Statistics for nuclear medicine. Part 4: Regression.
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Heparin↗
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Results for “Statistical Regression”
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Statistical assessment of ordinal outcomes in comparative studies.
Ordinal regression is a relatively new statistical method developed for analyzing ranked outcomes. In the past, ranked scales have often been analyzed without making full use of the ordinality of the data or, alternatively, by assigning arbitrary numerical scores to the ranks. While ordinal regression models are now available to make full use of ranked data, they are not used widely. This article, directed to clinical researchers and epidemiologists, provides a description of the properties of these methods. Using ordinal measures of back pain in a follow-up study of adolescent idiopathic scoliosis, we illustrate the advantages of those methods and describe how to interpret the estimated parameters. Comparisons with binary logistic regression are made to show why a single dichotomization of the ordinal scale may lead to incorrect inferences. Two ordinal models (the proportional odds and the continuation ratio models) are discussed, and the goodness-of-fit of these models is examined. We conclude that ordinal regression is a tool that is powerful, simple to use, and produces an interpretable parameter that summarizes the effect between groups over all levels of the outcome.
Epidemiologic Methods↗
Prospective breast cancer risk prediction model for women undergoing screening mammography.
BACKGROUND: Risk prediction models for breast cancer can be improved by the addition of recently identified risk factors, including breast density and use of hormone therapy. We used prospective risk information to predict a diagnosis of breast cancer in a cohort of 1 million women undergoing screening mammography. METHODS: There were 2,392,998 eligible screening mammograms from women without previously diagnosed breast cancer who had had a prior mammogram in the preceding 5 years. Within 1 year of the screening mammogram, 11,638 women were diagnosed with breast cancer. Separate logistic regression risk models were constructed for premenopausal and postmenopausal examinations by use of a stringent (P<.0001) criterion for the inclusion of risk factors. Risk models were constructed with 75% of the data and validated with the remaining 25%. Concordance of the predicted with the observed outcomes was assessed by a concordance (c) statistic after logistic regression model fit. All statistical tests were two-sided. RESULTS: Statistically significant risk factors for breast cancer diagnosis among premenopausal women included age, breast density, family history of breast cancer, and a prior breast procedure. For postmenopausal women, the statistically significant factors included age, breast density, race, ethnicity, family history of breast cancer, a prior breast procedure, body mass index, natural menopause, hormone therapy, and a prior false-positive mammogram. The model may identify high-risk women better than the Gail model, although predictive accuracy was only moderate. The c statistics were 0.631 (95% confidence interval [CI] = 0.618 to 0.644) for premenopausal women and 0.624 (95% CI = 0.619 to 0.630) for postmenopausal women. CONCLUSION: Breast density is a strong additional risk factor for breast cancer, although it is unknown whether reduction in breast density would reduce risk. Our risk model may be able to identify women at high risk for breast cancer for preventive interventions or more intensive surveillance.
Adult↗
Correlation of subepithelial haze and refractive regression 1 month after photorefractive keratectomy for myopia.
PURPOSE: To relate myopic regression after photorefractive keratectomy (PRK) to subepithelial haze at the first postoperative month. METHODS: One hundred nineteen eyes of 119 patients underwent excimer laser PRK for treatment of myopia up to -8.00 D. Eyes were examined at 1, 3, 6, 9, and 12 months after surgery. All eyes received fluorometholone 0.1% for the first 5 postoperative months in a tapered dose. Dexamethasone 0.1% qid for 1 month was prescribed to all eyes with a spherical equivalent refraction less than plano, followed by an augmented dose of fluorometholone 0.1%. Eyes with myopia greater than -0.75 D at 12 months, as well as those that had received dexamethasone at any postoperative interval--regardless of refractive outcome--were considered to be regressed. Eyes that regressed and those that did not regress were compared statistically (Chi-squared statistical criterion with Yate's correction) regarding haze grade. RESULTS: Forty-seven percent (56 of 119) of eyes regressed. In 89.28% (50 of 56) of eyes, subepithelial haze grade was 1 to 2, and in 10.71% (6 of 56), subepithelial haze was graded 0 to 0.5 at 1 month. Fifty-three percent of eyes (63 of 119) did not regress and in all, subepithelial haze was graded 0 to 0.5 at the first month. The correlation between regression and haze grade 1 or more at the first postoperative month was statistically significant (P<.001). CONCLUSION: Mild to marked subepithelial haze (grade 1 to 2) at the first postoperative month after PRK for myopia is strongly related to regression of initial refractive effect and increasing myopia.
