Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

THE MEASUREMENT OF HUMANISTIC AND DEHUMANISTIC BEHAVIORS IN HOSPITAL NURSING ENVIRONMENTS

The purpose of this investigation was to develop a reliable scale to measure the social environment of hospital nursing units according to the degree of humanistic and dehumanistic behaviors as perceived by nursing staff in hospitals. The study was based on a conceptual model proposed by Jan Howard, a sociologist. After reviewing the literature relevant to personalization of care, analyzing interviews with patients in various settings, and studying biological, psychological, and sociological frames of reference, Howard proposed the following necessary conditions for humanized health care. They were the dimensions of Irreplaceability, Holistic Selves, Freedom of Action, Status Equality, Shared Decision Making and Responsibility, Empathy, and Positive Affect.^ It was proposed that a scale composed of behaviors which reflected Howard's dimensions be developed within the framework of the social environment of nursing care units in hospitals. Nursing units were chosen because hospitals are traditionally organized around nursing care units and because patients spend the majority of their time in hospitals interacting with various levels of nursing personnel.^ Approximately 180 behaviors describing both patient and nursing staff behaviors which occur on nursing units were developed. Behaviors which were believed to be humanistic as well as dehumanistic were included. The items were classified under the dimensions of Howard's model by a purposively selected sample of 42 nurses representing a broad range of education, experience, and clinical areas. Those items with a high degree of agreement, at least 50%, were placed in the questionnaire. The questionnaire consisted of 169 items including six items from the Marlowe Crowne Social Desirability Scale (Short Form).^ The questionnaire, the Social Environment Scale, was distributed to the entire 7 to 3 shift nursing staff (603) of four hospitals including a public county specialty hospital, a public county general and acute hospital, a large university affiliated hospital with all services, and a small general community hospital. Staff were asked to report on a Likert type scale how often the listed behaviors occurred on their units. Three hundred and sixteen respondents (52% of the population) participated in the study.^ An item analysis was done in which each item was examined in relationship to its correlation to its own dimension total and to the totals of the other dimensions. As a result of this analysis, three dimensions, Positive Affect, Irreplaceability, and Freedom of Action were deleted from the scale. The final scale consisted of 70 items with 26 in Shared Decision Making and Responsibility, 25 in Holistic Selves, 12 in Status Equality, and seven in Empathy. The alpha coefficient was over .800 for all scales except Empathy which was .597.^ An analysis of variance by hospital was performed on the means of each dimension of the scale. There was a statistically significant difference between hospitals with a trend for the public hospitals to score lower on the scale than the university or community hospitals. That the scale scores should be lower in crowded, understaffed public hospitals was not unexpected and reflected that the scale had some discriminating ability. These differences were still observed after adjusting for the effect of Social Desirability.^ In summary, there is preliminary evidence based on this exploratory investigation that a reliable scale based on at least four dimensions from Howard's model could be developed to measure the concept of humanistic health care in hospital settings. ^