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Some recent developments for regression analysis of multivariate failure time data.

Cox's seminal 1972 paper on regression methods for possibly censored failure time data popularized the use of time to an event as a primary response in prospective studies. But one key assumption of this and other regression methods is that observations are independent of one another. In many problems, failure times are clustered into small groups where outcomes within a group are correlated. Examples include failure times for two eyes from one person or for members of the same family. This paper presents a survey of models for multivariate failure time data. Two distinct classes of models are considered: frailty and marginal models. In a frailty model, the correlation is assumed to derive from latent variables ("frailties") common to observations from the same cluster. Regression models are formulated for the conditional failure time distribution given the frailties. Alternatively, marginal models describe the marginal failure time distribution of each response while separately modelling the association among responses from the same cluster. We focus on recent extensions of the proportional hazards model for multivariate failure time data. Model formulation, parameter interpretation and estimation procedures are considered.

Clinical Trials as Topic

p53 protein accumulation predicts poor response to tamoxifen therapy of patients with recurrent breast cancer.

PURPOSE: Mutations of the p53 gene are frequently observed in primary breast cancer and accumulation of p53 protein has been used as a surrogate marker of p53 inactivation. Previous studies have shown that p53 accumulation is related to poor prognosis in primary breast cancer. We studied whether p53 protein accumulation is a predictive factor for response to tamoxifen treatment in patients with recurrent breast cancer. PATIENTS AND METHODS: Levels of p53, estrogen receptor (ER), progesterone receptor (PgR), and urokinase-type plasminogen activator (uPA) were assayed in cytosolic extracts derived from primary tumors of 401 tamoxifen-naive patients who developed recurrent disease. All patients in the study received tamoxifen therapy upon relapse (median follow-up, 69 months). Association of tested factors with response to tamoxifen treatment was studied by logistic regression analysis, and with survival after the start of treatment by Cox univariate and multivariate regression analysis. RESULTS: p53 levels (median, 0.23 ng/mg protein) were not related to ER or PgR levels, but positively correlated with uPA (P < .0001). In a test for trend, we observed an association of p53 protein levels with response to tamoxifen therapy. When dichotomized (at the median value), 42% in the p53-high versus 56% in the p53-low group showed a response. In multivariate analysis, including patient and tumor characteristics, p53 accumulation retained significance with the rate of response (odds ratio [OR], 0.48; 95% confidence interval [CI], 0.31 to 0.74; P < .001). Also in multivariate analysis, reduced survival after the start of tamoxifen therapy was observed in the p53-high group (relative hazards rate [RHR], 1.56, 95% CI, 1.17 to 2.10; P = .002). A statistically significant association between p53 levels and decreased tamoxifen response was seen only in the subset of patients whose tumors expressed low levels of ER or PgR (<75 fmol/mg protein). CONCLUSION: Measurement of primary tumor p53 levels may be effective in predicting response to tamoxifen therapy in recurrent breast disease. However, more confirming studies on the association between p53 protein accumulation and response to antiestrogen therapy are needed before tumor p53 levels can be used in routine clinical practice.

Adult

[Effect of the transfusion of blood and hemoderivatives on the prognosis of colorectal cancer].

In recent years in the literature several investigators described a negative effect of perioperative transfusion of blood and hemoderivatives on the prognosis of malignant tumors. Concerning the patients with colorectal carcinoma operated between 1979 and 1983 at Erlangen University Hospital these results could be proven. We observed a significantly worse 5-year survival rate for patients who received perioperative blood transfusion. However, multivariant analysis in Cox-regression model revealed other factors like tumor stage and localisation responsible for the poorer prognosis. Therefore blood transfusion seems not to have any influence on the prognosis itself. Furthermore we observed a significantly poorer prognosis concerning patients who perioperatively received fresh frozen plasma (FFP). Surprisingly multivariant analysis showed that FFP substitution in contrast to blood transfusion has an own prognostic influence. This difference in prognosis cannot be explained by selection criteria. The mechanism of the negative influence of FFP on the prognosis of colorectal carcinoma remains unclear and is investigated currently in prospective studies.

Aged

Therapy with recombinant human erythropoietin in patients with myelodysplastic syndromes.

