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A model for the internal evaluation of the quality of care after lung resection in the elderly.

OBJECTIVES: The objective of this study was to develop a logistic model for internal audit in a population of elderly patients submitted to lung resection. METHODS: Three hundred twenty-six patients older than 70 years of age and submitted to lung resection for lung carcinoma were retrospectively analyzed. Univariate and logistic regression analyses yielded a model for the prediction of postoperative complications that was validated by bootstrap resampling analysis. The model was then used to assess the performance of our unit during two successive periods of activity ('early', 1993-1999; 'late', 2000-2003). RESULTS: Significant independent predictors of postoperative complications were a low ppoFEV1 (P < 0.0001) the presence of concomitant cardiac disease (P = 0.01) and extended resection (P = 0.03). The observed morbidity rate in the late period was higher than that in the early period (48.3 vs. 33.8%; P = 0.008). The predicted morbidity rate was also higher in the late period, compared to that in the early period (44 vs. 39%; P = 0.003). Moreover, no differences were noted between predicted and observed morbidity rates in each of the two periods (early, P = 0.4 late, P = 0.5). CONCLUSIONS: We showed that applying a model of risk-adjustment in elderly patients submitted to lung resection was useful for the internal evaluation of the quality of care and prevented misleading information derived by the comparison of the crude rates of the observed morbidity.

Aged↗

Linear regression analysis of binary response data with mixed covariates - a simulation study.

In a clinical trial with binary outcome, analyses are required for treatment or study group comparisons adjusted for covariate effects. A special problem arises with "mixed binary and Gaussian covariates", i.e., when some covariates are binary and some are continuous and may be assumed to be Gaussian. The correct model for such a data structure is of the logistic form. In the past, analyses of such data have been carried out by linear regression as well as by logistic regression methods. In this article, computer simulation was used to study the type I error level of linear regression analysis tests for treatment comparisons, when applied to a binary outcome variate obeying a logistic model with mixed binary and Gaussian covariates. It was found that the true type I error level depends on the distribution of covariates among treatment groups and on the magnitudes of the actual covariate effects, and can differ importantly from that assumed under Gaussian theory. Some recommendations are made for developing computer package programs for this problem.

Clinical Trials as Topic↗

Models developed by three techniques did not achieve acceptable prediction of binary trauma outcomes.

BACKGROUND AND OBJECTIVES: To develop prediction models for outcomes following trauma that met prespecified performance criteria. To compare three methods of developing prediction models: logistic regression, classification trees, and artificial neural networks. METHODS: Models were developed using a 1996-2001 dataset from a major trauma center in Victoria, Australia. Developed models were subjected to external validation using the first year of data collection, 2001-2002, from a state-wide trauma registry for Victoria. Different authors developed models for each method. All authors were blinded to the validation dataset when developing models. RESULTS: Prediction models were developed for an intensive care unit stay following trauma (prevalence 23%) using information collected at the scene of the injury. None of the three methods gave a model that satisfied the performance criteria of sensitivity >80%, positive predictive value >50% in the validation dataset. Prediction models were also developed for death (prevalence 2.9%) using hospital-collected information. The performance criteria of sensitivity >95%, specificity >20% in the validation dataset were not satisfied by any model. CONCLUSION: No statistical method of model development was optimal. Prespecified performance criteria provide useful guides to interpreting the performance of developed models.

Adult↗

Economic efficiency of gate-keeping compared with fee for service plans: a Swiss example.

