QMRA for Drinking Water: 2. The Effect of Pathogen Clustering in Single‐Hit Dose‐Response Models

Spatial and/or temporal clustering of pathogens will invalidate the commonly used assumption of Poisson‐distributed pathogen counts (doses) in quantitative microbial risk assessment. In this work, the theoretically predicted effect of spatial clustering in conventional “single‐hit” dose‐response models is investigated by employing the stuttering Poisson distribution, a very general family of count distributions that naturally models pathogen clustering and contains the Poisson and negative binomial distributions as special cases. The analysis is facilitated by formulating the dose‐response models in terms of probability generating functions. It is shown formally that the theoretical single‐hit risk obtained with a stuttering Poisson distribution is lower than that obtained with a Poisson distribution, assuming identical mean doses. A similar result holds for mixed Poisson distributions. Numerical examples indicate that the theoretical single‐hit risk is fairly insensitive to moderate clustering, though the effect tends to be more pronounced for low mean doses. Furthermore, using Jensen's inequality, an upper bound on risk is derived that tends to better approximate the exact theoretical single‐hit risk for highly overdispersed dose distributions. The bound holds with any dose distribution (characterized by its mean and zero inflation index) and any conditional dose‐response model that is concave in the dose variable. Its application is exemplified with published data from Norovirus feeding trials, for which some of the administered doses were prepared from an inoculum of aggregated viruses. The potential implications of clustering for dose‐response assessment as well as practical risk characterization are discussed.     

Construct and Criterion Validity of a Norwegian Instrument for Health Related Quality of Life Among Elderly Women Living at Home

Purpose of the study: The aim of the current study is to validate an instrument consisting of five items and first used in the Nord-Trondelag Health Survey (HUNT-5), as a measure of health related quality of life (QOL) in a population of elderly women living at home. Design and methods: A random sample of 307 women aged 75 years and over (mean 80.8 years, response rate 74.5%) and living at home were interviewed using the HUNT-5 instrument, the 20-question version of the General Health Questionnaire (GHQ-20) and the respondents’ records of their health status and functional ability. Results: No significant relationships were found between age and the sumscores of GHQ-20 and HUNT-5. Factor analysis indicated that HUNT-5 is primarily unidimensional. The Cronbach α for HUNT-5 was 0.79 and that for GHQ-20 was 0.87. The correlation between the HUNT-5 and the GHQ-20 sumscores was 0.75 (p < 0.001). There were significant correlations between some of the health and function items and the two QOL instruments (ranging from 0.14 to 0.68). Implications: This evaluation supports the psychometric validity of HUNT-5 for elderly women living at home. It is important to take into consideration the women’s own experience of their health and functional ability in planning therapy and in obtaining the best possible QOL for them.     

Health, balance, and walking as correlates of climbing steps

The aim of this study was to investigate walking and health among woman age 75 yr or older, in the associations between the highest step up performed without support by an individual and balance, walking, and health among women age 75+. Records of the highest step, balance, walking, and health were made for 307 women age 75-93 yr living in the community. Eighty percent managed to climb steps higher than 20 cm. There was a statistically significant negative relationship between age and stair-climbing capacity. The highest steps registered were significantly and independently associated with a short time on the timed up-and-go test, long functional reach, low body weight, lack of perceived difficulty walking outdoors, low number of "missteps" when walking in a figure of 8, longer time in one-leg stance, ability to carry out tandem stance, no walking aids outdoors, and not being afraid of falling. These variables together explained 67% of the variance in the step-height score.     

QMRA for Drinking Water: 1. Revisiting the Mathematical Structure of Single‐Hit Dose‐Response Models

Dose‐response models are essential to quantitative microbial risk assessment (QMRA), providing a link between levels of human exposure to pathogens and the probability of negative health outcomes. In drinking water studies, the class of semi‐mechanistic models known as single‐hit models, such as the exponential and the exact beta‐Poisson, has seen widespread use. In this work, an attempt is made to carefully develop the general mathematical single‐hit framework while explicitly accounting for variation in (1) host susceptibility and (2) pathogen infectivity. This allows a precise interpretation of the so‐called single‐hit probability and precise identification of a set of statistical independence assumptions that are sufficient to arrive at single‐hit models. Further analysis of the model framework is facilitated by formulating the single‐hit models compactly using probability generating and moment generating functions. Among the more practically relevant conclusions drawn are: (1) for any dose distribution, variation in host susceptibility always reduces the single‐hit risk compared to a constant host susceptibility (assuming equal mean susceptibilities), (2) the model‐consistent representation of complete host immunity is formally demonstrated to be a simple scaling of the response, (3) the model‐consistent expression for the total risk from repeated exposures deviates (gives lower risk) from the conventional expression used in applications, and (4) a model‐consistent expression for the mean per‐exposure dose that produces the correct total risk from repeated exposures is developed.