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Theoretical and technical comments on regression and anti-regression.

Following a discussion of the 'classical' formulations on regression and fixation, the view is put forward that the distinction between various types of regression is on the whole superfluous. However, it is important to distinguish between 'latent' regression in the patient's 'present unconscious', the contents of which are defended against and kept from consciousness on the one hand, and 'manifest' regression on the other, in which current versions of developmentally earlier wishes and fantasies emerge overtly in acceptable form in thought and behaviour. The anti-regressive function can be regarded as being operative from early in development, and functions to a greater or lesser extent throughout our daily lives. As a concept it reflects the operation of all the defence mechanisms and manoeuvres which operate to protect consciousness and conscious awareness of behaviour. Because it reflects a general tendency of the mind to defend consciousness from unwelcome content arising in the present unconscious, it is consequently a major source of resistance in analysis. Analytic progress takes place when the patient gains sufficient security in an analysis-syntonic way to allow a progressively increasing capacity for controlled relaxation of the anti-regressive function to take place, and for previously unacceptable wishful phantasies to be tolerated and accepted by the patient. This relaxation of the anti-regressive function is allied to Ernst Kris's description of 'regression in the service of the ego'.

Awareness↗

Retro-regression--another important multivariate regression improvement.

We review the serious problem associated with instabilities of the coefficients of regression equations, referred to as the MRA (multivariate regression analysis) "nightmare of the first kind". This is manifested when in a stepwise regression a descriptor is included or excluded from a regression. The consequence is an unpredictable change of the coefficients of the descriptors that remain in the regression equation. We follow with consideration of an even more serious problem, referred to as the MRA "nightmare of the second kind", arising when optimal descriptors are selected from a large pool of descriptors. This process typically causes at different steps of the stepwise regression a replacement of several previously used descriptors by new ones. We describe a procedure that resolves these difficulties. The approach is illustrated on boiling points of nonanes which are considered (1) by using an ordered connectivity basis; (2) by using an ordering resulting from application of greedy algorithm; and (3) by using an ordering derived from an exhaustive search for optimal descriptors. A novel variant of multiple regression analysis, called retro-regression (RR), is outlined showing how it resolves the ambiguities associated with both "nightmares" of the first and the second kind of MRA.

Journal Article↗

Immunocytochemical analysis of the cellular infiltrate in primary regressing and non-regressing malignant melanoma.

Spontaneous regression occurs in a small proportion of malignant melanomas, and it is important to understand the processes involved in its induction as this may give a guide to future therapies for this disease. We have examined 36 primary malignant melanomas (19 regressing, 17 non-regressing) and identified the cellular phenotypes and activation states of the cells infiltrating regressing and non-regressing primary melanomas by immunochemistry. We have found a significantly increased number of CD3-positive cells and an increased ratio of CD4/CD8-positive cells infiltrating regressing compared to non-regressing tumors. In addition, the expression of the interleukin 2 receptor, an activation marker for T cells, was increased. However, there were no significant differences in class II MHC, CD1, intercellular adhesion molecule 1 (ICAM1), or melanoma-associated differentiation-antigen expression in these tumors. These data are consistent with melanoma regression being induced by activated CD4 T cells and do not seem to be related to the differentiation markers we have examined on these tumors.

Antibodies, Monoclonal↗

Regression analysis with categorized regression calibrated exposure: some interesting findings.

BACKGROUND: Regression calibration as a method for handling measurement error is becoming increasingly well-known and used in epidemiologic research. However, the standard version of the method is not appropriate for exposure analyzed on a categorical (e.g. quintile) scale, an approach commonly used in epidemiologic studies. A tempting solution could then be to use the predicted continuous exposure obtained through the regression calibration method and treat it as an approximation to the true exposure, that is, include the categorized calibrated exposure in the main regression analysis. METHODS: We use semi-analytical calculations and simulations to evaluate the performance of the proposed approach compared to the naive approach of not correcting for measurement error, in situations where analyses are performed on quintile scale and when incorporating the original scale into the categorical variables, respectively. We also present analyses of real data, containing measures of folate intake and depression, from the Norwegian Women and Cancer study (NOWAC). RESULTS: In cases where extra information is available through replicated measurements and not validation data, regression calibration does not maintain important qualities of the true exposure distribution, thus estimates of variance and percentiles can be severely biased. We show that the outlined approach maintains much, in some cases all, of the misclassification found in the observed exposure. For that reason, regression analysis with the corrected variable included on a categorical scale is still biased. In some cases the corrected estimates are analytically equal to those obtained by the naive approach. Regression calibration is however vastly superior to the naive method when applying the medians of each category in the analysis. CONCLUSION: Regression calibration in its most well-known form is not appropriate for measurement error correction when the exposure is analyzed on a percentile scale. Relating back to the original scale of the exposure solves the problem. The conclusion regards all regression models.

