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PubMed2002

A weighted estimating equation for linear regression with missing covariate data.

Linear regression is one of the most popular statistical techniques. In linear regression analysis, missing covariate data occur often. A recent approach to analyse such data is a weighted estimating equation. With weighted estimating equations, the contribution to the estimating equation from a complete observation is weighted by the inverse 'probability of being observed'. In this paper, we propose a weighted estimating equation in which we wrongly assume that the missing covariates are multivariate normal, but still produces consistent estimates as long as the probability of being observed is correctly modelled. In simulations, these weighted estimating equations appear to be highly efficient when compared to the most efficient weighted estimating equation as proposed by Robins et al. and Lipsitz et al. However, these weighted estimating equations, in which we wrongly assume that the missing covariates are multivariate normal, are much less computationally intensive than the weighted estimating equations given by Lipsitz et al. We compare the weighted estimating equations proposed in this paper to the efficient weighted estimating equations via an example and a simulation study. We only consider missing data which are missing at random; non-ignorably missing data are not addressed in this paper.

Adolescent↗
PubMed1991

A statistical assessment of orthodontic practices, product usage, and the development of skin lesions.

Recently there has been great interest in skin lesions on the hands of orthodontic personnel who are exposed to a wide variety of metals, bonding agents, and other materials. Thus this 1985 national survey of 448 Canadian orthodontists (response rate 49%) was undertaken to examine orthodontic practice activities, bonding agent and wire product use, and prevalence of skin lesions on the hands and their possible association with these products. About 13% of the 213 responding orthodontists and at least one other staff member in 18% of the orthodontic practices reported the occurrence of hand lesions (reactions) over the preceding 3 years typical of exposure to dental materials. In nearly one fourth of the offices, at least one person was affected. Regarding product use. Concise, Mono-Lok, and Endur bonding agents and stainless steel, Nitinol, and Elgiloy wires were used most often. The orthodontists reported frequent involvement in bonding activities and infrequent use of gloves. Of all the individual and combined materials and practice characteristics and activities tested singly and multivariately for statistical association with hand lesions, only the orthodontists' use of Mono-Lok, gloves, and the activity of frequently cleaning excess bonding agent were statistically related to the lesions. Multiple logistic regression suggested that the statistical effects of Mono-Lok use and removal of excess bonding agent were independent; thus removal of excess agent may have consequences for lesion development separate from Mono-Lok use.

Bisphenol A-Glycidyl Methacrylate↗
PubMed2004

Regression to the mean: what it is and how to deal with it.

BACKGROUND: Regression to the mean (RTM) is a statistical phenomenon that can make natural variation in repeated data look like real change. It happens when unusually large or small measurements tend to be followed by measurements that are closer to the mean. METHODS: We give some examples of the phenomenon, and discuss methods to overcome it at the design and analysis stages of a study. RESULTS: The effect of RTM in a sample becomes more noticeable with increasing measurement error and when follow-up measurements are only examined on a sub-sample selected using a baseline value. CONCLUSIONS: RTM is a ubiquitous phenomenon in repeated data and should always be considered as a possible cause of an observed change. Its effect can be alleviated through better study design and use of suitable statistical methods.

Cholesterol, HDL↗
PubMed2005

Parents' intentions to use paediatric nurse practitioner services in an emergency department.

