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PubMed2005

Performance of a mixed effects logistic regression model for binary outcomes with unequal cluster size.

When a clustered randomized controlled trial is considered at a design stage of a clinical trial, it is useful to consider the consequences of unequal cluster size (i.e., sample size per cluster). Furthermore, the assumption of independence of observations within cluster does not hold, of course, because the subjects share the same cluster. Moreover, when the clustered outcomes are binary, a mixed effect logistic regression model is applicable. This article compares the performance of a maximum likelihood estimation of the mixed effects logistic regression model with equal and unequal cluster sizes. This was evaluated in terms of type I error rate, power, bias, and standard error through computer simulations that varied treatment effect, number of clusters, and intracluster correlation coefficients. The results show that the performance of the mixed effects logistic regression model is very similar, regardless of inequality in cluster size. This is illustrated using data from the Prevention Of Suicide in Primary care Elderly: Collaborative Trial (PROSPECT) study.

Algorithms↗
PubMed2004

LIP index for peptide classification using MS/MS and SEQUEST search via logistic regression.

This study addresses the issue of peptide identification resulting from tandem mass spectrometry proteomics analysis followed by database search. This work shows that the Logistic Identification of Peptides (LIP) Index achieves high sensitivity and specificity for peptide classification relative to a manually verified "gold" standard and also accurately estimates the probability of a correct peptide match. The LIP Index is a weighted average of SEQUEST output variables based on logistic regression models and is a transparent, easy to use, inclusive, extendable, and statistically sound approach to classify correct peptide identifications. Modifications, such as normalizing cross-correlations (Xcorr) for peptide length, adjusting for charge state, and the number of tryptic termini, significantly improve the fit the logistic regression models, as well as increase sensitivity and specificity. The LIP Index also incorporates earlier developed statistical models on spectral quality assessment and peptide identification, which further improves sensitivity and specificity.

Algorithms↗
PubMed2003

Detecting patterns of occupational illness clustering with alternating logistic regressions applied to longitudinal data.

In longitudinal surveillance studies of occupational illnesses, sickness episodes are recorded for workers over time. Since observations on the same worker are typically more similar than observations from different workers, statistical analysis must take into account the intraworker association due to workers' repeated measures. Additionally, when workers are employed in groups or clusters, observations from workers in the same workplace are typically more similar than observations from workers in different workplaces. For such cluster-correlated longitudinal data, alternating logistic regressions may be used to model the pattern of occupational illness clustering. Data on 182 Latino farm workers from a 1999 North Carolina study on green tobacco sickness provided an estimated pairwise odds ratio for within-worker clustering of 3.15 (95% confidence interval (CI): 1.84, 5.41) and an estimated pairwise odds ratio for within-camp clustering of 1.90 (95% CI: 1.22, 2.97). After adjustment for risk factors, the estimated pairwise odds ratios were 2.13 (95% CI: 1.18, 3.86) and 1.41 (95% CI: 0.89, 2.24), respectively. In this paper, a comparative analysis of alternating logistic regressions with generalized estimating equations and random-effects logistic regression is presented, and the relative strengths of the three methods are discussed.

Agricultural Workers' Diseases↗
PubMed1999

Multiple-trait mapping of quantitative trait loci after selective genotyping using logistic regression.

Experiments to map QTL usually measure several traits, and not uncommonly genotype only those animals that are extreme for some trait(s). Analysis of selectively genotyped, multiple-trait data presents special problems, and most simple methods lead to biased estimates of the QTL effects. The use of logistic regression to estimate QTL effects is described, where the genotype is treated as the dependent variable and the phenotype as the independent variable. In this way selection on phenotype does not bias the results. If normally distributed errors are assumed, the logistic-regression analysis is almost equivalent to a maximum-likelihood analysis, but can be carried out with standard statistical packages. Analysis of a simulated half-sib experiment shows that logistic regression can estimate the effect and position of a QTL without bias and confirms the increased power achieved by multiple-trait analysis.

Genotype↗
PubMed2004

The use of a new logistic regression model for predicting the outcome of pregnancies of unknown location.

