S. le Cessie

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.

Ridge estimators in logistic regression

SUMMARY In this paper it is shown how ridge estimators can be used in logistic regression to improve the parameter estimates and to diminish the error made by further predictions. Different ways to choose the unknown ridge parameter are discussed. The main attention focuses on ridge parameters obtained by cross-validation. Three different ways to define the prediction error are considered: classification error, squared error and minus log-likelihood. The use of ridge regression is illustrated by developing a prognostic index for the two-year survival probability of patients with ovarian cancer as a function of their deoxyribonucleic acid (DNA) histogram. In this example, the number of covariates is large compared with the number of observations and modelling without restrictions on the parameters leads to overfitting. Defining a restriction on the parameters, such that neighbouring intervals in the DNA histogram differ only slightly in their influence on the survival, yields ridge-type parameter estimates with reasonable values which can be clinically interpreted. Furthermore the model can predict new observations more accurately.

Smoking is a risk factor for anti-CCP antibodies only in rheumatoid arthritis patients who carry HLA-DRB1 shared epitope alleles

Objectives: To study the gene–environment interaction of tobacco exposure and shared epitope on autoantibodies in patients with rheumatoid arthritis and undifferentiated arthritis. Methods: From incident cases of arthritis (n = 1305), patients who did not fulfil any classification criteria (undifferentiated arthritis (n = 486)) and those who fulfilled the American College of Rheumatology criteria for rheumatoid arthritis (n = 407) were identified. IgM rheumatoid factor (RF), anti-cyclic-citrullinated peptide (CCP) antibodies, and HLA-DRB1 alleles were determined. Results: In rheumatoid arthritis, an interaction was found between tobacco exposure and shared epitope for the presence of anti-CCP antibodies, as the odds ratio for anti-CCP antibodies in patients having both tobacco exposure (TE) and shared epitope (SE) was higher than the summed odds ratios of patients having only tobacco exposure or shared epitope (odds ratios: TE+/SE−, 1.07; TE−/SE+, 2.49; and TE+/SE+, 5.27—all relative to TE−/SE−). A similar effect was found for RF, but stratification showed that the interaction primarily associated with the anti-CCP antibody response. In patients with undifferentiated arthritis at two weeks, or with persistent undifferentiated arthritis after one year, no interaction between tobacco exposure and shared epitope was observed for the presence of autoantibodies. Conclusions: Tobacco exposure increases the risk factor for anti-CCP antibodies only in shared epitope positive patients with rheumatoid arthritis. The gene–environment interaction between smoking and shared epitope leading to autoantibodies is specific for rheumatoid arthritis and is not observed in undifferentiated arthritis.

Induction versus expectant monitoring for intrauterine growth restriction at term: randomised equivalence trial (DIGITAT)

Objective To compare the effect of induction of labour with a policy of expectant monitoring for intrauterine growth restriction near term. Design Multicentre randomised equivalence trial (the Disproportionate Intrauterine Growth Intervention Trial At Term (DIGITAT)). Setting Eight academic and 44 non-academic hospitals in the Netherlands between November 2004 and November 2008. Participants Pregnant women who had a singleton pregnancy beyond 36+0 weeks’ gestation with suspected intrauterine growth restriction. Interventions Induction of labour or expectant monitoring. Main outcome measures The primary outcome was a composite measure of adverse neonatal outcome, defined as death before hospital discharge, five minute Apgar score of less than 7, umbilical artery pH of less than 7.05, or admission to the intensive care unit. Operative delivery (vaginal instrumental delivery or caesarean section) was a secondary outcome. Analysis was by intention to treat, with confidence intervals calculated for the differences in percentages or means. Results 321 pregnant women were randomly allocated to induction and 329 to expectant monitoring. Induction group infants were delivered 10 days earlier (mean difference −9.9 days, 95% CI −11.3 to −8.6) and weighed 130 g less (mean difference −130 g, 95% CI −188 g to −71 g) than babies in the expectant monitoring group. A total of 17 (5.3%) infants in the induction group experienced the composite adverse neonatal outcome, compared with 20 (6.1%) in the expectant monitoring group (difference −0.8%, 95% CI −4.3% to 3.2%). Caesarean sections were performed on 45 (14.0%) mothers in the induction group and 45 (13.7%) in the expectant monitoring group (difference 0.3%, 95% CI −5.0% to 5.6%). Conclusions In women with suspected intrauterine growth restriction at term, we found no important differences in adverse outcomes between induction of labour and expectant monitoring. Patients who are keen on non-intervention can safely choose expectant management with intensive maternal and fetal monitoring; however, it is rational to choose induction to prevent possible neonatal morbidity and stillbirth. Trial registration International Standard Randomised Controlled Trial number ISRCTN10363217.