Adult↗
[Postural control related to age in patients with benign positional paroxysmal vertigo].
OBJECTIVE: To study the relationship between age and posturography in patients with benign positional paroxysmal vertigo. MATERIAL AND METHODS: Prospective study performed in 65 patients with benign positional paroxysmal vertigo (BPPV) in any variant. Sensory Organization Test outcomes were recorded and compared with their equivalents in a control group by means of scatter-plot diagrams and regression line. For statistical study, Mann-Whitney's U-test was used. RESULTS: Slope for regression lines in composite was -0.0934 in group NORMAL; in group BPPV it was -0.4284. This difference is due to conditions 5 and 6. Results were statistically significative. CONCLUSIONS: BPPV patients have a worse postural control than control group. The difference is bigger the older the patient is. It is due to a failure in conditions 5 and 6, so it should be from a vestibular origin.
Adult↗
A diagnostic for Cox regression with discrete failure-time models.
Changes in maximum likelihood parameter estimates due to deletion of individual observations are useful statistics, both for regression diagnostics and for computing robust estimates of covariance. For many likelihoods, including those in the exponential family, these delete-one statistics can be approximated analytically from a one-step Newton-Raphson iteration on the full maximum likelihood solution. But for general conditional likelihoods and the related Cox partial likelihood, the one-step method does not reduce to an analytic solution. For these likelihoods, an alternative analytic approximation that relies on an appropriately augmented design matrix has been proposed. In this paper, we extend the augmentation approach to explicitly deal with discrete failure-time models. In these models, an individual subject may contribute information at several time points, thereby appearing in multiple risk sets before eventually experiencing a failure or being censored. Our extension also allows the covariates to be time dependent. The new augmentation requires no additional computational resources while improving results.
Biometry↗
THE EVALUATION OF GERIATRIC PATIENTS FOLLOWING TREATMENT.
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Brain Diseases↗
Association of penile lichen sclerosus and oncogenic human papillomavirus infection.
BACKGROUND: Data on the prevalence of human papillomavirus (HPV) infection in patients with penile lichen sclerosus (LS) are scant and controversial. AIM: To investigate the prevalence of HPV infections in patients with penile LS. METHODS: HPV infection was assessed by polymerase chain reaction (PCR) in paraffin-embedded penile biopsies obtained from the glans or inner foreskin of 46 adult patients with penile LS, and in brush cytology smears of penile healthy mucosa from an equal number of randomly selected control males matched for age. Statistical evaluation was performed using conditional logistic regression analysis. RESULTS: PCR disclosed the presence of HPV infection in 17.4% of LS patients (HPV 16, six cases; HPV 18, one case; HPV 45, one case). Amongst the controls, HPV infection occurred in 8.7% of patients (HPV 16, two cases; HPV 53, one case; HPV 70, one case). Statistical regression analysis confirmed that the rate of HPV infection was higher amongst patients with genital LS than amongst healthy controls [odds ratio (OR), 2.55; 95% confidence interval (CI), 0.73-8.89]. CONCLUSIONS: Infection with oncogenic "high-risk" HPV types in patients with genital LS may enhance the risk of penile cancer arising on LS.
Adult↗
Statistical comparison of four effect sizes for single-subject designs.