BACKGROUND: The aim of this study was to generate and evaluate new logistic regression models from simple demographic and hormonal data to predict the outcome of pregnancies of unknown location (PULs). METHODS: Data were collected prospectively from 185 consecutive women classified as having a PUL by transvaginal scan; blood was taken at presentation and 48 h later to measure serum progesterone and HCG. These women were followed-up until the outcome was established: an intrauterine pregnancy (IUP), an ectopic pregnancy (EP) or a failing PUL. Three multi-categorical logistic regression models were tested. M1 was based on the HCG ratio (rate of change in HCG over 48 h), M2 was based on the average progesterone level (the mean of the progesterone level at 0 and 48 h) and M3 was based on the patient's age. RESULTS: A total of 102 failing PULs, 63 IUPs and 20 EPs were used in the training set to develop the new models. The best of these models, M3, gave a retrospective area under the receiver operating characteristic (ROC) curve of 0.984 for failing PUL, 0.995 for IUP and 0.920 for EP. All three models were tested prospectively on the test set of 196 cases. M1 outperformed M2 and M3 when tested prospectively. The area under the ROC curve (AUC) was 0.975 for failing PUL, 0.966 for IUP and 0.885 for EP. M1, for the detection of EP, had a sensitivity of 91.7%, a specificity of 84.2%, a positive likelihood ratio of 5.8, a positive predictive value of 27.5% and a negative predictive value of 99.4%. CONCLUSIONS: The logistic regression model M1, can predict which PULs will become failing PULs, IUPs and, most importantly, EPs based on the patient's HCG ratio alone.

Chorionic Gonadotropin↗
PubMed1997

Logistic regression when the outcome is measured with uncertainty.

In epidemiologic research, logistic regression is often used to estimate the odds of some outcome of interest as a function of predictors. However, in some datasets, the outcome of interest is measured with imperfect sensitivity and specificity. It is well known that the misclassification induced by such an imperfect diagnostic test will lead to biased estimates of the odds ratios and their variances. In this paper, the authors show that when the sensitivity and specificity of a diagnostic test are known, it is straightforward to incorporate this information into the fitting of logistic regression models. An EM algorithm that produces unbiased estimates of the odds ratios and their variances is described. The resulting odds ratio estimates tend to be farther from the null but have greater variance than estimates found by ignoring the imperfections of the test. The method can be extended to the situation where the sensitivity and specificity differ for different study subjects, i.e., nondifferential misclassification. The method is useful even when the sensitivity and specificity are not known, as a way to see the degree to which various assumptions about sensitivity and specificity affect one's estimates. The method can also be used to estimate sensitivity and specificity under certain assumptions or when a validation subsample is available. Several examples are provided to compare the results of this method with those obtained by standard logistic regression. A SAS macro that implements the method is available on the World Wide Web at http:@som1.ab.umd.edu/Epidemiology/software.h tml.

Adult↗
PubMed1999

Logistic regression analysis for more than one characteristic of exposure.

When more than one characteristic of an exposure is under study, it is easy to misinterpret the results of a logistic regression analysis that incorporates terms for each characteristic. For example, in a study of the risk of endometrial cancer in relation to the duration and the recency of use of estrogen replacement therapy (ERT), simultaneously including terms for duration and recency of exposure to ERT in a logistic model may leave the mistaken impression that it is possible to adjust for recency when a given duration of ERT use is compared with no use. In this article, the authors show why such an adjusted comparison is impossible, and they discuss several pitfalls in the interpretation of logistic regression coefficients when two or more characteristics of exposure are under study. They also suggest a method for avoiding these pitfalls.

Confounding Factors, Epidemiologic↗
PubMed2000

Problems due to small samples and sparse data in conditional logistic regression analysis.

Conditional logistic regression was developed to avoid "sparse-data" biases that can arise in ordinary logistic regression analysis. Nonetheless, it is a large-sample method that can exhibit considerable bias when certain types of matched sets are infrequent or when the model contains too many parameters. Sparse-data bias can cause misleading inferences about confounding, effect modification, dose response, and induction periods, and can interact with other biases. In this paper, the authors describe these problems in the context of matched case-control analysis and provide examples from a study of electrical wiring and childhood leukemia and a study of diet and glioma. The same problems can arise in any likelihood-based analysis, including ordinary logistic regression. The problems can be detected by careful inspection of data and by examining the sensitivity of estimates to category boundaries, variables in the model, and transformations of those variables. One can also apply various bias corrections or turn to methods less sensitive to sparse data than conditional likelihood, such as Bayesian and empirical-Bayes (hierarchical regression) methods.

