Explained variation in survival analysis

Evaluating hospital costs in type 2 diabetes care: does the choice of the model matter?

BACKGROUND

Awareness of the economic burden of diabetes has led to a number of studies on economic issues. However, comparison among cost-of-illness studies is problematic because different methods are used to arrive at a final cost estimate.

OBJECTIVE

The aim of the study is to show how estimates of hospitalisation costs for diabetic patients can vary significantly in relation to the statistical method adopted in the analysis.

RESEARCH DESIGN AND METHODS

The study analyses diabetic patients' costs as a function of demographic and clinical covariates, by applying the following statistical survival models: the parametric survival model assuming Weibull distribution, the Cox proportional hazard (PH) model and the Aalen additive regression for modelling costs. The Aalen approach is robust both for the non proportionality in hazard and for departures from normality. In addition it is able to easily model the effect of covariates on the extreme costs. This cost analysis is based on data collected for a retrospective observational study analysing repeated hospitalisations (N = 4816) in a cohort of 3892 diabetic patients.

RESULTS

There is agreement in all models with the effects of the considered covariates (age, sex, duration of disease and presence of other pathologies). An effect of over- or under-estimation, according to the chosen model due to arguably inappropriate model fitting, was observed, being more evident for some specific profiles of the patients, and overall accounting for as much as 20% of the estimated effect. The Aalen model was able to cope with all the other models in furnishing unbiased estimates with the advantage of a greater flexibility in representing the covariates' effect on the cost process.

CONCLUSIONS

An appropriate choice of the model is crucial in avoiding misinterpretation of cost determinants of type 2 diabetes care. For our data set the Aalen model proved itself to be a realistic and informative way to characterise the effect of covariates on costs.

Using mutual information to measure the impact of multiple genetic factors on AIDS

Since the discovery of the 32-base-pair deletion in the CCR5 chemokine receptor gene (CCR5-Delta32) and its effect on HIV-1 infection and AIDS progression, many genetic factors affecting AIDS have been identified. Here we quantify the impact of 13 of these factors on AIDS progression using a new statistic based on the mutual information between causal factors and disease, the explained fraction. The influence of causal factors on disease is commonly measured by the attributable fraction statistic, but the attributable fraction is a poor measure of the extent to which a factor explains disease because it considers only whether a factor is necessary, not whether it is sufficient. The definition of the explained fraction, which is analogous to R or the explained variation for regression models, extends naturally to multiple factor levels. Because the explained fraction is approximately additive, it can be used to estimate how much of epidemiological data is explained by known genetic or environmental factors, and conversely how much is yet to be explained by unknown factors. We show that 13 genetic factors can cumulatively explain 9% of slow progression to AIDS, an effect comparable to the effect of smoking on lung cancer.

Follicular thyroid carcinoma: the role of histology and staging systems in predicting survival

OBJECTIVE

To evaluate the risk factors including tumor histomorphology for survival specific to follicular thyroid carcinoma (FTC) and to apply commonly employed staging systems in predicting survival for patients with FTC.

SUMMARY BACKGROUND DATA

FTC is usually analyzed collectively with papillary thyroid carcinoma (PTC) in risk group analysis. Risk factors and risk group analysis are important in the management of patients with FTC, although current published therapeutic guidelines call for total thyroidectomy followed by radioactive iodine (I) ablation for all FTC patients.

METHODS

Over a 40-year period, 156 patients surgically treated for FTC with an average follow-up of 14.4 years were retrospectively studied after histologic reclassification according to the type and degree of invasiveness of the tumor. Potential risk factors for survival were calculated using multivariate analysis, and the prognostic accuracy of AMES risk group stratification, UICC/AJCC pTNM staging, Degroot classification, and MACIS scoring schemes in predicting survival was compared.

RESULTS

Seventeen (11%) patients had distant metastases at presentation, and bilateral thyroid resection was performed for 131 (84%) patients. Seventeen (11%) patients died of recurrent or metastatic disease. The overall and cancer-specific survival (CSS) rates at 10 years were 79% and 88%, respectively. None of the patients with minimally invasive (n = 49) or angioinvasive (n = 23) carcinomas died compared with 17 of 84 patients with widely invasive carcinomas (P = 0.0007). Using the Cox proportional hazards model, old age, the presence of distant metastases, and incomplete tumor excision were independent prognostic factors for survival. For patients who underwent curative treatment, old age and widely invasive carcinoma were risk factors for poor survival. All staging systems studied accurately predicted CSS, and the pTNM UICC/AJCC staging system yielded the best prognostic information.

CONCLUSIONS

Commonly adopted staging systems can be applied specifically to patients with FTC. The distinction of FTC in minimally invasive and widely invasive carcinoma based on the extent of invasiveness rather than vascular invasion is important in identifying low-risk FTC patients for a more conservative management.