STUDY OBJECTIVE: The impact of isolated gate-keeping on health care costs remains unclear. The aim of this study was to assess to what extent lower costs in a gate-keeping plan compared with a fee for service plan were attributable to more efficient resource management, or explained by risk selection. DESIGN: Year 2000 costs to the Swiss statutory sick funds and potentially relevant covariates were assessed retrospectively from beneficiaries participating in an observational study, their primary care physicians, and insurance companies. To adjust for case mix, two-part regression models of health care costs were fitted, consisting of logistic models of any costs occurring, and of generalised linear models of the amount of costs in persons with non-zero costs. Complementary data sources were used to identify selection effects. SETTING: A gate-keeping plan introduced in 1997 and a fee for service plan, in Aarau, Switzerland. PARTICIPANTS: Of each plan, 905 randomly selected adult beneficiaries were invited. The overall participation rate was 39%, but was unevenly distributed between plans. MAIN RESULTS: The characteristics of gate-keeping and fee for service beneficiaries were largely similar. Unadjusted total costs per person were Sw fr 231 (8%) lower in the gate-keeping group. After multivariate adjustment, the estimated cost savings achieved by replacing fee for service based health insurance with gate-keeping in the source population amounted to Sw fr 403-517 (15%-19%) per person. Some selection effects were detected but did not substantially influence this result. An impact of non-detected selection effects cannot be ruled out. CONCLUSIONS: This study hints at substantial cost savings through gate-keeping that are not attributable to mere risk selection.

Adult↗

Risk factors for infertility in nursing cows linked to calving.

An ecopathological survey was conducted between 1987 and 1989 in 116 French herds with 3,590 cows in order to study the risk factors for infertility linked to calving. Based upon an analysis model of etiological interactions, the complementary use of a logistic model and factorial analysis followed by classification allowed demonstration of the direct and indirect, effects upon infertility, breed factors, parity, fattening, comfort, calf characteristics (number, sex, weight, presentation), as well as the difficulty and complications which may have been associated with calving. By association, these factors determine the profile of the cows at risk.

Animal Husbandry↗

A statistical model for predicting response of breast cancer patients to cytotoxic chemotherapy.

A binary logistic model is used for predicting response to cytotoxic chemotherapy for a breast cancer patient on the basis of her tumor enzyme activity profile. The enzymes used in the model are lactate dehydrogenase, nicotinamide adenine dinucleotide phosphate-isocitrate dehydrogenase, and phosphoglucomutase, all of which were measured on primary tumor specimens from each patient. The statistical model provides an estimate of the probability that an individual will respond to treatment. Chemotherapeutic treatment consisting of combination cytotoxic drugs and subsequent evaluation of patient response followed cooperative group protocol guidelines, including outside review to confirm the patient evaluation. The model based on this study, which represents 5 years of patient follow-up, correctly predicts clinical outcome in 32 of the 37 cases available.

Antineoplastic Agents↗

Models for the incubation of AIDS and variations according to age and period.

The objective of the methods proposed is to provide a parametric model for the incubation of AIDS and to use the chosen parameterization to test for the effect of age at seroconversion, and, after adjusting for markers of immunosuppression, to assess variations in periods corresponding to different levels of use of AIDS therapies at the population level. We compared the fit of Weibull, log-normal and three-parameter logistic models incorporating truncation in prevalent cohort and interval censored data. We showed the advantages by restricting the analysis to follow-up durations of greater than five years to improve estimation of the tail of the distribution for the prediction of long-term survivors. We applied the proposed methods to the combination of 1649 seroprevalent and 476 seroconverters with 1022 and 177 AIDS cases, respectively, who have been followed in the Multicenter AIDS Cohort Study (MACS) up to April 1995. Differences according to age at seroconversion are quantified in terms of relative percentiles and their associated 95 per cent confidence intervals were calculated using methods of multiple imputation. Using the proposed methods, we found that the log-normal model provides a fit as good as the three-parameter logistic; both are close to the non-parametric estimate and are significantly better than the fit of the Weibull model. We found that the older the age at seroconversion, the shorter the time to AIDS (relative percentile = 0.72 for age > or = 40 versus age < 25), and that the incubation of AIDS in calendar periods where treatment has been widely administered has been significantly longer among individuals with low CD4 cell counts.

Acquired Immunodeficiency Syndrome↗

A simulation study of measurement error correction methods in logistic regression.