Controversy exists regarding appropriate methods for summarizing treatment outcomes for single-subject designs. Nonregression- and regression-based methods have been proposed to summarize the efficacy of single-subject interventions with proponents of both methods arguing for the superiority of their respective approaches. To compare findings for different single-subject effect sizes, 117 articles that targeted the reduction of problematic behaviors in 181 individuals diagnosed with autism were examined. Four effect sizes were calculated for each article: mean baseline reduction (MBLR), percentage of nonoverlapping data (PND), percentage of zero data (PZD), and one regression-based d statistic. Although each effect size indicated that behavioral treatment was effective, moderating variables were detected by the PZD effect size only. Pearson product-moment correlations indicated that effect sizes differed in statistical relationships to one another. In the present review, the regression-based d effect size did not improve the understanding of single-subject treatment outcomes when compared to nonregression effect sizes.
Behavior Therapy↗
Removal of naphthalene, phenanthrene, and pyrene by sorbents from hot gas.
It is the first time that the removal of polycyclic aromatic hydrocarbons (PAH) containing different aromatic rings number [naphthalene (Np), phenanthrene (Phe), and pyrene (Py)] from combustion hot gas has been carried out. The aim was to relate the sorbents textural characteristics with the adsorption capacity of these 2-4-ring PAH at the conditions emitted at energy generation. The sorbents textural parameters [total micropore volume (VN2), narrow micropore volume (VCO2), mesopore volume (VBJH), and the free active sites] were analyzed trying to correlate them with their Np, Phe, and Py adsorption capacities. To get this aim, single and multiple linear regressions (MLR) were applied to the three PAH. A principal component analysis was performed to generate new and uncorrelated variables. It enabled us to show that the relations between the textural parameters were analyzed using a principal components regression (PCR). The PCR analysis had a good statistical quality, but neither did it allow differentiating free active site types nor did VN2 and VCO2. The correlations were thus set up applying a MLR to the original variables. The regression statistical quality was similar to the PCR analysis, and it could give an easier explanation of the parameters that affected the adsorption. In Np adsorption, the 87% data variance was explained, and the adsorption was positively correlated to VCO2 and the micropore mean diameter (I.). In the Phe regression there was 98% variance explained, and its adsorption was positively correlated to the VN2 and the micropore distribution, n. Finally, in the Py adsorption, the 96% data variance was explained, and this adsorption was positively correlated to VN2 and VBJH. These dependencies were according to the molecular parameters of these compounds (molecular diameter and volatility) because the higher the number of aromatic rings of the PAH, the more favored the adsorbate-adsorbate interactions. Besides, the higher the mean diameter micropores, the lower the diffusional problems showed by Np, Phe, and Py.
Adsorption↗
Prognostic factors in multiple myeloma: a retrospective study using conventional statistical methods and a computer program.
The prognostic significance of age, sex, ethnic origin and various laboratory data was studied retrospectively in 69 patients with multiple myeloma using conventional statistical tests and the multiple regression computerized analysis. The conventional statistical analysis confirmed that age, anemia, uremia, hypoalbuminemia, hyperglobulinemia, hyperuricemia and IgA lambda type myeloma were associated with a poor prognosis. The multiple regression analysis indicated that age and blood urea nitrogen levels were the only variables which significantly affect the survival of patients with multiple myeloma. A correlation was found between blood urea nitrogen levels and other laboratory data of apparent prognostic value. The differences between our results and those of other authors are discussed and it is suggested that they may, in part, be due to the fact that the interplay between the various prognostic variables was not exposed in other studies.
Age Factors↗
Linearly divergent treatment effects in clinical trials with repeated measures: efficient analysis using summary statistics.
In many randomized clinical trials with repeated measures of a response variable one anticipates a linear divergence over time in the difference between treatments. This paper explores how to make an efficient choice of analysis based on individual patient summary statistics. With the objective of estimating the mean rate of treatment divergence the simplest choice of summary statistic is the regression coefficient of response on time for each subject (SLOPE). The gains in statistical efficiency imposed by adjusting for the observed pre-treatment levels, or even better the estimated intercepts, are clarified. In the process, we develop the optimal linear summary statistic for any repeated measures design with assumed known covariance structure and shape of true mean treatment difference over time. Statistical power considerations are explored and an example from an asthma trial is used to illustrate the main points.