Journal Article↗

A study of atherosclerosis regression in Macaca mulatta. V. Changes in abdominal aorta and carotid and coronary arteries from animals with atherosclerosis induced for 38 months and then regressed for 24 or 48 months at plasma cholesterol concentrations of 300 or 200 mg/dl.

Young adult male rhesus monkeys (Macaca mulatta) were fed an atherogenic diet for 38 months. After 38 months of atherosclerosis induction, a baseline group was selected and necropsied to determine the extent and severity of atherosclerosis before regression regimens were begun. The remaining animals were fed diets that varied in cholesterol concentration in order to maintain plasma cholesterol concentrations of approximately 200 or 300 mg/dl for either 24 or 48 months. The progression or regression of atherosclerosis in coronary arteries, abdominal aorta, and carotid arteries was determined by comparing them to the baseline group. Coronary artery atherosclerosis regressed in the majority of animals after 4 years but not after 2 years when plasma cholesterol concentrations were about 200 mg/dl. Among the animals maintained at plasma cholesterol concentrations of about 300 mg/dl, about half the animals progressed in the extent of coronary artery atherosclerosis while about half regressed. The majority of the animals that progressed in lesion extent were genetic hyperresponders to dietary cholesterol whereas those that regressed were predominantly hyporesponders, even though their plasma lipid concentrations were equivalent during the regression phase. The changes seen in atherosclerosis extent in the abdominal aorta were quite similar to the changes seen in coronary arteries. Changes at this site were not pronounced after 2 years, but after 4 years animals with plasma cholesterol concentrations of about 300 mg/dl progressed while the animals at 200 mg/dl were mostly unchanged. No evidence for atherosclerosis regression was found in the common carotid arteries or in the carotid bifurcations.

Animals↗

Regression of electrocardiographic left ventricular hypertrophy predicts regression of echocardiographic left ventricular mass: the LIFE study.

The electrocardiogram (ECG) is widely used for detection of left ventricular hypertrophy (LVH). However, whether changes in ECG LVH during antihypertensive therapy predict changes in LV mass remains unclear. Baseline and year-1 ECGs and echocardiograms were assessed in 584 hypertensive patients with ECG LVH by Sokolow-Lyon or Cornell voltage-duration product criteria at entry into the Losartan Intervention For Endpoint reduction in hypertension (LIFE) echocardiographic substudy. A >/=25% decrease in Cornell product defined regression of ECG LVH; a <25% decrease defined no significant regression; and an increase defined progression of ECG LVH. Regression of echocardiographic LVH was defined by a >/=20% reduction in LV mass. After 1 year of therapy, 155 patients (27%) had regression of ECG LVH, 286 (49%) had no significant change, and 143 (25%) had progression of ECG LVH. Compared with patients with progression of ECG LVH, patients with no significant decrease and patients with regression of ECG LVH had stepwise greater absolute decreases in LV mass (-16+/-33 vs -29+/-37 vs -32+/-41 g, P<0.001), greater percent reductions in LV mass (-5.7+/-14.6 vs -11.3+/-13.6 vs -12.3+/-15.6%, P<0.001), and were more likely to decrease LV mass by >/=20% (11.2 vs 24.8 vs 36.1%, P<0.001), even after adjusting for possible effects of baseline and change in systolic and diastolic pressures. Compared with progression of ECG LVH, regression of the Cornell product ECG LVH is associated with greater reduction in LV mass and a greater likelihood of regression of anatomic LVH.

Aged↗

Regressive eye movements and sentence parsing: on the use of regression-contingent analyses.

Altmann, Garnham, and Dennis (1992) recently advocated the use of a regression-contingent analysis in eye movement studies dealing with parsing of sentences containing temporary structural ambiguities. Using experimental sentences preceded by referentially supportive contexts, they demonstrated a different pattern of results when regressive eye movements were eliminated from the data set than when regressions were included. The regression-contingent analysis that they used involves an implicit assumption that regressive eye movements are a necessary consequence of subjects' being garden pathed. We report some data which demonstrate that garden path effects are sometimes even stronger in the absence of regressions and, thus, argue that readers can be garden pathed without making regressions.

Attention↗

Spontaneous regression of Friend virus-induced erythroleukemia. II. regression of Friend murine leukemia virus-induced lymphocytic leukemia.