We conducted a Phase I-II trial of recombinant human erythropoietin-beta (rhEPO) in patients with myelodysplastic syndrome (MDS). Patients with anemia and pathologically confirmed MDS were eligible for the study. Treatment consisted of rhEPO by subcutaneous injection thrice weekly for 6 weeks at one of three dose levels (100 U/kg (three patients), 200 U/kg (three patients) and 400 U/kg (14 patients)). Ferrous sulfate (325 mg po tid) was also administered if the transferrin saturation was below 30% (two patients). Patients were monitored with weekly CBC, white cell differential, and reticulocyte counts. Bone marrow examinations were performed at the conclusion of the treatment period and after a 2 week washout period. Patients who responded to therapy were continued on rhEPO at the same dose for 6 additional months. Response criteria included: 50% reduction in transfusion requirements compared with the 6 week pre-study period; doubling of reticulocyte count that was maintained on two determinations at least 1 week apart; or an increase in hemoglobin by at least 1.2 gm/dl without transfusions. Pre-treatment factors potentially predictive of response were analyzed by univariate analysis and in a multivariate fashion by classification and regression trees. Seven of the twenty patients sustained an untransfused rise in serum hemoglobin > or = 1.2 gm/dl. Four of the sixteen patients (including three of seven patients experiencing a rise in serum hemoglobin) who were transfusion-dependent prior to the study achieved a reduction or elimination of their transfusion requirements. Five of thirteen patients who received rhEPO during the extension phase had a continued response. A low baseline erythropoietin level (< 50 mU/ml) was the best predictor of hemoglobin response when controlling for other variables. rhEPO has a role in the treatment of certain patients with MDS, particularly in those whose endogenous serum erythropoietin levels are not markedly elevated.

Adult

A prospective, randomized double-blind trial comparing metoclopramide alone with metoclopramide plus dexamethasone in preventing emesis induced by high-dose cisplatin.

We observed 50 patients receiving high-dose cisplatin-based chemotherapy in a prospective, randomized double-blind trial. One group received metoclopramide (MCP) alone (total dose, 6 mg/kg), whereas the other group was given dexamethasone (DMS) (total dose, 60 mg) in addition to MCP. The patient characteristics of the two groups were comparable, confirming satisfactory randomization. Multivariate regression analysis failed to show any statistical significance in the antiemetic response between the two treatment groups. However, female patients receiving Adriamycin (Adria Laboratories, Columbus, OH) concurrently and obese persons exhibited more vomiting. The overall antiemetic response rate was 66%. Because the side effects were minimal, a higher dose of MCP is expected to improve emetic control without increasing toxicity. The use of a 36-hour assessment period in our study gave more meaningful data. An exponential increase in the dose of MCP is probably required, with respect to weight, to obtain the same antiemetic efficacy.

Adult

Analysis of relationships between symptoms and environmental factors over time.

Weekly respiratory symptom information was obtained on a random population of 3800 whites in Tucson. We asked weekly about 14 symptoms representing acute respiratory illnesses (ARI), rhinitis (Rh), and other conditions. The denominator for each week was about 80 randomly chosen subjects from the study population. Interactions of the air pollutants total suspended particulate, oxidants, carbon monoxide, nitrogen oxides for the basin, meteorological information, and aero-allergens were examined. The temporal and spatial interactions between the weekly symptoms and the environmental factors were tested utilizing multivariate methods such as Fourier analyses, multiple regression, and the stimulus-response method, adjusting for lags and controlling for season. Multiple regressions with a smoothing function (using fourier or other methods) yield significant correlations between symptoms and the environmental factors, and separate the ARI's from the Rh's and the miscellaneous symptoms.

Air Pollution

Trigeminal numbness and tic relief after microvascular decompression for typical trigeminal neuralgia.

OBJECTIVE: After most operative treatments for trigeminal neuralgia, long-term tic relief is closely correlated with postoperative numbness in the trigeminal distribution. Microvascular decompression (MVD) is proposed to relieve tic through a nontraumatic mechanism. We investigated the relationship between postoperative trigeminal numbness and tic relief in a large, prospectively followed cohort of patients treated with MVD for typical trigeminal neuralgia. METHODS: Of 1204 patients who underwent MVD for typical tic during a 20-year period, 522 had single MVDs on a single side, had not undergone ablative trigeminal procedures before or after MVD, and were still being followed in 1994. In 1994, patients graded facial numbness using a questionnaire (response rate, 92%) with a 5-point scale. Multivariate Cox and logistic regression methods were used. The analyses were adjusted for the time that had passed between the performance of MVD and the completion of the questionnaire (minimum, 2 yr). RESULTS: Seventeen percent of patients reported some degree of persistent facial numbness. Decompression of a vein at MVD (odds ratio, 2.5) and failure to find compression by the superior cerebellar artery (odds ratio, 2.0) independently predicted postoperative facial numbness, which in turn predicted postoperative burning and aching facial pain (odds ratio, 5.2-5.9). A trend toward worse outcome was noted in patients with numb faces (P = 0.3). Similar findings were noted in subgroups of patients in whom the superior cerebellar artery was decompressed at MVD (n = 381) and in whom a superior cerebellar artery with no vein was found (n = 120). In the latter subgroup, facial numbness (5.8% of patients) significantly predicted worse long-term outcome (P = 0.03). CONCLUSION: We found no evidence that postoperative trigeminal numbness predicts relief of typical tic after MVD. Trigeminal numbness was related to operative findings at MVD and predicted postoperative burning and aching facial pain. To minimize postoperative facial dysesthesia, trauma to the trigeminal root during MVD should be avoided when possible.