A Goodness-of-Fit Test for Binary Regression Models, Based on Smoothing Methods

A new global test statistic for models with continuous covariates and binary response is introduced. The test statistic is based on nonparametric kernel methods. Explicit expressions are given for the mean and variance of the test statistic. Asymptotic properties are considered and approximate corrections due to parameter estimation are presented. Properties of the test statistic are studied by simulation. The goodness-of-fit method is illustrated on data from a Dutch follow-up study on preterm infants. Recommendations for practitioners are given.

Effect of intensive exercise on patients with active rheumatoid arthritis: a randomised clinical trial.

OBJECTIVE To investigate the effects of a dynamic, intensive exercise regimen on pain, disease activity, and physical functioning in active rheumatoid arthritis (RA). METHODS 64 patients with RA with a mean age of 60 (13) years and mean disease duration of 8 (8) years, admitted to hospital because of active disease, were randomly assigned to an intensive exercise programme or to a conservative exercise programme during their period in hospital with a mean length of 30 (14) days. The intensive exercise programme consisted of knee and shoulder dynamic and isometric muscle strengthening exercises against resistance five times a week and conditioning bicycle training three times a week and was supplemental to the conservative exercise programme of range of motion and isometric exercises. Indices of disease activity, pain, muscle strength, and functional ability were assessed at 0, 3, 6, 12, and 24 weeks by a blinded observer. RESULTS The medical treatment during the study was the same in both groups. Both groups improved in measures of disease activity, differences between groups were not statistically significant. The mean improvement in disease activity score at 24 weeks in the intensive and conservative exercise group was −1.4 (1.5) and −0.7 (1.4), respectively. Measures of physical functioning improved significantly for patients in the intensive exercise group, and differences between groups were statistically significant for measures of muscle strength. CONCLUSION A short term intensive exercise programme in active RA is more effective in improving muscle strength than a conservative exercise programme and does not have deleterious effects on disease activity.

Logistic Regression for Correlated Binary Data

The modelling of correlated binary outcomes, in such a way that the marginal response probabilities are still logistic, is considered. Different association measures for the dependence between correlated observations are discussed. For paired correlated data the full likelihood can be evaluated; for an arbitrary number of correlated observations a pseudolikelihood approach to obtain parameter estimates is proposed. The results are illustrated on data from a Dutch follow‐up study on preterm infants.

Comparison of high and low intensity training in well controlled rheumatoid arthritis. Results of a randomised clinical trial.