We characterized several aspects of spontaneous regression of lymphocytic leukemia in mice. The disease, induced by the helper murine leukemia virus (MuLV) component obtained from the regressing Friend virus complex (RFV), was characterized by spleen and lymph node enlargement, thymus involvement, and anemia. Leukemia regression occurred in about 25% of infected mice and resulted in the return of lymphoid organs to near-normal weight and normal histology and the recovery from anemia. A tenfold to 1,000-fold decrease in virus titer was seen in those mice in which leukemia regressed when compared to leukemic animals, although infectious virus was still recoverable from apparently normal spleens. The sera of mice in which leukemia regressed contained potent virus-neutralizing activity that was associated mainly with immunoglobulins. These studies firmly supported the evidence that the regressing phenotype of RFV was due to its helper MuLV component (MuLV-RF).

Animals↗

Spontaneous regression of Friend virus-induced erythroleukemia. VI. Structural and antigenic differences between the regressing and conventional strains of virus.

The regressing and conventional strains of Friend virus were compared by neutralization assays, sodium dodecyl sulfate-polyacrylamide gel electrophoresis, and tryptic peptide mapping of the individual viral components. Neutralization rates of the two viruses differed in the presence of monospecific anti-gp70 antiserum and sera from regressed or immunized mice. Neutralization of regressing Friend virus, but not conventional Friend virus, occurred when the viruses were incubated with anti-p15(E) and complement. Human serum inactivated conventional Friend virus more rapidly than regressing Friend virus, probably as a result of virolysis induced by the reaction of viral p15(E) with human complement component C1. Structural differences between the viruses were detected in their gp70 viral glycoproteins and p15(E) and p12 proteins. Analysis of different stocks and clonal isolates of the viruses showed that the differences between the gp70 and p15(E), but not the p12 proteins, were associated with the regressing phenotype of the regressing strain of Friend virus.

Animals↗

The spontaneous regression of tufted angioma. A case of regression after two recurrences and a review of 27 cases reported in the literature.

BACKGROUND: Tufted angioma, a peculiar angioma that is characterized by tufts of capillary-sized vessels scattered 'cannonball fashion' within the dermis, is known, on occasion, to regress spontaneously. However, the appropriate waiting period for spontaneous regression has remained unclear. OBJECTIVE: To know the appropriate waiting period for spontaneous regression of tufted angioma. METHODS: We report here a case of tufted angioma that regressed spontaneously after the lesions had recurred twice. We also review previously reported cases of tufted angioma with spontaneous regression, including cases in the Japanese and non-Japanese literature. RESULTS: In 18 (86%) of the 21 cases, the waiting period was more than 6 months and in 20 cases (95%) it was less than 2 years. CONCLUSION: The appropriate wait for spontaneous regression might be between 6 months and 2 years.

Adult↗

Advanced statistics: linear regression, part II: multiple linear regression.

The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

Bias↗

Advanced statistics: linear regression, part I: simple linear regression.

Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.

Biometry↗

Spontaneous regression of Friend murine leukemia virus-induced erythroleukemia. IV. Effects of radiation and athymia on leukemia regression in mice.

The spontaneous regression of the erythroleukemia induced by the regressing Friend murine leukemia virus (F-MuLV) complex was inhibited by irradiation of the animals prior to F-MuLV inoculation. This inhibition was proportional to the dose of radiation used. Treatment of the mice with the bone-seeking isotope 89Sr also inhibited erythroleukemia regression, which implicates the same effector mechanisms involved in the resistance to F-MuLV or F-MuLV-induced immunosuprression. Erythroleukemias induced in athymic nude mice by the regressing F-MuLV complex exhibited higher rates of lethality than did the leukemias in heterozygous or homozygous thymus gland-containing controls. These data suggested the involvement of the immune system in erythroleukemia regression and the specific participation of thymus cells and an 89Sr-susceptible function, perhaps marrow-dependent cells, in the process of regression.

Animals↗

Efficient regression calibration for logistic regression in main study/internal validation study designs with an imperfect reference instrument.