Bias↗
PubMed1992

Correction of logistic regression relative risk estimates and confidence intervals for random within-person measurement error.

Frequently, covariates used in a logistic regression are measured with error. The authors previously described the correction of logistic regression relative risk estimates for measurement error in one or more covariates when a "gold standard" is available for exposure assessment. For some exposures (e.g., serum cholesterol), no gold standard exists, and one must assess measurement error via a reproducibility substudy. In this paper, the authors present measurement error methods for logistic regression when there is error (possibly correlated) in one or more covariates and one has data from both a main study and a reproducibility substudy. Confidence intervals from this procedure reflect error in parameter estimates from both studies. These methods are applied to the Framingham Heart Study, where the 10-year incidence of coronary heart disease is related to several coronary risk factors among 1,731 men disease-free at examination 4. Reproducibility data are obtained from the subgroup of 1,346 men seen at examinations 2 and 3. Estimated odds ratios comparing extreme quintiles for risk factors with substantial error were increased after correction for measurement error (serum cholesterol, 2.2 vs. 2.9; serum glucose, 1.3 vs. 1.5; systolic blood pressure, 2.8 vs. 3.8), but were generally decreased or unchanged for risk factors with little or no error (body mass index, 1.6 vs. 1.6; age 65-69 years vs. 35-44 years, 4.3 vs. 3.8; smoking, 1.7 vs. 1.7).

Adult↗
PubMed2004

Non-symmetrical double-logistic analysis of 24-h blood pressure recordings in normotensive and hypertensive rats.

OBJECTIVE: To determine the suitability of a new logistic curve fitting procedure to measure the diurnal rates of transition from the active to the asleep periods separately. METHOD: We applied this method to 24-h telemetry recordings of systolic, mean, diastolic arterial pressure (SAP, MAP, DAP, respectively), heart rate (HR) and locomotor activity of normotensive Sprague-Dawley rats (SDR) and spontaneously hypertensive rats (SHR). RESULTS: There was a similar pattern of higher awake and lower sleep values (16 +/- 1 mmHg SAP, 77 +/- 2 bpm HR and 40 +/- 2 units activity) in SHR. In SDR, awake-asleep differences were less for SAP (9 +/- 1 mmHg) but similar for HR (83 +/- 2 bpm). In SHR, while the blood pressure patterns were symmetrical, the rate of rise in activity and HR during arousal was more rapid than the rate of decline during the dark to light transition. By contrast in SDR, the arousal rate of increase in blood pressure and HR was much less than the rate of decline. Thus SHR have an exaggerated arousal surge in DAP compared with SDR. Double logistic provides a better fit than Cosinor or square wave and better estimates of day-night differences than partial Fourier. CONCLUSIONS: Analysis of 24-h recordings by a new logistic curve method reveals distinct asymmetric circadian patterns of cardiovascular and activity changes in rats. The greater surge in arousal blood pressure in SHR is not associated with differences in HR or activity changes and may be inherent to the underlying mechanisms contributing to the hypertension in SHR.

Animals↗
PubMed2003

Combining the performance strengths of the logistic regression and neural network models: a medical outcomes approach.

The assessment of medical outcomes is important in the effort to contain costs, streamline patient management, and codify medical practices. As such, it is necessary to develop predictive models that will make accurate predictions of these outcomes. The neural network methodology has often been shown to perform as well, if not better, than the logistic regression methodology in terms of sample predictive performance. However, the logistic regression method is capable of providing an explanation regarding the relationship(s) between variables. This explanation is often crucial to understanding the clinical underpinnings of the disease process. Given the respective strengths of the methodologies in question, the combined use of a statistical (i.e., logistic regression) and machine learning (i.e., neural network) technology in the classification of medical outcomes is warranted under appropriate conditions. The study discusses these conditions and describes an approach for combining the strengths of the models.