Analysis of Variance↗
Body weight change in relation to incidence of ischemic heart disease and change in risk factors for ischemic heart disease.
A representative population sample of middle-aged women was studied in 1968-1969 and re-studied in 1974-1975. A total of 1302 women participated in both studies (80.3% of the initial sample). A statistically significant correlation was found between weight gain and the incidences of angina pectoris and arterial hypertension. A statistically significant correlation was also found between cessation of smoking and weight gain. Regression analysis revealed statistically significant changes of systolic and diastolic blood pressures, fasting blood glucose, serum cholesterol, serum triglycerides and serum uric acid with changes in body weight.
Adult↗
Folliculotropic T cells in regressive basal cell carcinoma of skin.
The histologic features of regression may be found in some basal cell carcinomas (BCCs), and it is known that T-cell infiltrates have a significant role in host defense against this tumor. We examined 945 hair follicles (HFs) adjacent to 150 regressing BCCs of skin for the presence of inflammatory infiltrates and compared the results against 315 HFs in 50 samples of normal skin. Focal T-cell infiltrates localized mainly to the upper portion of the HFs were found in 14.5% of the follicles adjacent to regressing BCCs. A statistically significant increase of inflammation in HFs was observed in BCCs with active regression compared with BCCs with inactive and mixed regression (P < 0.05). An increase in the number of HFs involved by T lymphocytes was also found in regressing BCCs compared to normal skin ( P < 0.00005). These data suggest that the damage to the follicles is concordant with active regression of BCCs. We speculate that the immune-mediated regression of BCCs is not only specifically directed to the cells of the tumor but may also induce activated lymphocytes with cytotoxic capability to cross react with the follicular epithelium.
Antigens, CD↗
The statistical analysis of single-subject data: a comparative examination.
BACKGROUND AND PURPOSE: The purposes of this study were to examine whether the use of three different statistical methods for analyzing single-subject data led to similar results and to identify components of graphed data that influence agreement (or disagreement) among the statistical procedures. METHODS: Forty-two graphs containing single-subject data were examined. Twenty-one were AB charts of hypothetical data. The other 21 graphs appeared in Journal of Applied Behavioral Analysis, Physical Therapy, Journal of the Association for Persons With Severe Handicaps, and Journal of Behavior Therapy and Experimental Psychiatry. Three different statistical tests--the C statistic, the two-standard deviation band method, and the split-middle method of trend estimation--were used to analyze the 42 graphs. RESULTS: A relatively low degree of agreement (38%) was found among the three statistical tests. The highest rate of agreement for any two statistical procedures (71%) was found for the two-standard deviation band method and the C statistic. A logistic regression analysis revealed that overlap in single-subject graphed data was the best predictor of disagreement among the three statistical tests (beta = .49, P < .03). CONCLUSION AND DISCUSSION: The results indicate that interpretation of data from single-subject research designs is directly influenced by the method of data analysis selected. Variation exists across both visual and statistical methods of data reduction. The advantages and disadvantages of statistical and visual analysis are described.
Data Interpretation, Statistical↗
Comparison of fuzzy inference, logistic regression, and classification trees (CART). Prediction of cervical lymph node metastasis in carcinoma of the tongue.