AIM: This paper reports on a study investigating the factors which influence parental intent to use the services of a paediatric nurse practitioner in an emergency department. BACKGROUND: Research has shown that nurse practitioners provide quality care to paediatric and adult primary care and non-urgent emergency patients. Although there are studies that assess patient satisfaction with nurse practitioner care, there are few that report on what factors initially influence the public to use these services. No studies have examined the factors that affect parental decision-making to access nurse practitioner care in emergency settings for their children. METHODS: A questionnaire was completed by 100 parents who visited a tertiary paediatric emergency department for their child's non-urgent emergency care needs. Information captured included demographic variables, role responsibility tasks that parents would be willing to have a nurse practitioner provide, and parents' perceptions of the characteristics of the nurse practitioner role. Descriptive statistics and logistic regression were used to analyse the demographic data, percentiles were compiled for the role responsibility tasks, and logistic regression was used to analyse parents' perceptions of the characteristics of the nurse practitioner role. The data were collected in 2002. RESULTS: Eighty-three per cent of parents indicated their intention to access nurse practitioner services for a variety of childhood symptoms. Logistic regression revealed that the compatibility of nurse practitioner services with parents' beliefs and needs was the most statistically significant (P < 0.05) independent variable predicting parental intent to use these services. Demographic variables did not have a statistically significant influence. CONCLUSIONS: The public does not seem to understand fully the scope of nursing practice, and this is a concern if people are to feel comfortable with expanded roles for nurses. Thus, the public should be given information that not only describes the role of nurse practitioners, but also includes facts about the scope of practice of Registered Nurses as this may be helpful in producing a favourable attitude towards nurse practitioner care.

Adolescent↗
PubMed2005

The use of correlation and regression methods in optometry.

Correlation and regression are two of the statistical procedures most widely used by optometrists. However, these tests are often misused or interpreted incorrectly, leading to erroneous conclusions from clinical experiments. This review examines the major statistical tests concerned with correlation and regression that are most likely to arise in clinical investigations in optometry. First, the use, interpretation and limitations of Pearson's product moment correlation coefficient are described. Second, the least squares method of fitting a linear regression to data and for testing how well a regression line fits the data are described. Third, the problems of using linear regression methods in observational studies, if there are errors associated in measuring the independent variable and for predicting a new value of Y for a given X, are discussed. Finally, methods for testing whether a non-linear relationship provides a better fit to the data and for comparing two or more regression lines are considered.

Humans↗
PubMed2001

[Suggestions for standardized collection of morning urine for assessment of NTx levels in patients with osteoporosis].

UNLABELLED: The authors examined 79 patients (n = 79) with primary and secondary osteoporosis, incl.31 men (nM = 31) aged 31-61 years and 48 women (nF = 48, aged 33 to 65 years. In these patients they assessed NTx (amino-terminal telopeptide of type I collagen of the Ist organic bone matrix) in 24 (NTx24) and 2-hour morning (NTx2) diuresis (from 6 to 8 a.m.). OBJECTIVE: 1. To assess the relationship between values of NTx in th suggested 2-hour diuresis and NTx values in the standard 24- hour diuresis differentiated by sex. 2. To compare the ratio (index) of widths of 95% confidence intervals (CI) for NTx2 and NTx24 with the ratio (index) of reference widths (manual OSTEX, USA) for NTx in the first morning urine (NTx1) and for NTX24 differentiated by sex. 3. Evaluate the suggested 2-hour diuresis for assessment of NTx. STATISTICAL ANALYSIS: Stochastic-determinist linear regression analysis. RESULTS: 1. Between values NTx24 and NTx2 a statistically significant regression correlation was found (p < 0.001) (men: r = 0.352, women r2 = 0.781). The indices of widths of reference limits (IR) of OSTEX Co. USA reach values 2.1 times higher (0.7 times) than indices of widths of CI for osteoporosis (IO) in men as well as women. CONCLUSION: 1. Between values of NTx24 and NTx2 is a significant regression relation. Both urine samples can be used for assessment of the NTx level. 2. Higher values of IR and IO indices for women as well as men confirm a greater dispersal of NTx1 values as compared with NTx2 values. 3. Introduction of two-hour morning diuresis will reduce the extent of variation of NTx values during repeated examinations and provide more accurate information as compared with assessment of NTx in any of the first morning samples of urine according to instructions of the manufacturers of the kits.

Adult↗
PubMed1979

[Some remarks about the spatial differentiation of fertility in Poland].

"Some problems are discussed in connection with the estimation and interpretation of regression equations. Stability in time is suggested as one of the criteria of goodness of fit.... Several regression equations are estimated giving the gross reproduction rate as a linear function of the proportion of economically active females outside agriculture (SUMMARY IN ENG, RUS)

Birth Rate↗
PubMed1999

Tumour necrosis factor-alpha and interleukin-1 and -6 in fibrocystic breast disease.