An extension to the version of the regression calibration estimator proposed by Rosner et al. for logistic and other generalized linear regression models is given for main study/internal validation study designs. This estimator combines the information about the parameter of interest contained in the internal validation study with Rosner et al.'s regression calibration estimate, using a generalized inverse-variance weighted average. It is shown that the validation study selection model can be ignored as long as this model is jointly independent of the outcome and the incompletely observed covariates, conditional, at most, upon the surrogates and other completely observed covariates. In an extensive simulation study designed to follow a complex, multivariate setting in nutritional epidemiology, it is shown that with validation study sizes of 340 or more, this estimator appears to be asymptotically optimal in the sense that it is nearly unbiased and nearly as efficient as a properly specified maximum likelihood estimator. A modification to the regression calibration variance estimator which replaces the standard uncorrected logistic regression coefficient variance with the sandwich estimator to account for the possible misspecification of the logistic regression fit to the surrogate covariates in the main study, was also studied in this same simulation experiment. In this study, the alternative variance formula yielded results virtually identical to the original formula. A version of the proposed estimator is also derived for the case where the reference instrument, available only in the validation study, is imperfect but unbiased at the individual level and contains error that is uncorrelated with other covariates and with error in the surrogate instrument. Replicate measures are obtained in a subset of study participants. In this case it is shown that the validation study selection model can be ignored when sampling into the validation study depends, at most, only upon perfectly measured covariates. Two data sets, a study of fever in relation to occupational exposure to antineoplastics among hospital pharmacists and a study of breast cancer incidence in relation to dietary intakes of alcohol and vitamin A, adjusted for total energy intake, from the Nurses' Health Study, were analysed using these new methods. In these data, because the validation studies contained less than 200 observations and the events of interest were relatively rare, as is typical, the potential improvements offered by this new estimator were not apparent.

Adult↗

Parental report of the early development of children with regressive autism: the delays-plus-regression phenotype.

Most children with autism demonstrate developmental abnormalities in their first year, whereas others display regression after mostly normal development. Few studies have examined the early development of the latter group. This study developed a retrospective measure, the Early Development Questionnaire (EDQ), to collect specific, parent-reported information about development in the first 18 months. Based on their EDQ scores, 60 children with autism between the ages of 3 and 9 were divided into three groups: an early onset group (n = 29), a definite regression group (n = 23), and a heterogeneous mixed group (n = 8). Significant differences in early social development were found between the early onset and regression groups. However, over 50 percent of the children who experienced a regression demonstrated some early social deficits during the first year of life, long before regression and the apparent onset of autism. This group, tentatively labeled 'delays-plus-regression', deserves further study.

Autistic Disorder↗

Regression diagnostics for the class A regressive model with quantitative phenotypes.

Regression diagnostic methods are developed and investigated under the Class A regressive model proposed by Bonney [(1984) Am J Med Genet 18:731-749]. We call a family whose phenotypic distribution does not conform to the same genetic model as the majority of the families an etiotic family. The exact case-deletion approach for identifying etiotic families, based on examining the changes in each model parameter estimate by excluding one family at a time, is very time-consuming. We proposed three alternative diagnostic methods: the empirical influence function (EIF), the one-step approximation, and the approximated one-step approach. These methods can be computed efficiently and were incorporated into the existing software package S.A.G.E. A thorough Monte-Carlo investigation of the performance of the diagnostic methods was conducted and generally supports the EIF approach as the recommended alternative. The phenotypic variance is the parameter whose associated regression diagnostic most frequently and correctly identified etiotic families in the models that were examined. An analysis of body mass index data from 402 individuals in 122 Muscatine, Iowa families is used to illustrate the methods. A Class A regressive model with a recessive major locus and equal mother-offspring and father-offspring correlations provided the best-fitting model. The proposed regression diagnostics identified up to 7.4% of the 122 families as etiotic. As a result of this investigation, case-deletion diagnostic assessment is now a practical component in the analysis of quantitative family data.

Adolescent↗

Regression analysis with multiplicative and time-varying additive regression coefficients with examples from breast and colon cancer.

Regression analysis may be used to simplify the representation of mortality rates when there are many significant prognostic covariates or to adjust for confounding effects. The principal request of the regression model in this range of use is to have unbiased parameter estimates. A model with constant multiplicative and time-varying additive regression coefficients is discussed. The model allows some covariate effects to be multiplicative while allowing others to have a time-varying additive effect. Thus, it is a mix of classical Cox regression and Aalen's additive risk model. A major characteristic of cancer mortality rates, in contrast to general mortality rates, is that hazard rates, after a potentially initial increase, decrease, although not always tending to zero. Cancer diseases, like breast and colon cancer, have significantly increased cause-specific mortality rates even 20 years after diagnosis. Another major feature in cancer survival analysis is that many covariate effects are time-varying. Some covariate effects, like age at diagnosis, may only be significant for a limited time after diagnosis. Furthermore, some treatment procedures may initially decrease the mortality, while the long-term effect may be opposite. A third issue is that average covariate effects are very often not multiplicative. Estimation is carried out iteratively; the cumulative additive regression functions are estimated non-parametrically using a least-squares method and the multiplicative parameters are estimated from the partial likelihood. The method is applied on 3201 female breast cancer and 1372 male colon cancer patients.

Adult↗