Artificial Intelligence↗
PubMed2004

The impact of pharmacogenomic factors on steroid dependency in pediatric heart transplant patients using logistic regression analysis.

Many pharmacogenomic predictors of drug response are now available, and include both drug metabolism-disposition factors and drug targets. Information on statistical approaches to analyzing large clinical data sets in relation to genetic polymorphisms is limited. The objective of this study was to evaluate whether logistic regression could identify pharmacogenomic predictors of outcome in a large data set in a complex transplant patient population. Seventy pediatric heart transplant patients were studied. Patients were followed for at least 1 yr post-transplantation as outpatients, and weaned from corticosteroids if clinically appropriate. Logistic regression analysis was used to identify the predictors of steroid dependency. The dependent variable was the presence or absence of steroid therapy at 1 yr post-transplantation. The independent variables were the patients' transplant age, gender, MDR1 C3435T and G2677T, CYP3A53B and cytokine polymorphisms. By chi-square test for the MDR1 C3435T polymorphism, 12 of 18 (67%) patients in the CC group were still on prednisone, whereas only 18 of 47 (38%) of the CT/TT group were still receiving prednisone (p = 0.04). For the IL-10 groups, two of 15 patients with the high producer genotype (13.3%) remained on prednisone, in comparison with 16 of 28 patients with the intermediate producer genotype (57.1%) and 15 of 26 patients with the low producer genotype (57.7%, p = 0.01). Logistic regression analysis confirmed MDR1 C3435T (p = 0.021), and IL-10 polymorphisms (intermediate producer genotype p = 0.015; low producer genotype p = 0.013) as independent risk factors for steroid dependency at 1 yr after transplantation. This approach identifies pharmacogenomic factors, which can be studied more extensively in larger data sets, and used in prospective studies to individualize immunosuppressive therapy following solid organ transplantation.

Adolescent↗
PubMed2006

Predicting iatrogenic gall bladder perforation during laparoscopic cholecystectomy: a multivariate logistic regression analysis of risk factors.

BACKGROUND: Seventeen independent risk factors were examined using multivariate logistic regression analysis to develop a profile of patients most likely at risk from iatrogenic gall bladder perforation (IGBP) during laparoscopic cholecystectomy. METHODS: Since 1989, a prospectively maintained database on 856 (women, 659; men, 197) consecutive laparoscopic cholecystectomies by a single surgeon (R. J. F.) was analysed. The mean age was 48 years (range, 17-94 years). The mean operating time was 88 min (range, 25-375 min) and the mean postoperative stay was 1 day (range, 1-24 days). There were 311 (women, 214; men, 97) IGBP. Seventeen independent variables, which included sex, race, history of biliary colic, dyspepsia, history of acute cholecystitis, acute pancreatitis and jaundice, previous abdominal surgery, previous upper abdominal surgery, medical illness, use of intraoperative laser or electrodiathermy, performance of intraoperative cholangiogram, positive intraoperative cholangiogram, intraoperative common bile duct exploration, presence of a grossly inflamed gall bladder as seen by the surgeon intraoperatively and success of the operation, were analysed using multivariate logistic regression for predicting IGBP. RESULTS: Multivariate logistic regression analysis against all 17 predictors was significant (chi(2) = 94.5, d.f. = 17, P = 0.0001), and the variables male sex, history of acute cholecystitis, use of laser and presence of a grossly inflamed gall bladder as seen by the surgeon intraoperatively were individually significant (P < 0.05) by the Wald chi(2)-test. CONCLUSION: Laparoscopic cholecystectomy, using laser, in a male patient with a history of acute cholecystitis or during an acute attack of cholecystitis is associated with a significantly higher incidence of IGBP.

Adolescent↗
PubMed2005

A multivariate logistic regression equation to screen for dysglycaemia: development and validation.