The risk of developing breast cancer is higher in women presenting gross cystic disease (cysts > 3 mm in diameter) of the breast with intracystic K+/Na+ > 3 as compared with K+/Na+ < 3. The present study reports the levels of tumour necrosis factor-alpha (TNF-alpha), interleukin-1 (IL-1), and interleukin-6 (IL-6) in the breast cyst fluid of women with gross cystic disease and analyses the relationship between the intracystic concentration of these cytokines, sex steroid hormones, and the K+/Na+ ratio. The concentration of these cytokines, estradiol, testosterone, dehydroepiandrosterone sulfate (DHEA-S), and 17-OH-progesterone were determined in the breast cyst fluid of 54 women with gross cystic disease. No significant differences were found in the cystic levels of IL-1 between cysts with intracystic K+/Na+ < 3 and > 3. However, in cysts with intracystic K+/Na+ > 3 we found a lower concentration of IL-6 and TNF-alpha than in those with intracystic K+/Na+ < 3. Stepwise multiple linear regression analysis demonstrated that the concentration of IL-6 in breast cyst fluid was predicted statistically by a negative regression coefficient for the concentration of estradiol and DHEA-S, and by a positive regression coefficient for the concentration of TNF-alpha. The concentration of TNF-alpha in breast cyst fluid was predicted statistically by a positive regression coefficient for the concentration of IL-6, and by a negative regression coefficient for the concentration of estradiol. No candidate variable was included in the model to predict concentrations of IL-1 in breast cyst fluid. Our results indicate that IL-6 and TNF-alpha could have a local 'protector' role in gross cystic disease, and that they could be used as a marker to identify cyst type.

17-alpha-Hydroxyprogesterone↗
PubMed1993

[Usefulness of residuals in clinical research].

The simple linear regression analysis, multiple linear regression and logistic regression constitute powerful statistical analysis tools widely used in clinical research. These kinds of analyses are based upon mathematical models which at the same time are established on certain basic assumptions. The regression analysis assumptions are basically: a) that the model is really linear, b) that the distribution of data is normal (from a statistical point of view), c) that the variances of the employed data are homogeneous (homocedastics) and that the included data are independent. The regression diagnostic has become popular as a form to evaluate if the assumptions have been accomplished, one of its most important techniques is the residual analysis. A residual can be defined as the value which measures the distance between the regression line and the corresponding value of the variable "y". Among these kinds of residuals used to evaluate the assumptions of regression are: the crude residual, the standardized, of student and the jackknife. The most useful among them is the jackknife residual. The usefulness and limitations of the residuals in the evaluation of the regression analysis assumptions are described, basically referring to the identification and handling of extreme values (outliers).

Evaluation Studies as Topic↗
PubMed1996

Reconstruction of femur length from markers of its proximal end.

Length of femur and stature are of forensic and anthropological significance. Bony markers such as the head and neck of the femur can be of use in determining the femoral length when only a fragment of the proximal femur is available. A total of 171 South Indian unpaired femora, devoid of gross pathology and grouped by genders and sides, were used to measure the neck-shaft angle, neck length, intertrochanteric apical axis length, maximum vertical diameter of the femur head, and maximum femur length. The data were statistically analyzed for regression. Length of femur significantly correlated with the other dimensions. Simple (linear) regression equations of the length of femur against the neck-shaft angle, neck length, intertrochanteric apical axis length, and maximum vertical diameter of the head have been derived. The equations seem to be robust and can be used for different populations.

Adult↗
PubMed2006

Biosorption of reactive dye using acid-treated rice husk: factorial design analysis.

