 20% had estimates of 6-month survival that fell below 10% at any time during their hospitalization. For patients with long ICU stays, the mean predicted probability of 6-month survival was 0.46 on study Day 3 and 0.47 on study Day 14. Fewer than 40% of patients (or their surrogates) reported that their physicians had talked with them about their prognoses or preferences for life-sustaining treatment. Among the patients who preferred a palliative approach to care, only 29% thought that their care was consistent with that aim. Those who discussed their preferences for care with a physician were 1.9 times more likely to believe that treatment was in accord with their preferences for palliation (95% CI, 1.4-2.5) CONCLUSIONS: Prolonged ICU stays were expensive and were often followed by death or disability. Patients reported low rates of discussions with their physicians about their prognoses and preferences for life-sustaining treatments. Many preferred that care focus on palliation and believed that care was inconsistent with their preferences. Patients were more likely to receive care consistent with their preferences if they had discussed their care preferences with their physicians.

Activities of Daily Living↗
PubMed1998

Use of a prognostic treadmill score in identifying diagnostic coronary disease subgroups.

BACKGROUND: Exercise testing is useful in the assessment of symptomatic patients for diagnosis of significant or extensive coronary disease and to predict their future risk of cardiac events. The Duke treadmill score (DTS) is a composite index that was designed to provide survival estimates based on results from the exercise test, including ST-segment depression, chest pain, and exercise duration. However, its usefulness for providing diagnostic estimates has yet to be determined. METHODS AND RESULTS: A logistic regression model was used to predict significant (>/=75% stenosis) and severe (3-vessel or left main) coronary artery disease, and a Cox regression analysis was used to predict cardiac survival. After adjustment for baseline clinical risk, the DTS was effectively diagnostic for significant (P<0.0001) and severe (P<0.0001) coronary artery disease. For low-risk patients (score >/=+5), 60% had no coronary stenosis >/=75% and 16% had single-vessel >/=75% stenosis. By comparison, 74% of high-risk patients (score <-11) had 3-vessel or left main coronary disease. Five-year mortality was 3%, 10%, and 35% for low-, moderate-, and high-risk DTS groups (P<0.0001). CONCLUSIONS: The composite DTS provides accurate diagnostic and prognostic information for the evaluation of symptomatic patients evaluated for clinically suspected ischemic heart disease.

Adult↗
PubMed1998

Relationship between cancer patients' predictions of prognosis and their treatment preferences.

CONTEXT: Previous studies have documented that cancer patients tend to overestimate the probability of long-term survival. If patient preferences about the trade-offs between the risks and benefits associated with alternative treatment strategies are based on inaccurate perceptions of prognosis, then treatment choices may not reflect each patient's true values. OBJECTIVE: To test the hypothesis that among terminally ill cancer patients an accurate understanding of prognosis is associated with a preference for therapy that focuses on comfort over attempts at life extension. DESIGN: Prospective cohort study. SETTING: Five teaching hospitals in the United States. PATIENTS: A total of 917 adults hospitalized with stage III or IV non-small cell lung cancer or colon cancer metastatic to liver in phases 1 and 2 of the Study to Understand Prognoses and Preferences for Outcomes and Risks of Treatments (SUPPORT). MAIN OUTCOME MEASURES: Proportion of patients favoring life-extending therapy over therapy focusing on relief of pain and discomfort, patient and physician estimates of the probability of 6-month survival, and actual 6-month survival. RESULTS: Patients who thought they were going to live for at least 6 months were more likely (odds ratio [OR], 2.6; 95% confidence interval [CI], 1.8-3.7) to favor life-extending therapy over comfort care compared with patients who thought there was at least a 10% chance that they would not live 6 months. This OR was highest (8.5; 95% CI, 3.0-24.0) among patients who estimated their 6-month survival probability at greater than 90% but whose physicians estimated it at 10% or less. Patients overestimated their chances of surviving 6 months, while physicians estimated prognosis quite accurately. Patients who preferred life-extending therapy were more likely to undergo aggressive treatment, but controlling for known prognostic factors, their 6-month survival was no better. CONCLUSIONS: Patients with metastatic colon and lung cancer overestimate their survival probabilities and these estimates may influence their preferences about medical therapies.

Adult↗
PubMed1998

Development of a clinical prediction model for an ordinal outcome: the World Health Organization Multicentre Study of Clinical Signs and Etiological agents of Pneumonia, Sepsis and Meningitis in Young Infants. WHO/ARI Young Infant Multicentre Study Group.

This paper describes the methodologies used to develop a prediction model to assist health workers in developing countries in facing one of the most difficult health problems in all parts of the world: the presentation of an acutely ill young infant. Statistical approaches for developing the clinical prediction model faced at least two major difficulties. First, the number of predictor variables, especially clinical signs and symptoms, is very large, necessitating the use of data reduction techniques that are blinded to the outcome. Second, there is no uniquely accepted continuous outcome measure or final binary diagnostic criterion. For example, the diagnosis of neonatal sepsis is ill-defined. Clinical decision makers must identify infants likely to have positive cultures as well as to grade the severity of illness. In the WHO/ARI Young Infant Multicentre Study we have found an ordinal outcome scale made up of a mixture of laboratory and diagnostic markers to have several clinical advantages as well as to increase the power of tests for risk factors. Such a mixed ordinal scale does present statistical challenges because it may violate constant slope assumptions of ordinal regression models. In this paper we develop and validate an ordinal predictive model after choosing a data reduction technique. We show how ordinality of the outcome is checked against each predictor. We describe new but simple techniques for graphically examining residuals from ordinal logistic models to detect problems with variable transformations as well as to detect non-proportional odds and other lack of fit. We examine an alternative type of ordinal logistic model, the continuation ratio model, to determine if it provides a better fit. We find that it does not but that this model is easily modified to allow the regression coefficients to vary with cut-offs of the response variable. Complex terms in this extended model are penalized to allow only as much complexity as the data will support. We approximate the extended continuation ratio model with a model with fewer terms to allow us to draw a nomogram for obtaining various predictions. The model is validated for calibration and discrimination using the bootstrap. We apply much of the modelling strategy described in Harrell, Lee and Mark (Statist. Med. 15, 361-387 (1998)) for survival analysis, adapting it to ordinal logistic regression and further emphasizing penalized maximum likelihood estimation and data reduction.

Chi-Square Distribution↗