Late thyroid toxicity in 153 long-term survivors of allogeneic bone marrow transplantation for acute lymphoblastic leukaemia

The purpose of this study was to identify risk factors for hypothyroidism after bone marrow transplantation (BMT) for high-risk or relapsed acute lymphoblastic leukaemia (ALL) in children. In all, 388 children with acute lymphoblastic leukaemia underwent allogeneic bone marrow transplantation between 1984 and 1994. Overall 5-year survival was 54.6%. Thyroid function was assessed in the 153 patients with more than 5 years of follow-up. In total, 16 patients developed uncompensated hypothyroidism (UH) and 46 compensated hypothyroidism (CH) a median of 2.9 and 2.7 years, respectively, after BMT. Thyroid dysfunction-free survival rates were 73.2% after 5 years and 59.2% after 10 years. Three factors were significantly associated with the onset of hypothyroidism, namely age, bone marrow transplantation in second remission, and single-dose total body irradiation (TBI). Ultrasonography of the thyroid showed nodules in 10 of 35 patients. The median time from BMT to nodule detection was 7.8 years. Cytology (n=5) and surgery (n=4) showed no evidence of thyroid cancer. Four of the 14 patients who received cytoreduction without TBI but with busulphan and cyclophosphamide developed UH (n=2) or CH (n=2). We concluded that children who undergo BMT for ALL are at a high risk of subsequent thyroid dysfunction.

Evaluating survival model performance: a graphical approach

In the last decade, many statistics have been suggested to evaluate the performance of survival models. These statistics evaluate the overall performance of a model ignoring possible variability in performance over time. Using an extension of measures used in binary regression, we propose a graphical method to depict the performance of a survival model over time. The method provides estimates of performance at specific time points and can be used as an informal test for detecting time varying effects of covariates in the Cox model framework. The method is illustrated on real and simulated data using Cox proportional hazard model and rank statistics.

A time-dependent discrimination index for survival data

To derive models suitable for outcome prediction, a crucial aspect is the availability of appropriate measures of predictive accuracy, which have to be usable for a general class of models. The Harrell's C discrimination index is an extension of the area under the ROC curve to the case of censored survival data, which owns a straightforward interpretability. For a model including covariates with time-dependent effects and/or time-dependent covariates, the original definition of C would require the prediction of individual failure times, which is not generally addressed in most clinical applications. Here we propose a time-dependent discrimination index Ctd where the whole predicted survival function is utilized as outcome prediction, and the ability to discriminate among subjects having different outcome is summarized over time. Ctd is based on a novel definition of concordance: a subject who developed the event should have a less predicted probability of surviving beyond his/her survival time than any subject who survived longer. The predicted survival function of a subject who developed the event is compared to: (1) that of subjects who developed the event before his/her survival time, and (2) that of subjects who developed the event, or were censored, after his/her survival time. Subjects who were censored are involved in comparisons with subjects who developed the event before their observed times. The index reduces to the previous C in the presence of separation between survival curves on the whole follow-up. A confidence interval for Ctd is derived using the jackknife method on correlated one-sample U-statistics.The proposed index is used to evaluate the discrimination ability of a model, including covariates having time-dependent effects, concerning time to relapse in breast cancer patients treated with adjuvant tamoxifen. The model was obtained from 596 patients entered prospectively at Istituto Nazionale per lo Studio e la Cura dei Tumori di Milano (INT). The model discrimination ability was validated on an independent testing data set of 175 patients provided by Centro Regionale Indicatori Biochimici di Tumore (CRIBT) in Venice.

Explained variation and predictive accuracy in general parametric statistical models: the role of model misspecification

When studying a regression model measures of explained variation are used to assess the degree to which the covariates determine the outcome of interest. Measures of predictive accuracy are used to assess the accuracy of the predictions based on the covariates and the regression model. We give a detailed and general introduction to the two measures and the estimation procedures. The framework we set up allows for a study of the effect of misspecification on the quantities estimated. We also introduce a generalization to survival analysis.

Prognostic scoring systems in patients with follicular thyroid cancer: a comparison of different staging systems in predicting the patient outcome

BACKGROUND

The use of prognostic scoring systems is important for predicting the survival of individuals with thyroid carcinoma. Relatively few studies have addressed this issue for patients with follicular thyroid cancer. The goal of this retrospective study was to establish the best and most pertinent prognostic scoring system to predict survival in patients with follicular thyroid cancer.

METHODS

We selected 86 patients with follicular thyroid cancer treated at University of California, San Francisco (UCSF) hospitals from January 1954 to April 1998. The mean follow-up time was 11.5 years. There were 60 women (70%) and 26 men (30%), with a mean age if 48.6 years. Prognostic scoring systems included tumor, node, metastases (TNM), European Organization for Research and Treatment of Cancer (EORTC), Age, Grade, Extent, Size (AGES), Age, Metastases, Extent, Size (AMES), and the Metastases, Age, Completeness of resection, Invasion, Size (MACIS). Survival time was calculated using the Kaplan-Meier method. Using Cox proportional hazards analysis, the relative importance of each scoring method was determined by calculating the proportion of variation in survival time explained (PVE).