OBJECTIVE: To investigate the benefit of intensive dynamic exercises in comparison to range of motion (ROM) and isometric exercises in rheumatoid arthritis. METHODS: 100 consecutive rheumatoid arthritis patients on stable medication were randomly assigned to (1) intensive dynamic group exercises which included full weight bearing exercises and conditioning exercises on a stationary bicycle while the heart rate was maintained at 70-85% of the age predicted maximum heart rate, (2) range of motion (ROM) exercises and isometric exercises in a group, (3) individual isometric and ROM exercises, and (4) home instructions for isometric and ROM exercises. Variables of physical condition, muscle strength, joint mobility, daily functioning (HAQ), and disease activity were assessed before and after the 12 week exercise course, and 12 weeks thereafter. An intention to treat analysis was performed. RESULTS: Increases in aerobic capacity (n = 77), muscle strength, and joint mobility in the high intensity exercise programme were respectively 17%, 17% and 16% and differed significantly from the changes in aerobic capacity, muscle strength, and joint mobility in the other exercise groups. No deterioration of disease activity was observed. Twelve weeks after discontinuation of the exercise course the gain in physical capacity had disappeared. CONCLUSIONS: Intensive dynamic training is more effective in increasing aerobic capacity, joint mobility, and muscle strength than ROM exercises and isometric training in rheumatoid arthritis patients with well controlled disease.

Radiological outcome after four years of early versus delayed treatment strategy in patients with recent onset rheumatoid arthritis

Objective: To determine the effect of different treatment strategies (early versus delayed) on the radiological progression of joint damage during 4 years. Additionally, to determine the effect of treatment strategy on the association of HLA class II alleles and joint damage. Methods: Progression of radiographic damage and association of radiographic damage and genetic predisposition were compared in two cohorts, one treated according to the delayed treatment strategy (initial treatment with analgesics), the other treated according to the early treatment strategy (treatment with disease modifying antirheumatic drugs (DMARDs) chloroquine or sulfasalazine). Radiographic damage was measured by the modified Sharp-van der Heijde method. Genetic predisposition was determined by high resolution HLA-DR and DQ typing. Results: A completers-only analysis of 153 patients (originally 206 patients) in a non-randomised design showed less radiographic progression from 0 to 4 years in the early treatment group (median Sharp progression rate 1.3 points/year, n = 75) than in the delayed treatment group (2.5 points/year, n = 78) (p = 0.03). The progression from 1 to 4 years did not differ significantly between the groups. At 4 years, joint destruction in both groups was positively correlated with the presence of the shared epitope. Conclusions: The beneficial effect of early DMARD treatment on the radiological progression of joint damage is still present at 4 years. However, the rate of joint destruction from 1 to 4 years did not differ between the delayed and early treatment group. Neither the radiographic nor the immunogenetic data suggest that longlasting disease modification has been induced by early treatment.

Treatment characteristics and the risk of inhibitor development: a multicenter cohort study among previously untreated patients with severe hemophilia A

Context: The development of inhibitory antibodies against infused factor (F) VIII is a major complication of treatment of patients with severe hemophilia A.Objective: This study was set up to examine the effects of treatment‐related factors on inhibitor development among previously untreated patients with severe hemophilia A.Design, setting and patients: In this multicenter cohort study, we combined individual patient data obtained from four recombinant FVIII product registration studies (Kogenate®, Kogenate Bayer®, Recombinate®, ReFacto®) that were performed between 1989 and 2001. From the databases we selected all 236 previously untreated patients with severe hemophilia A who were subsequently treated with FVIII on at least 50 days.Main outcome measures: Clinically relevant inhibitor development, defined as the occurrence of at least two positive inhibitor titers and a decreased recovery.Results: 67 patients (28%) developed clinically relevant inhibitors (44 high‐titer) at a median of ten exposure days. Age at first exposure was not associated with inhibitor development. Peak treatment moments and surgical procedures were related to an increased inhibitor risk [adjusted relative risk 1.6 (95% confidence interval 1.0–2.6) and 2.7 (95% confidence interval 1.3–5.7), respectively]. A shorter duration between exposure days was associated with an increased risk of inhibitor development. There was a possible association between dosing of FVIII and inhibitor development, which largely disappeared after adjustment for confounding factors.Interpretation: These findings show that intensive treatment periods are associated with an increased risk of inhibitor development in previously untreated patients with severe hemophilia A. Our results do not support the notion that age at first exposure is associated with the risk of developing inhibitors.