Measurement error models in logistic regression have received considerable theoretical interest over the past 10-15 years. In this paper, we present the results of a simulation study that compares four estimation methods: the so-called regression calibration method, probit maximum likelihood as an approximation to the logistic maximum likelihood, the exact maximum likelihood method based on a logistic model, and the naive estimator, which is the result of simply ignoring the fact that some of the explanatory variables are measured with error. We have compared the behavior of these methods in a simple, additive measurement error model. We show that, in this situation, the regression calibration method is a very good alternative to more mathematically sophisticated methods.

Calibration↗

[Modeling correlated data in epidemiology: mixed or marginal model?].

Correlated observations (within centers, families, subjects,.) are common in epidemiology. Even when one is only interested in the modeling of means according to risk factors, it is also necessary to model the variance-covariance matrix of the observations in order to make correct inferences on the parameters of interest. All the more so when the aim of the survey is the measurement of these correlations or of the variance of the random effects from which they are assumed to originate. We discuss, within the framework of the linear and of the logistic models, the implications of two choices for the modeling of covariances. The mixed model shows the unobserved elements responsible for the similarity between certain observations. In a longitudinal survey, for instance, one can use a random effect, specific to each subject, expressing how much a subject's trajectory is translated as compared to what is expected according to its characteristics (age, sex,.). The marginal approach leads to modeling separately the means and the covariance matrix of the observations. The distinction between these two approaches is important for non linear models, in particular the logistic one. We insist on the interconnection between a mixed model formulation and a marginal one, as well as on the implication of the choice in terms of the parameters' interpretation.

Epidemiologic Research Design↗

Time factor in postoperative radiotherapy: a multivariate locoregional control analysis in 868 patients.

PURPOSE: To study locoregional tumor control in postoperative radiotherapy (PRT) for head-and-neck cancer in relation to the position and duration of treatment gaps, duration of the interval surgery-radiotherapy, and to the other potentially prognostic variables. METHODS AND MATERIALS: The retrospective study included 868 patients with cancer of the larynx, oral cavity, oropharynx, and hypopharynx treated in Gliwice between 1980 and 1997. Mean total radiation dose, dose per fraction, overall radiation treatment time (OTT), and the interval surgery-PRT were 62.8 Gy, 2.1 Gy, 45 days, and 63 days, respectively. No interruptions during PRT (except for weekend breaks) appeared in 30% of patients, whereas 19% had more than 5 days of gap. The actuarial locoregional recurrence-free survival (RFS) has been examined using multivariate Cox regression model, and the ultimate locoregional tumor control probability using a logistic model. RESULTS: Increased duration of treatment gaps, positive resection margins, pathologically proven metastases to the neck nodes, and extralaryngeal site of cancer were significantly related to a decrease in RFS. The duration of time interval surgery-PRT appeared, by contrast, only borderline significant for RFS. The relative risk of locoregional recurrence was approximately the same for the gaps in days 1-21 as for the "late" gaps (days >21), except in a subgroup of patients with positive clinical margins. The logistic analysis revealed a significant time-related displacement of the dose-response curves for PRT. The detriment from the protraction of OTT appeared to be larger than the benefit from the equivalent shortening of OTT. CONCLUSIONS: Although the conclusions from this study must be regarded as only hypothesis-generating, we assume that a highly significant adverse influence of radiation treatment gaps on the rate of tumor control is consistent with rapid repopulation of cancer clonogenes during PRT. Lack of significant effect of the position of gaps on locoregional tumor control after radical surgery may suggest that a lag time for the onset of repopulation in PRT is short. A less likely explanation is that the total amount of regeneration during OTT is the same, regardless of the timing of the gap, even if all the repopulation occurred late. The magnitude of the detriment in tumor control from prolonged interval surgery-PRT indicates that repopulation of cancer cells between surgery and radiotherapy is not as fast as between the fractions of radiotherapy.

Adult↗

Mathematical modelling of microbial growth in packaged refrigerated beef stored at different temperatures.

