Testing for lack of fit in inverse regression—with applications to biophotonic imaging

Summary.  We propose two test statistics for use in inverse regression problems Y = K θ + ɛ , where K is a given linear operator which cannot be continuously inverted. Thus, only noisy, indirect observations Y for the function θ are available. Both test statistics have a counterpart in classical hypothesis testing, where they are called the order selection test and the data-driven Neyman smooth test. We also introduce two model selection criteria which extend the classical Akaike information criterion and Bayes information criterion to inverse regression problems. In a simulation study we show that the inverse order selection and Neyman smooth tests outperform their direct counterparts in many cases. The theory is motivated by data arising in confocal fluorescence microscopy. Here, images are observed with blurring, modelled as convolution, and stochastic error at subsequent times. The aim is then to reduce the signal-to-noise ratio by averaging over the distinct images. In this context it is relevant to decide whether the images are still equal, or have changed by outside influences such as moving of the object table.     

Model checks for Cox-type regression models based on optimally weighted martingale residuals

We introduce directed goodness-of-fit tests for Cox-type regression models in survival analysis. “Directed” means that one may choose against which alternatives the tests are particularly powerful. The tests are based on sums of weighted martingale residuals and their asymptotic distributions. We derive optimal tests against certain competing models which include Cox-type regression models with different covariates and/or a different link function. We report results from several simulation studies and apply our test to a real dataset.     

Estimation of unimodal densities based on the <Emphasis Type="Italic">FQ</Emphasis>-System

Based on an FQ-System for continuous unimodal distributions, which was introduced by Scheffner (1998), we propose a pure data-driven method for density estimation, which provides good results even for small samples. This procedure does not involve any problems or uncertainties as e.g. bandwidth selection for kernel density estimates.     

Interactional harmony at 7 and 10 months of age predicts security of attachment as measured by Q-sort ratings

Fifty-eight infants and their mothers were observed at home for 45 minutes at seven and ten months of age using a detailed behavioral checklist. During these observations, the degree of mutual interactional engagement was also rated on a 4-point scale every 20 seconds. The attachment security of 38 infants was assessed at 13 months using mothers' reports on the Attachment Q-set (AQS, Waters, 1987). Composite measures of mother-infant interaction derived from the behavioral observations were moderately stable over time. Measures of maternal interactive behaviors and ratings of mutual engagement were highly correlated. Mothers' and infants' behaviors were combined into an index of behavioral harmony that was sensitive to differences in the infants' attachment security three and six months later. Using a stepwise multiple regression, 43% of the variance in the AQS-scores was explained by behavioral harmony at seven months, mutual engagement at 10 months, and infant fuss/cry at seven months.     

Characteristics of men and women who complete or exit from an on‐line internet sexuality questionnaire: A study of instrument dropout biases

This study compared respondents who completed an Internet sexuality questionnaire and those who dropped out before completion. The study was in Swedish and comprised 3,614 respondents over a 2‐week period (53% males, 47% females). There were significant differences between males, of whom 51% dropped out before completion of the 175‐item questionnaire, and females, of whom 43% dropped out. Dropout in both genders followed a curve of negative acceleration. The data suggest that dropout is likely to be significant and gender and demographically biased, and to occur significantly earlier for men than for women. Geography, education, sexual orientation, age, relationship status, living arrangements, and Internet connection speed were related to dropout for men, while only relationship status and living arrangements, which were in the opposite direction from men, were related to dropout in women.     

Limitations of family therapy

Summary This paper concerns inself with therapeutic difficulties in marital and family therapy due to an inability to resolve value discrepancies between the therapist and the family in question. The guarded prognosis due to lack in motivation to change is reinforced by the presence of chronic pathology, cultural differences, and the unwillingness or inability of the family/couple to engage in a valid therapeutic contract. This is especially true when acting-out adolescents are involved. This, and the limitations imposed by an agency and a private practice setting, is exemplified to two case illustrations. Clinical course, details, and psychodynamics are discussed as are the pros and cons of treating such families. Recommendations concerning modifications in techniques of intervention are made. The cases lead to the conclusion that while traditional (or even untraditional) psychotherapeutic procedures are likely to prove ineffective, an analysis of negative outcomes might help to devise strategies to cope with such families and lead to further theory building. References to the pertinent literature are made.     

Testing noninferiority in three‐armed clinical trials based on likelihood ratio statistics

Clinical noninferiority trials with at least three groups have received much attention recently, perhaps due to the fact that regulatory agencies often require that a placebo group be evaluated along with a new experimental drug and an active control. The authors discuss likelihood ratio tests for binary endpoints and various noninferiority hypotheses. They find that, depending on the particular hypothesis, the test reduces asymptotically either to the intersection‐union test or to a test which follows asymptotically a mixture of generalized chi‐squared distributions. They investigate the performance of this asymptotic test and provide an exact modification. They show that this test considerably outperforms multiple testing methods such as the Bonferroni adjustment with respect to power. They illustrate their methods with a cancer study to compare antiemetic agents. Finally, they discuss the extension of the results to other settings, such as Gaussian endpoints.