Decompression, Surgical

Physical workload and ergonomic factors associated with prevalence of back and neck pain in urban transit operators.

STUDY DESIGN: Back and neck pain was studied cross-sectionally in 1,449 urban transit drivers by linking medical data, self-reported ergonomic factors, and company records on job history. OBJECTIVES: The goal was to examine the relation between physical workload, ergonomic factors, and the prevalence of back and neck pain. SUMMARY OF BACKGROUND DATA: Researchers, to date, have not found an independent effect of ergonomic factors on back and neck pain while accounting for the effects of past and current physical workload. METHODS: Self-reported ergonomic factors, vehicle type, physical workload (measured as duration of driving), height, weight, age, and gender were analyzed in relation to back and neck pain, using multivariable logistic regression models. RESULTS: Physical workload showed a positive dose-response relation with back and neck pain after controlling for vehicle type, height, weight, age, and gender. The odds ratio for 10 years of driving was 3.43. Additional adjustment for ergonomic factors decreased this odds ratio to 2.55. Six out of seven ergonomic factors were significantly related to the prevalence of back and neck pain after adjustment for age, gender, height, weight, and physical workload. Problems with adjusting the seat had the largest effect (odds ratio = 3.52). Women had back and neck pain twice as frequently as men. CONCLUSION: The results support the hypothesis of a causal role of physical workload for the development of back and neck pain. Ergonomic factors partially mediated the risk of back and neck pain associated with driving, suggesting a potential for prevention of back and neck pain by ergonomic redesign of transit vehicles. Elevated risks for back and neck pain for female drivers were not explained by anthropometric and ergonomic factors.

Adult

[Interferon treatment of chronic hepatitis C--assessment of predictive factors to the effect of interferon treatment using multivariate analysis with the logistic regression model].

We treated 156 chronic hepatitis C patients with alpha-interferon (IFN) and assessed the response rate and the predictive factors to the effect of IFN treatment. Complete response (CR) rate was 39.1%, and CR with serum HCV-RNA disappearance rate was 29%. CR to IFN treatment was dependent on HCV serotype and serum HCV-RNA. Patients of serotype II and low serum HCV-RNA were effective to IFN treatment.

Adult

Statistical modeling of dose-response relationships in clinical trials--a case study.

This paper presents a model-based assessment of the relationship between the dose of a test treatment and response. The data set used in the analysis describes the results of two clinical trials that were designed to assess the dose-response relationship of a test treatment. The models described in the paper are fit using weighted regression as implemented by the SAS procedure CATMOD. Relationships between weighted regression and other similar procedures are discussed.

Anticholesteremic Agents

HLA-DR2, a marker for class I antigen sensitization.

After analysis of 423 hemodialysis patients in a transfusion program and 461 cadaver-donor renal transplants, we found that HLA-DR2 frequency was significantly higher in the responder (36%) than in the nonresponder patient group (19%), according to the percentage of PRA (panel reactive antibodies). Among DR2+ patients, the percentage of hypersensitized patients was twice that of DR2- patients. Graft survival curves in cadaver-donor renal transplants indicated a significantly lower survival when recipients were DR2+, even in recipient-donor pairs identical for class II antigens but mismatched for class I antigens. The prognostic probability of low response to transfusions by a stepwise logistic regression analysis showed the influence of sex and DR2 phenotype. By multivariant discriminant analysis, we found that the DR2 phenotype was one of the most influential transfusion sensitization risk factors. Our preliminary conclusion is that DR2 can be related to immune responsiveness to class I antigens.

Antilymphocyte Serum

Physicians, pharmaceutical sales representatives, and the cost of prescribing.