Gompertz and logistic models were fitted to experimental counts of microorganisms growing in beef stored at 0, 4, 7, 9 and 10 degrees C. Samples were packaged in polyethylene (high gaseous permeability) and in EVA/SARAN/EVA (low gaseous permeability) films, being EVA ethyl vinyl acetate and SARAN polyvinyl and polyvinylidene chloride copolymer. Lag phase duration (LPD) and specific growth rate (mu) were obtained as derived parameters for lactic acid bacteria, Enterobacteriaceae, Pseudomonas sp. and psychrotrophic microorganisms. The reciprocal of LPD was fitted to an Arrhenius type equation; LPD of lactic acid bacteria showed a marked dependence on temperature, with activation energy values (ELPD) of 222.2 and 216.9 kJ/mol for polyethylene and ESE respectively. The effect of initial microbial population at different storage temperatures on adaptation period was analyzed. As the initial microbial population increased, adaptation period decreased for all studied microorganisms and for both packaging films. The effect of temperature on specific growth rate was better interpreted by the Arrhenius model than by the linear or the square root equations. Psychrotrophic microorganisms in beef showed the highest activation energy values for specific growth rate (E mu) in both packaging films, being E mu 85.50 and 103.10 KJ/mol for polyethylene and ESE film respectively. In both films, Enterobacteriaceae showed the lowest E mu values, being 15.33 and 59.89 kJ/mol in ESE and polyethylene respectively. The final number of microorganisms (maximum population density) did not show significant changes with storage temperature.

Animals↗

A time-dependent logistic hazard function for modeling variable age of onset in analysis of familial diseases.

The paper presents an extension of the regressive logistic models proposed by Bonney [Biometrics 42:611-625, 1986], to address the problems of variable age-of-onset and time-dependent covariates in analysis of familial diseases. This goal is achieved by using failure time data analysis methods, and partitioning the time of follow up in K mutually exclusive intervals. The conditional probability of being affected within the kth interval (k = 1...K) given not affected before represents the hazard function in this discrete formulation. A logistic model is used to specify a regression relationship between this hazard function and a set of explanatory variables including genotype, phenotypes of ancestors, and other covariates which can be time dependent. The probability that a given person either becomes affected within the kth interval (i.e., interval k includes age of onset of the person) or remains unaffected by the end of the kth interval (i.e., interval k includes age at examination of the person) are derived from the general results of failure time data analysis and used for the likelihood formulation. This proposed approach can be used in any genetic segregation and linkage analysis in which a penetrance function needs to be defined. Application of the method to familial leprosy data leads to results consistent with our previous analysis performed using the unified mixed model [Abel and Demenais, Am J Hum Genet 42:256-266, 1988], i.e., the presence of a recessive major gene controlling susceptibility to leprosy. Furthermore, a simulation study shows the capability of the new model to detect major gene effects and to provide accurate parameter estimates in a situation of complete ascertainment.

Adolescent↗

Modern psychometric methods for detection of differential item functioning: application to cognitive assessment measures.