RESULTS

Kaplan-Meier analysis indicated that all scoring systems were significant predictors of survival time (p < 0.0001). The PVE associated with each system was (from highest to lowest) 0.48 for MACIS, 0.46 for AGES, 0.44 for EORTC, 0.40 for AMES, and 0.33 for TNM. These results indicate that the MACIS scoring system accounted for a great proportion of explained variance in survival and is a more precise predictor of survival compared to the other scoring systems.

CONCLUSIONS

TNM, EORTC, AGES, AMES, and MACIS, all provided useful prognostic information about the survival in our 86 patients with follicular thyroid cancers. The MACIS classification, however, was the most accurate predictor using PVE as a method of evaluation. Future scoring systems considering additional prognostic factors, may obtain a higher PVE.

A new measure of prognostic separation in survival data

Multivariable prognostic models are widely used in cancer and other disease areas, and have a range of applications in clinical medicine, clinical trials and allocation of health services resources. A well-founded and reliable measure of the prognostic ability of a model would be valuable to help define the separation between patients or prognostic groups that the model could provide, and to act as a benchmark of model performance in a validation setting. We propose such a measure for models of survival data. Its motivation derives originally from the idea of separation between Kaplan-Meier curves. We define the criteria for a successful measure and discuss them with respect to our approach. Adjustments for 'optimism', the tendency for a model to predict better on the data on which it was derived than on new data, are suggested. We study the properties of the measure by simulation and by example in three substantial data sets. We believe that our new measure will prove useful as a tool to evaluate the separation available-with a prognostic model.

The prognostic value of functional capacity evaluation in patients with chronic low back pain: part 1: timely return to work

STUDY DESIGN

Historical cohort study.

OBJECTIVES

We examined the validity of the Isernhagen Work Systems' Evaluation in predicting timely return to work.

SUMMARY OF BACKGROUND DATA

Functional Capacity Evaluations are used commonly to determine readiness for return to work, yet little is known of their validity.

METHODS

Workers' compensation claimants undergoing Functional Capacity Evaluations following work-related low back injury were studied. Two cohorts were formed, one on which exploratory analyses were conducted and a second for confirmation. Evaluation indicators were the number of tasks in the protocol rated as failed and performance during the floor-to-waist lift task. The primary outcome investigated was time receiving total temporary disability benefits (as a surrogate of return to work) and a secondary outcome was time until claim closure in the year following Evaluation. Cox proportional-hazards regression was used to determine the prognostic effect of Evaluation crudely and after controlling for potential confounders.

RESULTS

Few patients (4%) were found to pass all Evaluation tasks, yet most experienced total temporary disability suspension and claim closure within 1 year following Functional Capacity Evaluations. Better Evaluation performance was related to faster time to suspension of total temporary disability benefits and claim closure after controlling confounding factors, but explained little of the variation in these outcomes (approximately 10%). Performance on the floor-to-waist lift was as predictive as the number of failed tasks in the entire Functional Capacity Evaluations protocol.

CONCLUSIONS

Better performance on Evaluation was weakly associated with faster recovery; however, the amount of variation explained was small. One task in the Evaluation was as predictive as the entire protocol.

Predictive accuracy and explained variation

Measures of the predictive accuracy of regression models quantify the extent to which covariates determine an individual outcome. Explained variation measures the relative gains in predictive accuracy when prediction based on covariates replaces unconditional prediction. A unified concept of predictive accuracy and explained variation based on the absolute prediction error is presented for models with continuous, binary, polytomous and survival outcomes. The measures are given both in a model-based formulation and in a formulation directly contrasting observed and expected outcomes. Various aspects of application are demonstrated by examples from three forms of regression models. It is emphasized that the likely degree of absolute or relative predictive accuracy often is low even if there are highly significant and relatively strong covariates.