AIMS: To develop and validate an empirical equation to screen for dysglycaemia [impaired fasting glucose (IFG), impaired glucose tolerance (IGT) and undiagnosed diabetes]. METHODS: A predictive equation was developed using multiple logistic regression analysis and data collected from 1032 Egyptian subjects with no history of diabetes. The equation incorporated age, sex, body mass index (BMI), post-prandial time (self-reported number of hours since last food or drink other than water), systolic blood pressure, high-density lipoprotein (HDL) cholesterol and random capillary plasma glucose as independent covariates for prediction of dysglycaemia based on fasting plasma glucose (FPG)>or=6.1 mmol/l and/or plasma glucose 2 h after a 75-g oral glucose load (2-h PG)>or=7.8 mmol/l. The equation was validated using a cross-validation procedure. Its performance was also compared with static plasma glucose cut-points for dysglycaemia screening. RESULTS: The predictive equation was calculated with the following logistic regression parameters: P=1+1/(1+e-X)=where X=-8.3390+0.0214 (age in years)+0.6764 (if female)+0.0335 (BMI in kg/m2)+0.0934 (post-prandial time in hours)+0.0141 (systolic blood pressure in mmHg)-0.0110 (HDL in mmol/l)+0.0243 (random capillary plasma glucose in mmol/l). The cut-point for the prediction of dysglycaemia was defined as a probability>or=0.38. The equation's sensitivity was 55%, specificity 90% and positive predictive value (PPV) 65%. When applied to a new sample, the equation's sensitivity was 53%, specificity 89% and PPV 63%. CONCLUSIONS: This multivariate logistic equation improves on currently recommended methods of screening for dysglycaemia and can be easily implemented in a clinical setting using readily available clinical and non-fasting laboratory data and an inexpensive hand-held programmable calculator.

Adult↗
PubMed2006

Investigation of the ability of haplotype association and logistic regression to identify associated susceptibility loci.

While finely spaced markers are increasingly being used in case-control association studies in attempts to identify susceptibility loci, not enough is yet known as to the optimal spacing of such markers, their likely power to detect association, the relative merits of single marker versus multimarker analysis, or which methods of analysis may be optimal. Some investigations of these issues have used markers simulated under different theoretical models of population evolution. However the HapMap project and other sources provide real datasets which can be used to obtain a more realistic view of the performance of these approaches. SNPs around APOE and from two HapMap regions were used to obtain information regarding linkage disequilibrium (LD) relationships between polymorphisms, and these real patterns of LD were used to simulate datasets such as would be obtained in case-control studies were these SNPs to influence susceptibility to disease. The datasets obtained were analysed using tests for heterogeneity of estimated haplotype frequencies and using logistic regression analyses in which only main effects from each marker were considered. All markers surrounding the putative susceptibility locus were analysed, using sets of either 1, 2, 3 or 4 markers at a time. Some markers within 150 kb of the susceptibility locus were able to detect association. At distances less than 100 kb there was no correlation between the distance from the susceptibility locus and the strength of evidence for association. When the average inter-locus spacing is 25 kb many loci would not be detected, while when the spacing is as low as 2 kb one can be fairly confident that at least one marker will be in strong enough LD with the susceptibility locus to enable association to be detected, if the susceptibility locus has a strong enough effect relative to the sample size. With an inter-locus spacing of 4 kb some susceptibility loci did not have a marker locus in strong LD, potentially undermining the ability to detect association. There was little difference in the performance of haplotype-based analysis compared with logistic regression considering effects of each marker as separate. Multimarker analysis on occasion produced results which were much more highly significant than single marker analysis, but only very rarely. Our results support the view that if markers are randomly selected then a spacing as low as 2 kb is desirable. Multimarker analysis can sometimes be more powerful than single marker analysis so both should be performed. However, because it is rare for multimarker analysis to be much more highly significant than single marker analysis one should strongly suspect that when such results occur they may be due to mistakes in genotyping or through some other artefact. Haplotype analysis may be more prone to such problems than logistic regression, suggesting that the latter method might be preferred.

Apolipoproteins E↗
PubMed1993

Determinants of success of coronary angioplasty in patients with a chronic total occlusion: a multiple logistic regression model to improve selection of patients.