Cognitive screening tests and items have been found to perform differently across groups that differ in terms of education, ethnicity and race. Despite the profound implications that such bias holds for studies in the epidemiology of dementia, little research has been conducted in this area. Using the methods of modern psychometric theory (in addition to those of classical test theory), we examined the performance of the Attention subscale of the Mattis Dementia Rating Scale. Several item response theory models, including the two- and three-parameter dichotomous response logistic model, as well as a polytomous response model were compared. (Log-likelihood ratio tests showed that the three-parameter model was not an improvement over the two-parameter model.) Data were collected as part of the ten-study National Institute on Aging Collaborative investigation of special dementia care in institutional settings. The subscale KR-20 estimate for this sample was 0.92. IRT model-based reliability estimates, provided at several points along the latent attribute, ranged from 0.65 to 0.97; the measure was least precise at the less disabled tail of the distribution. Most items performed in similar fashion across education groups; the item characteristic curves were almost identical, indicating little or no differential item functioning (DIF). However, four items were problematic. One item (digit span backwards) demonstrated a large error term in the confirmatory factor analysis; item-fit chi-square statistics developed using BIMAIN confirm this result for the IRT models. Further, the discrimination parameter for that item was low for all education subgroups. Generally, persons with the highest education had a greater probability of passing the item for most levels of theta. Model-based tests of DIF using MULTILOG identified three other items with significant, albeit small, DIF. One item, for example, showed non-uniform DIF in that at the impaired tail of the latent distribution, persons with higher education had a higher probability of correctly responding to the item than did lower education groups, but at less impaired levels, they had a lower probability of a correct response than did lower education groups. Another method of detection identified this item as having DIF (unsigned area statistic=3.05, p<0.01, and 2.96, p<0.01). On average, across the entire score range, the lower education group's probability of answering the item correctly was 0.11 higher than the higher education group's probability. A cross-validation with larger subgroups confirmed the overall result of little DIF for this measure. The methods used for detecting differential item functioning (which may, in turn, be indicative of bias) were applied to a neuropsychological subtest. These methods have been used previously to examine bias in screening measures across education and ethnic and racial subgroups. In addition to the important epidemiological applications of ensuring that screening measures and neuropsychological tests used in diagnoses are free of bias so that more culture-fair classifications will result, these methods are also useful for the examination of site differences in large multi-site clinical trials. It is recommended that these methods receive wider attention in the medical statistical literature.

Aged↗

Lipoprotein oxidation and progression of carotid atherosclerosis.

BACKGROUND: Epidemiological studies and animal experiments have provided evidence supporting the role of lipid peroxidation in atherogenesis and cardiovascular diseases. Direct evidence linking lipid oxidation to atherosclerotic progression in humans, however, has been lacking. We investigated the association of lipid oxidation products with the progression of early carotid atherosclerosis in hypercholesterolemic men from eastern Finland. METHODS AND RESULTS: Twenty subjects with a fast progression and 20 with no progression of carotid atherosclerosis in 3 years were selected from > 400 participants in the Kuopio Atherosclerosis Prevention Study. Progression of carotid atherosclerosis was assessed by high-resolution B-mode ultrasonography. Serum 7 beta-hydroxycholesterol, a major oxidation product of cholesterol in membranes and lipoproteins, and seven other cholesterol oxidation products were measured by isotope dilution-mass spectrometry, lipid hydroperoxides in LDL fluorometrically as thiobarbituric acid-reactive substances (TBARS) and oxidation susceptibility of LDL and VLDL kinetically. High concentrations of serum 7 beta-hydroxycholesterol (beta = 47, P = .0005), cigarette smoking (beta = .35, P = .0167), and LDL TBARS (beta = .23, P = .0862) and an increased oxidation susceptibility of VLDL + LDL (beta = .22 P = .1114) were the strongest predictors of a 3-year increase in carotid wall thickness of more than 30 variables tested in step-up least-squares regression models. A 10-variable model explained 60% of the atherosclerotic progression. In a multivariate logistic model, the risk of experiencing a fast progression increased by 80% (P = .013) per unit (microgram/L) of 7 beta-hydroxycholesterol. CONCLUSIONS: The findings of this study provide further evidence to support an association between lipid oxidation and atherogenesis in humans.

Arteriosclerosis↗

Mitotic rate and younger age are predictors of sentinel lymph node positivity: lessons learned from the generation of a probabilistic model.