Comparing the importance of prognostic factors in Cox and logistic regression using SAS

Two SAS macro programs are presented that evaluate the relative importance of prognostic factors in the proportional hazards regression model and in the logistic regression model. The importance of a prognostic factor is quantified by the proportion of variation in the outcome attributable to this factor. For proportional hazards regression, the program %RELIMPCR uses the recently proposed measure V to calculate the proportion of explained variation (PEV). For the logistic model, the R(2) measure based on squared raw residuals is used by the program %RELIMPLR. Both programs are able to compute marginal and partial PEV, to compare PEVs of factors, of groups of factors, and even to compare PEVs of different models. The programs use a bootstrap resampling scheme to test differences of the PEVs of different factors. Confidence limits for P-values are provided. The programs further allow to base the computation of PEV on models with shrinked or bias-corrected parameter estimates. The SAS macros are freely available at www.akh-wien.ac.at/imc/biometrie/relimp

Impact of comorbidity on lung cancer survival

Lung cancer is associated with smoking and age, both of which are associated with comorbidity. We evaluated the impact of comorbidity on lung cancer survival. Data on 56 comorbidities were abstracted from the records of a cohort of 1,155 patients. Survival effects were evaluated with Cox regression (outcome crude death). The adjusted R(2) statistic was used to compare the survival variation explained by predictive variables. No comorbidity was observed in 11.7% of patients, while 54.3% had 3 or more (mean 2.97) comorbidities. In multivariate analysis, 19 comorbidities were associated with survival: HIV/AIDS, tuberculosis, previous metastatic cancer, thyroid/glandular diseases, electrolyte imbalance, anemia, other blood diseases, dementia, neurologic disease, congestive heart failure, COPD, asthma, pulmonary fibrosis, liver disease, gastrointestinal bleeding, renal disease, connective tissue disease, osteoporosis and peripheral vascular disease. Only the latter was protective. Some of the hazards of comorbidities were explained by more directly acting comorbidities and/or receipt of treatment. Stage explained 25.4% of the survival variation. In addition to stage, the 19 comorbidities explained 6.1%, treatments 9.2%, age 3.7% and histology 1.3%. Thirteen uncommon comorbidities (prevalence <6%) affected 21.2% of patients and explained 3.5% of the survival variation. Comorbidity count and the Charlson index were significant predictors but explained only 2.5% and 2.0% of the survival variation, respectively. Comorbidity has a major impact on survival in early- and late-stage disease, and even infrequent deleterious comorbidities are important collectively. Comorbidity count and the Charlson index failed to capture much information. Clinical practice and trials need to consider the effect of comorbidity in lung cancer patients.

Predictors of long-term outcomes in older breast cancer survivors: perceptions versus patterns of care

PURPOSE

There are few data on sequelae of breast cancer treatments in older women. We evaluated posttreatment quality of life and satisfaction in a national population.

PATIENTS AND METHODS

Telephone surveys were conducted with a random cross-sectional sample of 1,812 Medicare beneficiaries 67 years of age and older who were 3, 4, and 5 years posttreatment for stage I and II breast cancer. Regression models were used to estimate the adjusted risk of decrements in physical and mental health functioning by treatment. In a subset of women (n = 732), additional data were used to examine arm problems, impact of cancer, and satisfaction, controlling for baseline health, perceptions of ageism and racism, demographic and clinical factors, region, and surgery year.

RESULTS

Use of axillary dissection was the only surgical treatment that affected outcomes, increasing the risk of arm problems four-fold (95% confidence interval, 1.56 to 10.51), controlling for other factors. Having arm problems, in turn, exerted a consistently negative independent effect on all outcomes (P </=.001). Processes of care were also associated with quality of life and satisfaction. For example, women who perceived high levels of ageism or felt that they had no choice of treatment reported significantly more bodily pain, lower mental health scores, and less general satisfaction. These same factors, as well as high perceived racism, were significantly associated with diminished satisfaction with the medical care system.

CONCLUSION

With the exception of axillary dissection, the processes of care, and not the therapy itself, are the most important determinants of long-term quality of life in older women.

Application of staging systems for differentiated thyroid carcinoma in an endemic goiter region with iodine substitution

OBJECTIVE

To evaluate and compare staging systems for differentiated thyroid carcinoma and predicted outcome in an endemic goiter region with iodine substitution and to examine the risk profile of differentiated thyroid carcinoma and compare it against nongoiter regions.

SUMMARY BACKGROUND DATA

Differentiated (papillary or follicular) thyroid carcinoma has a favorable prognostic outcome. In numerous studies prognostic factors have been identified and staging systems created, particularly in Anglo-American centers (nonendemic goiter regions), to evaluate individual prognostic outcome.

METHODS

In a retrospective study, the authors assessed 440 patients with differentiated thyroid carcinoma (papillary, n = 293; follicular, n = 147) and a long-term follow-up of median 10.6 years to determine the predictive accuracy of nine staging systems applicable to the study population; the systems were compared by calculating the proportion of variation explained.

RESULTS

With regard to cause-specific mortality, the difference between the respective stages and/or risk groups was highly significant for every staging system. By means of calculating the proportion of variation explained, MACIS scoring supplied the most reliable prognostic information for differentiated thyroid carcinoma (relative importance 16.93%). EORTC and UICC/AJCC systems had a relative importance of 16.34% and 13.96%, respectively, also a high level of accuracy; this implies that they are superior to the other six staging systems. If we separate papillary and follicular carcinoma, for the former the MACIS score with a relative importance of 15.05% is clearly superior to the other staging systems, whereas for the latter the EORTC score and the UICC/AJCC staging system, with relative importance of 17.04% and 16.58%, respectively, yield the best prognostic information.