OBJECTIVE: To evaluate the influence of primary care physicians' attitudes toward and use of information provided by pharmaceutical representatives on prescribing costs in ambulatory practice. DESIGN: A mailed questionnaire collected information about physician demographic and practice characteristics and attitudes toward and use of information provided by pharmaceutical representatives. PARTICIPANTS: Kentucky physicians practicing primary care adult medicine (family medicine, general practice, general medicine; n = 1603). MAIN OUTCOME MEASURE: Relative cost of prescribing, based on physician responses to treatment choices for ambulatory clinical scenarios in primary care. A multivariable regression model assessed predictive relationships between independent variables and prescription costs. RESULTS: Four hundred forty-six returned questionnaires were suitable for analysis. No significant differences were noted in age, gender, days worked per week, or years since graduation between responders and a sample of nonresponders. A significant positive correlation was found between physician cost of prescribing and perceived credibility, availability, applicability, and use of information provided by pharmaceutical representatives (P < .01, Pearson's Product-Moment Correlation Coefficient). Physicians in academic or hospital-based practice settings had significantly lower prescribing costs than physicians in nonacademic and nonhospital practices (P = .001, analysis of variance). Frequency of use of information provided by pharmaceutical representatives (P = .01, multiple linear regression) and the group practice setting (P = .02, multiple linear regression) remained significant, independent positive predictors of cost in the multivariable regression model. CONCLUSIONS: Frequency of use of information provided by pharmaceutical representatives and the group practice, nonacademic and nonhospital setting may be associated with increased primary care physician prescribing costs.

Attitude of Health Personnel

Diffusion of innovative approaches to managing hypoplastic left heart syndrome.

OBJECTIVE: To study the perceptions of outcome and the diffusion into practice of innovative approaches such as palliative surgery and heart transplantation to treat hypoplastic left heart syndrome. DESIGN: A forced-choice questionnaire was sent to 108 US neonatology section heads. Responses were analyzed using Wilcoxon matched pairs, chi 2 analysis, and multivariant logistic regression. RESULTS: Ninety-three questionnaires (86%) were returned. All respondents discussed palliative surgery or transplantation or both with parents; 71 (76%) of 93 also discussed comfort care. Nineteen (24%) of 80 recommended comfort care only, 51 (64%) of 80 recommended surgery only, and 10 (12%) of 80 recommended both. Of the 61 respondents recommending one or both surgical procedures, palliative surgery was recommended by 44 and transplantation by 33. Respondents perceived that transplantation was associated with a lower 1-year mortality than palliative surgery (P < .001) and with a better quality of life (P < .001). CONCLUSIONS: Palliative surgery and transplantation are widely used to treat hypoplastic left heart syndrome. The continued availability of comfort care suggests that these surgical procedures are still in transition from experimental technology to standard of care.

Cardiac Surgical Procedures

Acute promyelocytic leukemia. Therapy results and prognostic factors.

From December 1976 to July 1986, 34 patients with acute promyelocytic leukemia (APL) were treated with daunorubicin (DNR) alone and simultaneous supportive therapy with low-dose heparin, platelet transfusions, and fresh frozen plasma. Two consecutive maintenance therapy regimens were employed in patients who achieved complete remission (CR): (1) a classical maintenance with methotrexate and 6-mercaptopurine, with DNR plus methyl-GAG re-inductions; (2) from 1982 an intensive sequential combination therapy regimen was administered. CR was achieved in 23 patients (68%). Only one patient had leukemic resistance. Other failures were a consequence of post-chemotherapy complications. A multivariate logistic regression analysis has been performed to evaluate the prognostic importance on response to remission induction of 25 patient and disease characteristics at diagnosis. The significant variables in decreasing order of significance were: serum albumin level, fever at diagnosis, serum creatinine level, and age. The median duration of remission and survival by Kaplan-Meier analysis were projected to be 24 and 25 months, respectively. Relapses occurred in 11 of 23 CR patients. Nine patients remained in the first remission from 5+ to 37+ months. Short-term (CR) and long-term results (duration of remission and survival) in APL treated for induction with DNR alone were similar to those obtained in other subtypes of acute myeloblastic leukemia by intensive combination chemotherapy.

Adolescent

Sex and diagnostic evaluation of possible coronary artery disease after exercise treadmill testing at one academic teaching center.

