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We propose to perform model check for the Cox and Aalen regression models using martingale residual processes grouped after the risk score. Asymptotic distributions of the grouped martingale residual processes are deduced, so both formal and graphical model check can be performed. The method is validated by stochastic simulation. A data example with patients with primary biliary cirrhosis of the liver is discussed.

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A socio-ecologic conceptual model for periodontal diseases has been proposed. The model, which includes 4 items: health-care organization, human biology, behavioral factors, and environment, has been tested on a random-sample of 50-year-old Oslo citizens. The investigation is based on a clinical examination as well as a questionnaire and structured interview. A logistic regression model was used to study associations between risk factors and the probability of deep periodontal pockets (> 5.5 mm). The risk of periodontal pockets was positively associated with: short duration of education, being of male gender, previous periodontal treatment, poor oral hygiene and infrequent toothbrushing. Variables describing behavioral factors and human biology were the items found to be most closely associated with periodontal pocketing.

A random sample of 35-year-old subjects from Oslo took part in a dental survey in 1973 and were re-examined in 1988. Eighty-one subjects (85%) attended the final examination. The need for periodontal treatment was assessed by the Periodontal Treatment Need System (PTNS), and the oral hygiene by the Simplified Oral Hygiene Index (OHI-S). The participants attended a structured interview and answered a questionnaire about general and dental health habits as well as psycho-social factors. Only small changes in the distribution of subjects in the different PTNS categories were found to have taken place during the 15 years. In 1973, 56.8% were in need of scaling (Class B) and 32.1% had one or more deep inflamed pockets (Class C), and in 1988 the scores were 54.3% and 30.1% respectively. A logistic regression model was used to study the associations between risk factors and increased treatment need, as expressed by increase in the number of C-quadrants. Increased number of C-quadrants was positively associated both with short duration of education and with no interdental cleaning. Using a socio-ecological model for periodontal diseases, variables describing the items "behaviour" and "environment" were found to be most closely associated with increased need for periodontal treatment.