CONCLUSIONS

By applying staging systems in an endemic goiter region with iodine substitution, the best prognostic information for papillary thyroid carcinoma has been achieved with the MACIS score, while for follicular thyroid carcinoma the EORTC score and the UICC/AJCC system have the best prognostic accuracy. Because of the individual factors, which are easy to obtain and generally available (age, T, N, M classification), the uncomplicated handling, and the widespread use and the good predictive accuracy, the UICC/AJCC classification is the staging system of choice for comparing published results.

Measuring explained variation in linear mixed effects models

We generalize the well-known R(2) measure for linear regression to linear mixed effects models. Our work was motivated by a cluster-randomized study conducted by the Eastern Cooperative Oncology Group, to compare two different versions of informed consent document. We quantify the variation in the response that is explained by the covariates under the linear mixed model, and study three types of measures to estimate such quantities. The first type of measures make direct use of the estimated variances; the second type of measures use residual sums of squares in analogy to the linear regression; the third type of measures are based on the Kullback-Leibler information gain. All the measures can be easily obtained from software programs that fit linear mixed models. We study the performance of the measures through Monte Carlo simulations, and illustrate the usefulness of the measures on data sets.

Sequelae of axillary lymph node dissection in older women with stage 1 and 2 breast carcinoma

BACKGROUND

There are few data on the long-term sequelae of axillary dissection among older breast carcinoma patients. We describe the impact of axillary dissection in a cohort of older women.

METHODS

A longitudinal cohort of 571 patients with Stage 1 and 2 breast carcinoma, 67 years and older, diagnosed between 1995 and 1997 from 29 hospitals in five regions, and followed for 2 years. Data were collected from patients and medical charts. The primary outcome was posttreatment quality of life. Generalized estimation equation longitudinal modeling was used to evaluate the outcome, controlling for baseline function, comorbidity, age, clinical status, and other factors.

RESULTS

Sixty percent of women reported arm problems at some time in the 2 years after surgery. The cumulative risk of having arm problems 2 years posttreatment was three times higher (95% confidence interval 1.94-4.67) for women who underwent axillary surgery compared with women without axillary surgery, controlling for covariates. The effects of having axillary dissection and arthritis were multiplicative 2 years postsurgery. Arm problems were, in turn, the primary determinate of lower physical and mental functioning (P = 0.0001 and 0.04, respectively), controlling for other factors. Undergoing axillary dissection did not lessen fears about recurrence.

CONCLUSIONS

Arm problems after axillary dissection have a consistent negative impact on quality of life, suggesting that the risks may outweigh the potential benefits in this population.

Measuring comorbidity in patients with head and neck cancer

BACKGROUND

Comorbidities are diseases or conditions that coexist with a disease of interest. The importance of comorbidities is that they can alter treatment decisions, change resource utilization, and confound the results of survival analysis.

OBJECTIVE

The objective of this study was to determine the best comorbidity index to use in survival analysis of patients with squamous cell carcinoma of the head and neck.

METHOD

Four validated indexes, with very different methodologies (i.e., the Charlson Index, the Cumulative Illness Rating Scale, the Kaplan-Feinstein Classification, the Index of Co-existent Disease), were tested using data from 379 unselected consecutive patients with complete 3-year follow-up from the Kingston Regional Cancer Center. Kaplan-Meier analysis and Cox Proportional Hazards Regression were used to stratify patients into three levels of increasing severity of comorbidity for each index. The Proportion of Variance Explained and Receiver Operating Characteristics curves were used to compare the performance of the indexes.

CONCLUSION

The Kaplan-Feinstein Classification was the most successful in stratifying patients in this population.

Survival and symptom progression in a geographically based cohort of patients with primary biliary cirrhosis: follow-up for up to 28 years

BACKGROUND & AIMS

Although several excellent studies have described the natural history of primary biliary cirrhosis, most were reported from tertiary referral centers. We examined the prognosis of primary biliary cirrhosis in a comprehensive geographically defined cohort.

METHODS

We followed up 770 primary biliary cirrhosis patients prevalent between January 1987 and December 1994 until death, transplantation, or censor on January 1, 2000, by interview and review of case notes and death certificates. Analysis of survival data was performed with Kaplan-Meier methods and Cox regression.