BACKGROUND: Sentinel lymph node (SLN) biopsy allows surgeons to identify patients with subclinical nodal involvement who may benefit from lymphadenectomy and, possibly, adjuvant therapy. Several factors have been variably, and sometimes discordantly, reported to have predictive value for SLN metastasis to best select which patients require SLN biopsy. METHODS: We reviewed 419 patients who underwent SLN biopsy for melanoma from a prospectively collected melanoma database. To derive a probabilistic model for the occurrence of a positive SLN, a multivariate logistic model was fit by using a stepwise variable selection method. The accuracy of each model was evaluated by using receiver operator characteristic curves. RESULTS: On univariate analysis, the number of mitoses per square millimeter, increasing Breslow depth, decreasing age, ulceration, and melanoma on the trunk showed a significant relationship to a positive SLN. Multivariate analysis revealed that once age, mitotic rate, and Breslow thickness were included, no other factor, including ulceration, was significantly associated with a positive SLN. The data suggest that younger patients with tumors <1 mm may still have a substantial risk for a positive SLN, especially if the mitotic rate is high. CONCLUSIONS: In addition to Breslow depth, mitoses per square millimeter and younger age were factors identified as independent predictors of a positive SLN. This model may identify patients with thin melanoma at sufficient risk for metastases to justify SLN biopsy.

Adult↗

Mechanisms of cuticular uptake of xenobiotics into living plants: evaluation of a logistic-kinetic penetration model.

The objective of this study was to determine whether a logistic-kinetic penetration model could be applied to whole plant uptake. Uptake over 24 h was determined for three model compounds, applied in the presence and absence of surfactants, into the leaves of two plant species. Data for two time intervals were used in the model to predict uptake at intermediate intervals and compared with experimental results. Overall, the model fit the whole plant uptake data well. The study confirmed that an increase (or decrease) in active ingredient (ai) concentration or an increase in contact area will have no effect on the penetration rate factor, q, within the normal working concentration range. This enabled uptake to be predicted at different times for concentrations of ai not already studied, having first derived q for one concentration of the formulation of interest and having 24 h (maximum) uptake results for all formulations and concentrations of interest. The advantages of the models and equations described are that few variables are required, and they are simple to measure.

Carbon Radioisotopes↗

Design and analysis of drug combination experiments.

In this paper we present and discuss a novel, simple and easy to implement parametric modeling approach to assess synergy. An extended three parameter log-logistic model is used to analyse the data and calculate confidence intervals of the interaction indices. In addition the model corrects for the bias due to plate-location effects. The analysis is performed with PROC NLMIXED and SAS-code is provided. The approach is illustrated using data coming from an oncology study in which the inhibition effect of a combination of two compounds is studied using 96-well plates and a fixed-ratio design.

Algorithms↗

Interaction between enalapril and aspirin on mortality after acute myocardial infarction: subgroup analysis of the Cooperative New Scandinavian Enalapril Survival Study II (CONSENSUS II)

The use of angiotensin-converting enzyme (ACE) inhibitors early after an acute myocardial infarction to reduce mortality has been studied in several trials with inconsistent results. Aspirin (ASA) has become a well-documented therapeutic adjunct in patients with coronary heart disease. Attention has recently been focused on a possible interaction between ASA and ACE inhibitors. We therefore reanalyzed data from the Cooperative New Scandinavian Enalapril Survival Study II (CONSENSUS II) to find any evidence of differential effects of the ACE inhibitor enalapril in subgroups defined by use of ASA at baseline. Logistic regression tested the multiplicative interaction. We used Rothman synergy index S, which would be equal to unity under additivity, and less than unity when suggesting antagonism, to examine the postulated interaction with departure from an additive model. Logistic regression showed that the enalapril-ASA interaction term was a significant predictor of mortality at the end of the study (p = 0.047), and was a borderline significant predictor of mortality 30 days after randomization (p = 0.085). The Rothman synergy index S was 0.66 (95% confidence interval 0.46 to 0.94) for mortality at the end of the study, and 0.68 ( 0.44 to 1.04) for 30-day mortality, indicating antagonism between enalapril and ASA with departure from an additive model. Thus, we found evidence of enalapril-ASA interaction. The effect of enalapril was less favorable among patients taking ASA than among patients not taking ASA at baseline.

Aged↗