Trina Hosmer

A COMPARISON OF GOODNESS-OF-FIT TESTS FOR THE LOGISTIC REGRESSION MODEL

Recent work has shown that there may be disadvantages in the use of the chi-square-like goodness-of-fit tests for the logistic regression model proposed by Hosmer and Lemeshow that use fixed groups of the estimated probabilities. A particular concern with these grouping strategies based on estimated probabilities, fitted values, is that groups may contain subjects with widely different values of the covariates. It is possible to demonstrate situations where one set of fixed groups shows the model fits while the test rejects fit using a different set of fixed groups. We compare the performance by simulation of these tests to tests based on smoothed residuals proposed by le Cessie and Van Houwelingen and Royston, a score test for an extended logistic regression model proposed by Stukel, the Pearson chi-square and the unweighted residual sum-of-squares. These simulations demonstrate that all but one of Roystons tests have the correct size. An examination of the performance of the tests when the correct model has a quadratic term but a model containing only the linear term has been fit shows that the Pearson chi-square, the unweighted sum-of-squares, the Hosmer-Lemeshow decile of risk, the smoothed residual sum-of-squares and Stukels score test, have power exceeding 50 per cent to detect moderate departures from linearity when the sample size is 100 and have power over 90 per cent for these same alternatives for samples of size 500. All tests had no power when the correct model had an interaction between a dichotomous and continuous covariate but only the continuous covariate model was fit. Power to detect an incorrectly specified link was poor for samples of size 100. For samples of size 500 Stukels score test had the best power but it only exceeded 50 per cent to detect an asymmetric link function. The power of the unweighted sum-of-squares test to detect an incorrectly specified link function was slightly less than Stukels score test. We illustrate the tests within the context of a model for factors associated with low birth weight.

The inverse relationship between number of steps per day and obesity in a population-based sample – the AusDiab study

Background:Physical activity (PA) is inversely associated with obesity but the effect has been difficult to quantify using questionnaires. In particular, the shape of the association has not yet been well described. Pedometers provide an opportunity to better characterize the association.Methods:Residents of households over the age of 25 years in randomly selected census districts in Tasmania were eligible to participate in the AusDiab cross-sectional survey conducted in 1999–2000. 1848 completed the AusDiab survey and 1126 of these (609 women and 517 men) wore a pedometer for 2-weekdays. Questionnaire data on recent PA, TV time and other factors were obtained. The outcomes were waist circumference (in cm) and body mass index (BMI) (kg/m2).Results:Increasing daily steps were associated with a decline in the obesity measures. The logarithmic nature of the associations was indicated by a sharper decline for those with lower daily steps. For example, an additional 2000 steps for those taking only 2000 steps per day was associated with a reduction of 2.8 (95% confidence interval (CI): 2.1,4.4) cm in waist circumference among men (for women; 2.2 (95% CI: 0.6, 3.9 cm)) with a baseline of only 2000, steps compared to a 0.7 (95% CI 0.3, 1.1) cm reduction (for women; 0.6 (95% CI: 0.2, 1.0)) for those already walking 10 000 steps daily. In the multivariable analysis, clearer associations were detected for PA and these obesity measures using daily step number rather than PA time by questionnaire.Interpretation:Pedometer measures of activity indicate that the inverse association between recent PA and obesity is logarithmic in form with the greatest impact for a given arithmetic step number increase seen at lower levels of baseline activity. The findings from this study need to be examined in prospective settings.

Reduced voluntary activity precedes adult-onset obesity in Nhlh2 knockout mice.

Targeted deletion of the neuronal basic helix-loop-helix transcription factor Nhlh2 results in adult-onset obesity in mice. Measurement of body weight and body composition in animals aged 3-25 weeks indicates that while male and female Nhlh2 knockout (N2KO) animals both show adult-onset obesity, the time frame for development of obesity is different, with females becoming obese by 7 weeks of age and males becoming obese by 10 weeks of age. Heterozygous (HET) animals also become obese but with a slower onset, indicating a dosage effect for the activity of the Nhlh2 transcription factor. Food intake, body temperature, and voluntary activity were measured in both preobese and obese N2KO, HET, and wild-type (WT) animals to determine which factors contributed to weight gain. While increased food intake and decreased body temperature were found in older obese N2KO animals, only reduced physical activity preceded the onset of obesity in N2KO mice. N2KO animals had no deficit in either circadian rhythm or balance and motor control, indicating that reduced voluntary activity is the result of a behavioral change. These data demonstrate a role for the Nhlh2 transcription factor in controlling genes important to energy expenditure, and more specifically voluntary physical activity of animals.