RESULTS

Median patient survival was 9.3 years from diagnosis. Patient age, alkaline phosphatase, albumin, and bilirubin at diagnosis independently predicted survival in Cox modeling. Prothrombin time and histologic stage did not independently affect survival. Observed survival was predicted well by this model and by the Mayo prognostic score (R2(M) = 0.37 and 0.18, respectively; R2(M) is a likelihood-based measure of the percentage information gain from the model due to covariates). Forty-two percent of deaths were caused by liver disease. Thirty-nine patients had liver transplantations by the censor date. Survival was much poorer than for an age- and sex-matched control population (standardized mortality ratio = 2.87 [1.73 excluding liver deaths]). The most common symptoms at diagnosis were pruritus (18.9%) and fatigue (21.0%). Twenty-six percent of patients developed liver failure by 10 years after diagnosis.

CONCLUSIONS

Although primary biliary cirrhosis is often now diagnosed at an early stage, the diagnosis still carries important prognostic implications. A significant proportion of patients develop liver failure, require transplantation, or die prematurely after this diagnosis.

Accuracy of point predictions in survival analysis

Survival time prediction is important in many applications, particularly for patients diagnosed with terminal diseases. A measure of prediction error taken from the medical literature is advocated as a practicable method of quantifying reliability of point predictions. Optimum predictions are derived for familiar survival models and the accuracy of these predictions is investigated. We argue that poor predictive capability is inherent to standard survival models with realistic parameter values. A lung cancer example is used to illustrate difficulties in prediction in practice.

Is familial non-medullary thyroid carcinoma more aggressive than sporadic thyroid cancer? A multicenter series

BACKGROUND

The aggressiveness of familial non-medullary thyroid cancer (FNMTC) has been a subject of debate. The purpose of the study was to determine whether FNMTC is more aggressive than sporadic thyroid cancer.

METHODS

A multicenter retrospective matched-case control study of FNMTC versus sporadic non-medullary thyroid cancer was conducted. Disease-free survival (time to recurrence) for both groups was compared.

RESULTS

Forty-eight familial cases were compared with 144 age-, gender-, and stage-matched controls. Patients with FNMTC had a significantly shorter disease-free survival compared with sporadic non medullary thyroid cancer. Patients with FNMTC who presented with evidence of distant metastasis, or who were from families with more than 2 thyroid cancer-affected members, had the worst prognosis. The available staging systems were less likely to predict the outcome in patients with FNMTC than in patients with sporadic non-medullary thyroid cancer unless one accounted for the strength of family history in the staging system.

CONCLUSIONS

FNMTC is more aggressive than sporadic non-medullary thyroid cancer. The best predictors of a poor outcome in patients with FNMTC are the number of family members affected by thyroid cancer and evidence of distant metastasis.

Comparing tumour staging and grading systems: a case study and a review of the issues, using thymoma as a model

We consider the problem of comparing alternative cancer staging and grading systems. Statistical comparisons are on the basis of the ability to predict survival, but more qualitative criteria, such as parsimony, and distinctive prognostic separability of the categories are relevant also. Furthermore, some staging systems are clearly ordinal, while others are not. Three candidate statistical measures are studied and compared: explained variation; area under the ROC curve; and the probability of concordance of stage and survival. Each of these has individual strengths and weaknesses. A data set involving the staging of thymoma is analysed in detail to motivate the problem and illustrate the results.

Using SAS to calculate the Kent and O'Quigley measure of dependence for Cox proportional hazards regression model

Kent and O'Quigley (1988) apply the concept of information gain to define a measure of dependence (R-squared measure) between explanatory variables and a censored response variable within the framework of the Cox model. Two SAS macros to calculate this measure are presented. The first one is based on a Newton-Raphson search and makes use of the SAS IML procedure. The second one is a simple grid search using SAS DATA steps and Base-SAS procedures.

Medullary thyroid carcinoma: clinical characteristics, treatment, prognostic factors, and a comparison of staging systems

BACKGROUND

The clinical courses of patients with medullary thyroid carcinoma (MTC) vary, and a number of prognostic factors have been studied, but the significance of some of these factors remains controversial.

METHODS

The study group consisted of 104 patients with MTC or C-cell hyperplasia managed at the hospitals of the University of California, San Francisco, between January 1960 and December 1998. Patients were classified as having sporadic MTC, familial non-multiple endocrine neoplasia (MEN) MTC, MEN 2A, or MEN 2B. The TNM, European Organization for Research and Treatment of Cancer (EORTC), National Thyroid Cancer Treatment Cooperative Study (NTCTCS), and Surveillance, Epidemiology, and End Results (SEER) extent-of-disease stages were determined for each patient. The predictive values of these staging or prognostic scoring systems were compared by calculating the proportion of variance explained (PVE) for each system.

