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Longitudinal data sets from certain fields of biomedical research often consist of several variables repeatedly measured on each subject yielding a large number of observations. This characteristic complicates the use of traditional longitudinal modelling strategies, which were primarily developed for studies with a relatively small number of repeated measures per subject. An innovative way to model such 'wide' data is to apply functional regression analysis, an emerging statistical approach in which observations of the same subject are viewed as a sample from a functional space. Shen and Faraway introduced an F test for linear models with functional responses. This paper illustrates how to apply this F test and functional regression analysis to the setting of longitudinal data. A smoking cessation study for methadone-maintained tobacco smokers is analysed for demonstration. In estimating the treatment effects, the functional regression analysis provides meaningful clinical interpretations, and the functional F test provides consistent results supported by a mixed-effects linear regression model. A simulation study is also conducted under the condition of the smoking data to investigate the statistical power for the F test, Wilks' likelihood ratio test, and the linear mixed-effects model using AIC.
OBJECTIVE: To understand how views and approaches concerning risks and benefits may be affected by dynamic contexts and processes related to clinical roles and relationships. METHODS: We conducted two in-depth, semi-structured interviews with 50 doctors who became patients due to serious illnesses, concerning their experiences before and after diagnosis. RESULTS: As patients, these doctors gained critical new insights into the processes and contexts of communication about risks and benefits. Doctors and patients often varied in how they viewed and weighed risks and benefits (e.g., as "good' or "bad"). These data suggest a model in which patients undergo several dynamic processes: seeking statistics, accepting doctors' framing of statistics, being influenced by media hype, seeing statistics as relevant or not, over-valuing risks, weighing the importance of risks and benefits, interpreting statistics as good or bad, accepting or denying statistics and odds, and making treatment decisions. These processes are affected by external factors (e.g., doctors ordering tests, framing statistics, and often over- versus under-valuing risks), and internal factors (e.g., depression, denial of illness, optimism versus pessimism, magical thinking--that doctors are immune to disease--and rationalizations). CONCLUSIONS: Doctors and patients are engaged in complex, dynamic processes that shape patients' approaches toward risks and benefits. PRACTICE IMPLICATIONS: These data highlight the need for increased attention toward these issues in medical educational and care.
Departure of a sample from a normal distribution should be assessed by a quantity that is meaningful in terms of the data, rather than merely by the P-value from a test statistic. Indices of departure based on the Shapiro-Francia W' and the Shapiro-Wilk W statistics are derived, and shown to have a natural interpretation in relation to the normal probability plot. A new diagnostic plot is proposed. An example is given which shows the relationship between one of the new indices and errors in calculated reference ranges due to non-normality of the data.