Controversy exists as to whether a sex bias exists that affects the diagnostic approach to suspected coronary artery disease: previous studies have used coronary angiography, but not other noninvasive testing, as a primary end point. This investigation examined posttest sex differences in diagnostic evaluation after exercise treadmill testing according to a broader end point than just coronary angiography alone. The design was a cohort analytic study with a 90-day follow-up. The study was done at the Cleveland Clinic Foundation, an academic group practice. Patients included consecutive adults (1023 men and 579 women) with chest pain but no documented coronary disease who were referred for symptom-limited exercise treadmill testing without adjunctive imaging; none had undergone prior invasive cardiac procedures. Main outcome measures included (1) performance of any subsequent diagnostic study (invasive or noninvasive) and (2) performance of coronary angiography as the next diagnostic study. During follow-up, 89 (8.7%) men and 48 (8.3%) women underwent a second diagnostic study (odds ratio 0.95; 95% confidence interval 0.66 to 1.37; p > 0.8), whereas 64 (6.3%) men and 21 (3.6%) women went straight to coronary angiography (odds ratio 0.56; 95% confidence interval 0.34 to 0.93; p = 0.02). In multivariable logistic regression analyses, which considered baseline clinical characteristics, the ST-segment response, and other prognostically important exercise responses, women tended to be less likely than men to be referred to any second test (adjusted odds ratio 0.70; 95% confidence interval 0.42 to 1.19; p > 0.1) but were markedly and significantly less likely to be referred straight to coronary angiography (adjusted odds ratio 0.33; 95% confidence interval 0.17 to 0.65). After exercise treadmill testing, women were only slightly less likely than men to be referred for subsequent diagnostic testing; they were, however, much less likely to be referred straight to coronary angiography as opposed to another noninvasive study.

Academic Medical Centers

Prognostic value of B-cell mitogen-induced and spontaneous thymidine uptake in vitro in chronic B-lymphocytic leukaemia cells.

Blood lymphocytes from 50 patients with chronic B-lymphocytic leukaemia (B-CLL) were cultured in vitro with and without the polyclonal B-cell activators (PBA) dextran sulphate (DxS), lipopolysaccharide from E. coli (LPS), and Epstein Barr virus (EBV). Patients with blood lymphocytes that showed a high spontaneous or PBA-induced 3H-thymidine uptake in 4 d cultures had a significantly shorter therapy-free survival than patients whose lymphocytes showed a low thymidine uptake. The DxS-induced cellular thymidine uptake was the most powerful predictor of prognosis. Eighteen patients with leukaemic cells responding to DxS stimulation had a median therapy-free survival of 17 months and a probability of 5 year therapy-free survival of less than 0.1, whereas for 30 patients with DxS unresponsive cells the corresponding figures were greater than 120 months and greater than 0.7, respectively (log rank, P less than 0.0001). A multivariate Cox's regression analysis revealed that the DxS-induced leukaemic cell response was of greater prognostic importance than clinical features such as blood counts and staging according to Rai and Binet. Therefore PBA-induced leukaemic cell thymidine uptake seems valuable in the prediction of prognosis in B-CLL.

Adult

A survey screen for prediction of apnea.

Questionnaire data from patients presenting at three sleep disorders centers were used to develop and assess a screening tool for sleep apnea based on the reporting of the frequency of various symptoms of sleep apnea and other sleep disorders plus age, body mass index (BMI) and gender. Patients were not specifically referred for suspicion of sleep apnea. Separate factor analyses of survey responses from 658, 193 and 77 respondents from the first, second and third sites, respectively, each yielded four orthogonal factors, one of which accounted for all the questions concerned with the frequency of disordered breathing during sleep. The survey was shown to be reliable in a subset of patients from one of the sites (test-retest correlation = 0.92). Survey data were then compared to a clinical measure of sleep apnea (respiratory disturbance index) obtained from polysomnography. A multivariable apnea risk index including survey responses, age, gender and BMI was estimated using multiple logistic regression in a total sample of 427 respondents from two of the sites. Predictive ability was assessed using receiver operating characteristic (ROC) curves. The area under the ROC curve was 0.79 (p < 0.0001). For BMI alone, it was 0.73, and for an index measuring the self-report of the frequency of apnea symptoms, it was 0.70. The multivariable apnea risk index has potential utility in clinical settings.

Adult

Predicting local recurrence of carcinoma of the rectum after preoperative radiotherapy and surgery.

A prospective study of prognostic factors has been carried out in a group of 186 patients with tethered rectal carcinomas. Of these, 97 were randomized to surgery alone and 89 to receive preoperative radiotherapy (20 Gy in four fractions). DNA ploidy was determined by flow cytometry. DNA aneuploidy was detected in 60 patients (62 per cent) in the surgery only group, but in only 33 patients (37 per cent) after radiotherapy (P less than 0.01). There was a significant reduction in local recurrence in irradiated patients (P less than 0.0001). DNA diploid tumours were less likely to recur locally. This was more marked in the radiotherapy group (P = 0.01) than in the surgery only group (P = 0.06). After radiotherapy, only the surgeons' assessments of a 'curative' resection and DNA ploidy were independent predictors of local recurrence in multivariate regression analysis, whilst Dukes' classification was not. In conclusion, DNA ploidy may indicate response to radiotherapy and is an important predictor of subsequent local tumour progression.

Combined Modality Therapy