OBJECTIVE: To study the determinants of success of coronary angioplasty in patients with chronic total occlusions, and to formulate a multiple logistic regression model to improve selection of patients. DESIGN: A retrospective analysis of clinical and angiographic data on a consecutive series of patients. PATIENTS: 312 patients (mean age 55, range 31 to 79 years, 86% men) who underwent coronary angioplasty procedure for a chronic total occlusion between 1981 and 1992. RESULTS: Procedural success was achieved in 191 lesions (61.2%). A major complication occurred in six patients (1.9%). Multiple stepwise logistic regression analysis identified the presence of bridging collaterals (p < 0.001), the absence of a tapered entry configuration (p < 0.001), estimated duration of occlusion of greater than three months (p = 0.001), and a vessel diameter of less than 3 mm (p = 0.003) as independent predictors of procedural failure. The logistic regression model was used to classify patients into groups of high, intermediate, and low probability of procedural success with cut off points of 70% and 30%. The predictive value for procedural success (probability > or = 70%) was 91% (95% confidence intervals (95% CI) 83% to 96%) and predictive value for procedural failure (probability < 30%) was 81% (95% CI 64% to 92%). CONCLUSIONS: Percutaneous transluminal coronary angioplasty of chronic total occlusions is associated with a low risk of acute complication. Procedural success is influenced by easily identifiable clinical and angiographic features and the multiple regression model described may help to improve selection of patients.

Adult↗
PubMed2005

MELPREDICT: a logistic regression model to estimate CDKN2A carrier probability.

BACKGROUND: Heritable alterations in CDKN2A account for a subset of familial melanoma cases although no robust method exists to identify those at risk of being a mutation carrier. METHODS: We set out to construct a model for estimating CDKN2A mutation carrier probability using a cohort of 116 consecutive familial cutaneous melanoma patients evaluated at Massachusetts General Hospital Pigmented Lesion Center between April 2001 and September 2004. Germline CDKN2A and CDK4 status on the familial melanoma cases and clinical features associated with mutational status were then used to build a multiple logistic regression model to predict carrier probability and performance of model on external validation. RESULTS: From the 116 kindreds prone to melanoma in the Boston area, 13 CDKN2A mutation carriers were identified and 12 were subsequently used in the modeling. Proband age at diagnosis, number of proband primaries, and number of additional family primaries were most closely associated with germline mutations. The estimated probability of the proband being a mutation carrier based on the logistic regression model (MELPREDICT) is given by e(L)/(1 + e(L) where L = 1.99+[0.92x(no. of proband primaries)]+[0.74x(no. of additional family primaries)]-[2.11xln(age)]. The mean estimated probabilities for subjects in the Boston dataset were 55.4% and 5.1% for the mutation carriers and non-carriers respectively. In a receiver operator characteristic analysis, the area under the curve was 0.881 (95% confidence interval 0.739 to 1.000) for the Boston model set (n = 116) and 0.803 (0.729 to 0.877) for an external Toronto hereditary melanoma cohort (n = 143). CONCLUSIONS: These results represent the first-iteration logistic regression model to approximate CDKN2A carrier probability. Validation of this model with an external dataset revealed relatively robust performance.

Adolescent↗
PubMedDate not supplied

A new logistic regression approach for the evaluation of diagnostic test results.

The value of a dichotomous diagnostic test is often described in terms of sensitivity, specificity, and likelihood ratios (LRs). Although it is known that these test characteristics vary between subgroups of patients, they are generally interpreted, on average, without considering information on patient characteristics, such as clinical signs and symptoms, or on previous test results. This article presents a reformulation of the logistic regression model that allows to calculate the LRs of diagnostic test results conditional on these covariates. The proposed method starts with estimating logistic regression models for the prior and posterior odds of disease. The regression model for the prior odds is based on patient characteristics, whereas the regression model for the posterior odds also includes the diagnostic test of interest. Following the Bayes theorem, the authors demontsrate that the regression model for the LR can be derived from taking the differences between the regression coefficients of the 2 models. In a clinical example, they demonstrate that the LRs of positive and negative test results and the sensitivity and specificity of the diagnostic test varied considerably between patients with different risk profiles, even when a constant odds ratio was assumed. The proposed logistic regression approach proves an efficient method to determine the performance of tests at the level of the individual patient risk profile and to examine the effect of patient characteristics on diagnostic test characteristics.

Angiography↗