A factorial experimental design technique was used to investigate the biosorption of reactive red RGB (lambda(max)=521 nm) from water solution on rice husk treated with nitric acid. Biosorption is favored because of abundance of biomass, low cost, reduced sludge compared to conventional treatment techniques and better decontamination efficiency from highly diluted solutions. Factorial design of experiments is employed to study the effect of four factors pH (2 and 7), temperature (20 and 40), adsorbent dosage (5 and 50mg/L) and initial concentration of the dye (50 and 250 mg/L) at two levels low and high. The efficiency of color removal was determined after 60 min of treatment. Main effects and interaction effects of the four factors were analyzed using statistical techniques. A regression model was suggested and it was found to fit the experimental data very well. The results were analyzed statistically using the Student's t-test, analysis of variance, F-test and lack of fit to define most important process variables affecting the percentage dye removal. The most significant variable was thus found to be pH.

Acids↗
PubMed1992

Isoleucine requirements of the chicken: requirement for maintenance.

1. The maintenance requirement of adult male cockerels for isoleucine was measured by nitrogen balance. Measured amounts of a diet first-limiting in isoleucine were fed by tube each day for 6 d to give a range of intakes of from 0 to 100 mg isoleucine/kg body weight. A nitrogen-free diet containing energy, vitamins and both major and trace minerals was offered ad libitum during that time. Two series of diets were used, an unbalanced series, as described above, and a balanced series, in which synthetic L-isoleucine was added to each diet in the unbalanced series. Excreta were collected in bags during the last 3 d of the balance period and the N content of the excreta was analysed on wet, homogenised samples. 2. The resultant linear regressions were not statistically different for the unbalanced and the balanced series indicating that the response measured was to isoleucine. The pooled regression equation was: N retention = -144.14 (+/- 8.5) + 2.421 (+/- 0.19)I where I is the intake of isoleucine in mg/kg body weight day. The isoleucine required to maintain the body at zero N retention was therefore calculated to be 60 (+/- 3.2) mg/kg body weight day. 3. A case has been made for the expression of the amino acids required for maintenance to be in terms not of body weight but scaled according to the degree of maturity of the animal, and on this basis the amount of isoleucine required for maintenance was calculated to be 300 mg per unit of maintenance protein (Pm 0.73 mu) per day.

Amino Acids↗
PubMed2001

Clinical utility of monitoring tacrolimus blood concentrations in liver transplant patients.

The relationship between the dose of tacrolimus, trough tacrolimus blood concentration, and selected clinical endpoints (acute rejection, nephrotoxicity, and other toxicities) were examined in a prospective, multicenter clinical trial to validate the use of an enzyme-linked immunosorbent assay (ELISA) for monitoring whole-blood concentrations of tacrolimus in liver transplant patients. A total of 111 subjects from six transplant centers were evaluated over 12 weeks posttransplantation. In addition to trough tacrolimus blood concentrations, hematocrit, ALT, AST, GGTP, alkaline phosphatase, total bilirubin, serum creatinine, BUN, serum potassium, serum magnesium, blood glucose, and serum albumin were also measured. The relationship between trough tacrolimus blood concentrations and clinical endpoints was analyzed using both a logistic regression model and a Cox proportional hazard model. By logistic regression analysis, a statistically significant (p = 0.0465) relationship between increasing trough tacrolimus blood concentrations and decreasing risk of acute rejection was demonstrated over a 7-day time window. Nephrotoxicity and other toxicities also demonstrated statistically significant relationships with trough tacrolimus blood concentrations. The results of the Cox analysis were consistent with the logistic regression analysis. Using receiver operator characteristic curves, trough tacrolimus concentrations as measured by the ELISA method were able to differentiate the occurrence of nephrotoxicity and toxicity from nonevents. To minimize nephrotoxicity of tacrolimus, it is necessary to maintain trough blood concentrations below 15 ng/ml. This study demonstrates that the ELISA method used to measure tacrolimus blood concentrations in this study provides information of predictive value for managing the risk of nephrotoxicity, other toxicity, and rejection in liver transplant patients.

Administration, Oral↗
PubMed1997

Estimation of excess risk from case-control data using Aalen's linear regression model.