RESULTS

Fifty-six percent of the patients had sporadic MTC, 22% had familial MTC, 15% had MEN 2A, and 7% had MEN 2B. The overall average age at diagnosis was 38 years, and patients with sporadic MTC presented at an older age (P < 0.05). Thirty-two percent of the patients with hereditary MTC were diagnosed by screening (genetic and/or biochemical). These patients had a lower incidence of cervical lymph node metastasis (P < 0.05) and 94.7% were cured at last follow-up (P < 0.0001) compared with patients not screened. Patients with sporadic MTC who had systemic symptoms (diarrhea, bone pain, or flushing) had widely metastatic MTC and 33.3% of those patients died within 5 years. Overall, 49.4% of the patients were cured, 12.3% had recurrent MTC, and 38.3% had persistent MTC. The mean follow-up time was 8.6 years (median, 5.0 years) with 10.7% (n=11) and 13.5% (n=14) cause specific mortality at 5 and 10 years, respectively. Patients with persistent or recurrent MTC who died of MTC lived for an average of 3.6 years (ranging from 1 month to 23.7 years). Patients who had total or subtotal thyroidectomy were less likely to have persistent or recurrent MTC (P < 0.05), and patients who had total thyroidectomy with cervical lymph node clearance required fewer reoperations for persistent or recurrent MTC (P < 0.05) than patients who underwent lesser procedures. In univariate analysis, age, gender, clinical presentation, TNM stage, sporadic/hereditary MTC, distant metastasis, and extent of thyroidectomy were significant prognostic factors. Only age and stage, however, remained independent prognostic factors in multivariate analysis. The TNM, EORTC, NTCTCS, and SEER staging systems were all accurate predictors of survival, but the EORTC prognostic scoring system had the highest PVE in this cohort.

CONCLUSIONS

Screening for MTC and early treatment (total thyroidectomy with central neck lymph node clearance) had nearly a 100% cure rate. Patients with postoperative hypercalcitoninemia without clinical or radiologic evidence of residual tumor after apparently curative surgery may enjoy long term survival but have occult MTC. Only patient age at presentation and TNM stage were independent predictors of survival. The EORTC criteria, which included the greatest number of significant prognostic factors in our cohort, had the highest predictive value.

Predictive accuracy and explained variation in Cox regression

We suggest a new measure of the proportion of the variation of possibly censored survival times explained by a given proportional hazards model. The proposed measure, termed V, shares several favorable properties with an earlier V1 but also improves the handling of censoring. The statistic contrasts distance measures between individual 1/0 survival processes and fitted survival curves with and without covariate information. These distance measures, Dx and D, respectively, are themselves informative as summaries of absolute rather than relative predictive accuracy. We recommend graphical comparisons of survival curves for prognostic index groups to improve the understanding of obtained values for V, Dx, and D. Their use and interpretation is exemplified for a Yorkshire lung cancer study on survival. From this and an overview for several well-known clinical data sets, we show that the likely amount of relative or absolute predictive accuracy is often low even if there are highly significant and relatively strong prognostic factors.

Risk factors for chronic renal dysfunction in cardiac allograft recipients

Renal dysfunction is one of the most common and threatening complications in heart transplant recipients. Even if ciclosporin seems to play a central role in inducing renal damage, other factors may concur or predispose to renal injury. In order to identify factors responsible for renal dysfunction, we retrospectively studied a cohort of 114 cardiac transplant recipients during a follow-up period of at least 3 years. The patients had a normal renal function before and 0.5 months after heart transplantation. Doubling of baseline serum creatinine or attainment of serum creatinine steadily above 176.8 micromol/l (2.0 mg/dl) was used as criterion to define the end-point renal dysfunction. A series of clinical and laboratory variables were obtained from the patients' charts at different time intervals, and their prognostic value for the occurrence of renal dysfunction was calculated by Cox proportional hazards models. 23 out of 114 patients reached the end point after a median time period of 21 months. High serum triglyceride, alanine aminotransferase, alkaline phosphatase, ciclosporin, urea, glucose, and hemoglobin levels were shown to be associated with the development of renal dysfunction. Four variables, i.e., triglyceride, ciclosporin, urea, and alkaline phosphatase, had an independent prognostic value. Our results confirm a role for ciclosporin in inducing renal dysfunction and identify hyperlipidemia and an increased plasma urea level as risk factors for renal dysfunction in heart transplant recipients.

Assessment and comparison of prognostic classification schemes for survival data

Prognostic classification schemes have often been used in medical applications, but rarely subjected to a rigorous examination of their adequacy. For survival data, the statistical methodology to assess such schemes consists mainly of a range of ad hoc approaches, and there is an alarming lack of commonly accepted standards in this field. We review these methods and develop measures of inaccuracy which may be calculated in a validation study in order to assess the usefulness of estimated patient-specific survival probabilities associated with a prognostic classification scheme. These measures are meaningful even when the estimated probabilities are misspecified, and asymptotically they are not affected by random censorship. In addition, they can be used to derive R(2)-type measures of explained residual variation. A breast cancer study will serve for illustration throughout the paper.