OBJECTIVES: In this paper three statistical methods [logistic regression, classification and regression tree (CART), and fuzzy inference] for the prediction of lymph node metastasis in carcinoma of the tongue are compared. METHODS: A retrospective collection of data in 75 patients treated for tongue cancer was carried out at the Clinic and Policlinic for Oral and Maxillo-facial Surgery at the University Hospital of Freiburg in Germany between January 1990 and December 1999; biopsy material was used for laboratory evaluations. Statistical methods for the prediction of lymph node metastasis were compared using ROC curves and accuracy rates. RESULTS: All three methods show similar results for the prediction of lymph node metastasis with slightly superior results for fuzzy inference and CART. A great overlap is apparent in the ROC curves. The best result observed for fuzzy inference and CART was a sensitivity of 79.2% [95% confidence interval: (57.8%; 92.9%)] and a specificity of 86.3% (73.7%; 94.3%); the best result for predictions based on the logistic regression was a sensitivity of 66.7% (44.7%; 84.4%) and a specificity of 80.4% (66.9%; 90.2%). Accuracy rates of fuzzy method and CART were higher [accuracy rate for fuzzy method and CART: 84% (73.7%; 91.4%), for logistic regression method: 73.3%, 95%-CI: (61.9%; 82.9%)]. CONCLUSIONS: From a clinical point of view, the predictive ability of the three methods is not sufficiently large to justify use of these methods in daily practice. Other factors probably on the molecular level are needed for the prediction of lymph node metastasis.
Decision Support Techniques↗
On the statistical modelling of coronary arteriographic data: dynamics of coronary atherosclerosis related to systemic and focal parameters. REGRESS Study Group. Regression Growth Evaluation Statin Study.
Existing methods to analyse data from repeated arteriographic progression/regression studies are restrictive and do not fully explore the dynamics of coronary artherosclerosis. We present a new approach making a distinction between new occlusions, new lesions, and growth of existing lesions. Random effect models, based on the logistic, the Poisson, and the normal distribution are proposed with correlation depending on distance. The data from the Regression Growth Evaluation Statin Study (REGRESS) are used to validate the model. Lipid lowering treatment of pravastatin resulted in less growth of existing lesions and fewer new lesions than when placebo was given. Fewer new lesions were found in segments influenced by percutaneous transluminal coronary angioplasty (PTCA) than in segments not influenced by PTCA. Similarly, the growth of lesions influenced by PTCA was smaller than lesions not influenced by PTCA. More new occlusions were found in segments influenced by coronary arterial bypass grafting (CABG) than in segments not influenced by CABG, but 98 per cent of the new occlusions were located proximal to the bypass anastomosis. Similarly, existing lesions proximal to the bypass anastomosis showed larger growth (p < 0.001). We conclude that our new approach for analysing the arteriographic data from repeated coronary arteriographic studies appeared a fruitful way to analyse the dynamics of coronary atherosclerosis.
Angioplasty, Balloon, Coronary↗
Impact of minimum hematocrit during cardiopulmonary bypass on mortality in patients undergoing coronary artery surgery.
BACKGROUND: The hematocrit on cardiopulmonary bypass (CPB) frequently falls to a low level during many cardiac surgical procedures. This study was designed to explore the impact on mortality of minimum hematocrit level achieved during the CPB after coronary artery surgery. METHODS AND RESULTS: Two thousand seven hundred thirty-eight sequential isolated coronary artery surgery patients during a 42-month period at a tertiary academic center were included in this study. Thirty-one standardized preoperative risk factors used in a multiple logistic regression revealed eight statistically significant independent predictors for postoperative mortality. Minimum hematocrit level during CPB was then added to the regression model and was found to be an independent risk factor for mortality. The entire patient population was divided into dichotomous groups using different minimum hematocrit levels on CPB for the determination of cutoff points by multiple logistic regression. After adjusting for other risk factors, the minimum hematocrit level of 14% was found to be a statistically significant cutoff point. Patients with minimum hematocrit levels < or =14% were found to have an increased probability of risk-adjusted mortality (odds ratio, 2.70; P=.002). A subgroup analysis revealed that high-risk patients with minimum hematocrit levels < or =17% were found to have a significantly increased probability of postoperative mortality (odds ratio, 2.20; P=.017). CONCLUSIONS: Minimum hematocrit level during CPB is an independent risk factor for mortality after coronary artery surgery. There is a significantly increased risk of mortality for hematocrit levels < or =14%. For high-risk patients, there is a significantly increased risk of mortality for hematocrit levels < or =17%.
Adult↗