We introduce methods for statistical inference in Aalen's non-parametric linear regression model of disease incidence (Aalen, 1989, Statistics in Medicine 8, 907-925) from nested case-control data. These methods provide the basis for estimation of excess risk as a linear function of dose and absolute risk for a given exposure history. The methods are illustrated by estimating excess and absolute risks associated with radon exposure and smoking from nested case-control samples from the Colorado Plateau uranium miners cohort.

Adult↗
PubMed1995

Logistic regression with incompletely observed categorical covariates--investigating the sensitivity against violation of the missing at random assumption.

Missing values in the covariates are a widespread complication in the statistical inference of regression models. The maximum likelihood principle requires specification of the distribution of the covariates, at least in part. For categorical covariates, log-linear models can be used. Additionally, the missing at random assumption is necessary, which excludes a dependence of the occurrence of missing values on the unobserved covariate values. This assumption is often highly questionable. We present a framework to specify alternative missing value mechanisms such that maximum likelihood estimation of the regression parameters under a specified alternative is possible. This allows investigation of the sensitivity of a single estimate against violations of the missing at random assumption. The possible results of a sensitivity analysis are illustrated by artificial examples. The practical application is demonstrated by the analysis of two case-control studies.

ABO Blood-Group System↗
PubMed1992

Analysis of concentration-response relationships by seemingly unrelated nonlinear regression (SUNR) technique.

In performing statistical evaluation of concentration-response relationship in pharmacological studies, all the commercially available statistical packages assume each data point is an independent measure of the drug response, and do not account for the dependence between the multiple measurements taken from the same subject (tissue, animal, or sample). Seemingly unrelated nonlinear regression (SUNR) is a statistical technique that takes into account both within-and between-subject variance. This technique has been implemented in an SAS-based interactive program called SUNR. The statistical analyses are based upon the original work by Gallant (Gallant, 1975, J Econometrics 3:35-50; Gallant and Goebel, 1976, JASA 71:961-967), which has been further developed by Muller and Helms (1984) (Presented at ASA meeting in Washington, D.C.) To test this program, we have analyzed both simulated and actual data with SUNR, comparing our results to those of several popular statistical programs. All the programs yielded essentially the same estimates for the EC50, minimum and maximum response in both the simulated and experimental data sets. However, our results differed markedly from the commercial packages in the estimates of standard errors associated with the estimated maxima. When analyzing simulated data, which were far less noisy than the experimental data, differences between the analyses were minimal. However, in the analyses of experimental data, the standard errors calculated by the commercial programs appear to significantly underestimate the standard error. Using SUNR, however, the 95% confidence limits on the maxima are markedly wider, and, importantly, always cover the observed actual data range.

Animals↗
PubMed1992

Infant mortality and crisis in Mexico.

Data derived from the Encuesta Nacional de Fecundidad y Salud (ENFES) confirm that overall levels of infant mortality in Mexico have been steadily declining. However, a more specific analysis furnishes evidence that this decline has occurred at varying rates within different social groups, reflecting an increase in social inequalities. The analytical strategy used in this article leads to three basic conclusions: (1) the impact of the economic crisis on infant mortality is reflected not in a reversal of the declining trend but an increase in social inequalities; (2) certain variables universally accepted as determinants of infant mortality, such as mother's education, seem nonsignificant for some social sectors; and (3) certain biodemographic characteristics assumed to have a uniform mortality-related behavior vary among sectors, suggesting that even these constants are determined by social factors.

Educational Status↗
PubMed1989

Statistical analysis of epidemiologic data of pregnancy outcomes.

In this paper, a generalized logistic regression model for correlated observations is used to analyze epidemiologic data on the frequency of spontaneous abortion among a group of women office workers. The results are compared to those obtained from the use of the standard logistic regression model that assumes statistical independence among all the pregnancies contributed by one woman. In this example, the correlation among pregnancies from the same woman is fairly small and did not have a substantial impact on the magnitude of estimates of parameters of the model. This is due at least partly to the small average number of pregnancies contributed by each woman.

Abortion, Spontaneous↗