ECL cell tumor and poorly differentiated endocrine carcinoma of the stomach: prognostic evaluation by pathological analysis

BACKGROUND & AIMS

Gastric endocrine tumors show a wide spectrum of clinical behavior, and prognostic assessement of individual tumors is difficult. The aims of this work were to identify predictors of tumor malignancy and patient outcome and to provide a rationale for treatment guidelines.

METHODS

Gastric endocrine tumors (86 enterochromaffin-like cell carcinoids and 16 poorly differentiated carcinomas) were investigated for 15 clinicopathologic variables and for expression of Ki67, P53, and BCL-2 proteins. Data were analyzed by univariate and multivariate statistics for evidence of tumor malignancy and patient survival.

RESULTS

Histological grades 2 and 3, size >/=3 cm, 9 or more mitoses, or >/=300 Ki67-positive cells per 10 high-power fields identified 26 of 33 (79%) malignant (metastatic or deeply invasive) tumors, and size <1 cm and/or growth restricted to the mucosa characterized 46 of 69 (67%) tumors with benign behavior during a median follow-up of 39 months. Malignancy-predictive models were developed using angioinvasion, size, clinicopathologic type, mitotic index, and Ki67 index. The same variables, in addition to deep gastric wall invasion and histological grade, predicted patient outcome.

CONCLUSIONS

Criteria for the assessment of malignancy risk and patient outcome were developed for the different tumors, providing a basis for treatment guidelines.

Assessing life expectancies of older nursing home residents

OBJECTIVE

Care of nursing home (NH) residents is often based on the usual survival of the home's residents. In order to improve our understanding of this population, and, thus, ultimately facilitate individualization of their care, we developed a mathematical model that predicts their survival.

SETTING

The Jewish Home and Hospital (JHH), a nursing home.

PARTICIPANTS

1145 older residents who were at the JHH from January 1, 1986, through July 1, 1986.

MEASUREMENTS

Information abstracted from medical records and JHH computerized data: clinical, demographic, and dependencies in activities of daily living (ADLs).

MAIN OUTCOME MEASURE

survival from July 1, 1986.

DESIGN

Retrospective cohort study via medical chart review. The study period covered admission to JHH through January 17, 1996. Accelerated failure time (AFT) models generated the life expectancy model derived from 50% of the study group and were validated on the remaining sample. We computed predicted AFT and proportional hazards (PH) life expectancies.

RESULTS

Significant, independent predictors of decreased survival were male gender, increased age, increase in summary ADL index, and impairment of cardiac, respiratory, neurological, and endocrine/metabolic systems. The interaction between gender and respiratory system impairment was significant. The Spearman correlation coefficients between the observed survivals and those predicted by the Phase I model are 0.49 for Phase I residents and 0.42 for Phase II residents. Our sample life table includes NH residents with different risk profiles and their associated survival estimates as well as interquartile ranges. AFT and PH survivals were similar.

CONCLUSION

This first comprehensive model that predicts survival of NH residents can help formulate public health policies and identify appropriate NH residents for clinical trials. The model is a promising step toward improving the health care of NH residents.

Critical study of prognostic factors in childhood acute lymphoblastic leukaemia: differences in outcome are poorly explained by the most significant prognostic variables. Fralle group. French Acute Lymphoblastic Leukaemia study group

We determined the proportion of survival variability explained by the usual prognostic factors in childhood acute lymphoblastic leukaemia (ALL) during a prognostic study of 1552 patients enrolled in three consecutive Fralle group protocols (Fralle 83, Fralle 87 and Fralle 89). The event-free survival rates at 5 years were 54.8% (SD 1.9), 43.1%) (SD 2.7) and 55.6% (SD 2.2), respectively. In the univariate analysis the following variables were predictive of poor outcome: male gender, elevated leucocytosis (> 50 x 10(9)/l), circulating blastosis. haemoglobin >12 g/dl, platelet count <100 x 10(9)/l, age under 1 year or over 9 years, enlarged mediastinum, nodes, spleen and liver, T phenotype, absence of CD10+ cells; testicular and meningeal involvement, poor response to induction therapy (CCSG M3), and LDH >400 U/l. Among the cytogenetic features, hyperdiploidy had a protective effect, whereas hypodiploidy, translocation and other structural abnormalities had a negative influence, particularly in cases of t(9;22) or t(4;11). Multivariate analysis summarized the prognostic information in terms of four variables: age, gender, leucocytosis and cytogenetic features. Missing data had little influence on the results. However, despite their significance in the multivariate analysis, these four variables each had very low predictive power (1.1% for gender, 2.0% for age, 3.5% for leucocytosis, and 1.6% for cytogenetic features). Thus, the most significant prognostic factors in childhood ALL each explain no more than 4% of the variability in prognosis. This may explain the disappointing practical value of these factors and underlines the need for prognostic tools in childhood ALL.