Effect of understory and border vegetation composition on phytophagous and predatory mites in Massachusetts commercial apple orchards

Abstract Ground cover and border composition were determined using ordination in 28 Massachusetts commercial apple orchard blocks. The presence or absence of phytophagous and predatory mites was recorded after 2 min timed scans of ten randomly selected apple leaves and of the five most commonly occurring plants at ten aisle, row, and border sampling sites. Orchard ground cover vegetation was very diverse. Grasses were the predominant ground-cover in aisles, with broadleaf plants predominant in the rows. Orchard borders were somewhat less diverse than the orchards themselves. Rubus spp. were the most frequently occurring border plants. All types of phytophagous and predatory mites examined were significantly more likely to be found on herbaceous forbs and woody plants (dicots) than on grasses (monocots).

Oestrogen treatment for tall stature in girls: estimating the effect on height and the error in height prediction

Objective  To determine the effect of oestrogen treatment on attenuating the growth of tall girls after adjusting for error in height prediction.

A comparison of the maximum likelihood and discriminant function estimators of the coefficients of the logistic regression model for mixed continuous and discrete variables

A model for mixed continuous and discrete variables suggested by Chang and Afifi (1974) and Krzanowski (1975) is used to explore the bias in the discriminant function (DF) approach to estimation of the coefficients in the multiple1ogistic regression model. When the data come from this mixed variable model the DF estimator of the coefficients of the continuous variables are asymptotically unbiased. The DF estimator of the intercept and coefficients for the discrete variables may be severely biased. The magnitude of the bias is shown to depend in a systematic way on the true value of the coefficients and the underlying probabilities of the out-come of discrete variables. The implications for analysis are discussed.

Use of visual traps for monitoring insect pests in the Massachusetts apple IPM program

Abstract Visual traps were evaluated for effectiveness as monitoring devices for the tarnished plant bug (Lygus lineolaris, TPB), European apple sawfly (Hoplocampa testudinea, EAS) and apple blotch leafminer (Phyllonorycter crataegella, ABLM). Results indicate: 1. A significant positive linear relationship between on-tree fruit injury surveys and cumulative captures on white, sticky-coated rectangles of TPB adults, for the tree development periods silver tip through tight cluster or silver tip through late pink, and for captures of EAS adults in blocks receiving no pre-bloom insecticide sprays. 2. A significant positive relationship with linear and quadratic components between on-tree fruit injury surveys and cumulative captures on white rectangles of EAS adults in blocks that did receive pre-bloom insecticide sprays. 3. A significant positive relationship with linear and quadratic components between peak mines per leaf and cumulative captures of ABLM adults on tent-shaped, red enamel (sticky side up) traps for silver tip through late pink or silver tip through two weeks past petal fall. Provisional economic injury levels are suggested as 2.0% and 0.7% fruit injury and 0.13% mines per leaf for TPB, EAS and first generation ABLM, respectively. Provisional action threshold levels based on these economic injury levels are presented for TPB (cumulative capture of 2.4 per trap for silver tip through tight cluster or 4.2 per trap for silver tip through late pink respectively), EAS (cumulative capture of 4.7 per trap in blocks that received no pre-bloom insecticides, or 5.5 per trap in blocks receiving pre-bloom insecticides) and ABLM (cumulative capture of 13 moths per trap from silver tip through late pink).

A comparison of three methods of estimating the logistic regression coefficients

A Sampling experiment performed using data collected for a large clinical trial shows that the discriminant function estimates of the logistic regression coefficients for discrete variables may be severely biased. The simulations show that the mixed variable location model coefficient estimates have bias which is of the same magnitude as the bias in the coefficient estimates obtained using conditional maximum likelihood estimates but require about one-tenth of the computer time.

Imaging: A Tool for Data Reduction

Abstract This article illustrates the use of high-resolution color graphic images obtained from raster terminals to reduce an immense amount of data into a few meaningful time series. The steps that were taken to achieve this data reduction and their appropriate images are given. The time series were analyzed using Box and Jenkins time series methods (see also McCleary and Hay 1980), and the results are discussed.

Communications: the internal structure

The ultimate goal of a university computing center is to serve the users. This paper intends to show what the typical demands of internal center groups are on one another, how the demands may be analyzed in order to resolve priority conflicts,and what inter-group communications are necessary to enable the internal support groups to provide the users with timely, competent service and reliable, accurate information.