Linear Regression
Gary L. Rosner, Purushottam W. Laud, Wesley O. Johnson in Bayesian Thinking in Biostatistics, 2021
To construct an informative prior for τ, we ask an expert to think about a percentile for the response values in the population of individuals corresponding to a particular predictor vector, say . To be specific, the quantile equals . We elicit a best guess for this quantile, conditional on the best guess for from the elicitation in Section 7.3.3. Setting this elicited value to leads to a best guess for σ, and subsequently to one for . While this can be used to specify a central value for the prior distribution, we need additional information to express uncertainty about the best guess for τ. We illustrate using the FEV data.
Quantitative Methods for Analyzing Experimental Studies in Patient Ergonomics Research
Richard J. Holden, Rupa S. Valdez in The Patient Factor, 2021
The data generated from patient ergonomics studies are inherently noisy. That is, not every participant responds identically to the same stimulus. Nor does an individual participant respond identically to a repeated stimulus. Visual methods and normality tests are frequently used to understand the characteristics of the data’s distribution. Frequency distributions, box plots, stem-and-leaf plots, probability–probability plots, and quantile–quantile plots are commonly used visual methods to explore the overall distribution of data and to make an educated decision to include a data point in the statistical analysis. In our case study, the frequency distributions of the perceived workload experienced by the 50 participants as they completed the tasks using the conversational and conventional interfaces are shown in Figure 11.2.
Working with continuous outcome variables
Ewen Harrison, Pius Riinu in R for Health Data Science, 2020
Quantile-quantile sounds more complicated than it really is. It is a graphical method for comparing the distribution (think shape) of our own data to a theoretical distribution, such as the normal distribution. In this context, quantiles are just cut points which divide our data into bins each containing the same number of observations. For example, if we have the life expectancy for 100 countries, then quartiles (note the quar-) for life expectancy are the three ages which split the observations into 4 groups each containing 25 countries. A Q-Q plot simply plots the quantiles for our data against the theoretical quantiles for a particular distribution (the default shown below is the normal distribution). If our data follow that distribution (e.g., normal), then our data points fall on the theoretical straight line.
Association between participation in the Northern Finland Birth Cohorts and cardiometabolic disorders
Published in Annals of Medicine, 2023
Martta Kerkelä, Mika Gissler, Tanja Nordström, Olavi Ukkola, Juha Veijola
The cumulative incidence rates of cardiometabolic disorders in all hospital-treated cardiovascular disorders (including inpatient and specialized outpatient visits) were calculated for the study and comparison cohorts covering the full follow-up (age 7 to 50 years in NFBC1966; age 0 to 29 years in NFBC1986). Different types of diabetes mellitus were examined from 1987 onwards (age 2 to 29 years in NFBC1986 and age 22 to 50 years in NFBC1966). Due to the small number of cases of hyperlipidaemia and coronary artery disorders in the younger population (follow-up ends at age 29 years), the separate diagnosis classes are not included in the analysis. Risk ratios (RRs) with 95% confidence intervals (CIs) were calculated by sex separately in each diagnosis group. The age of the first onset of cardiometabolic diagnosis (median with IQR) is reported in each diagnosis group. The difference between the medians is estimated using quantile estimation (QE) and Q with p-values are reported [27]. The age of the first onset of cardiometabolic disorders was plotted over the full follow-up period in both NFBCs, separated by sex. Cumulative incidences of cardiometabolic-related causes of death were calculated to NFBC1966 and comparison cohorts at age 0 to 50 years. The age of death caused by any cardiometabolic disorders (median with IQR) by sex is also reported. Analysis was performed using R version 1.4.1106.
Prevalence of bilateral vestibulopathy among older adults above 65 years on the indication of vestibular impairment and the association with Dynamic Gait Index and Dizziness Handicap Inventory
Published in Disability and Rehabilitation, 2023
Katrine Storm Piper, Carsten Bogh Juhl, Hanne Elkjaer Andersen, Jan Christensen, Kasper Søndergaard
Quantile–quantile plots and histograms were applied to visually examine the distribution of data. Descriptive data were reported as means and standard deviations (SDs) for continuous data (age and biothesiometry) and numbers (n) with percentages (%) for categorical data (sex, walking aid, and symptomatology). The covariates age, sex, walking aid (yes/no), and peripheral vibratory sense (normal/decreased) were chosen a priori based on literature review [1,2]. Sensibility was categorized as normal when biothesiometry of both feet were ≤25 volts and pathological if either right or left foot were above 25 V [18,28]. Thus, a decreased sensibility of one foot was considered being enough to affect the standing and walking balance. Mann–Whitney test was performed of non-normally distributed data, logistic regression with normally distributed continuous data, and χ2 for categorical variables. The prevalence of BV was estimated as the percentage of patients identified with BV divided by the total number of patients tested with vHIT.
The Impact of Online and Offline Social Support on the Mental Health of Carers of Persons with Cognitive Impairments
Published in Journal of Gerontological Social Work, 2023
Eun-Hye Grace Yi, Margaret E. Adamek, Michin Hong, Yvonne Lu, David Wilkerson
A significant association between life factors, such as health and socioeconomic status, and mental health has been reported in previous studies (Thunyadee et al., 2015). In this study, life stressors were measured with the level of family income and health status. The respondents’ subjective health that was originally measured using a 5-point Likert scale (1 = excellent: 5 = poor) was recoded as binary (1 = good or excellent health) because of skewed distribution. Income is one of the most challenging variables to measure accurately. In the original data, household annual income level was measured using nine categories (e.g., $0–$9,999, $10K-$14,999, $15K–19,999). For our study, the median income of each category was divided by the number of household members to get a proxy per capita income. Then, we created quantiles with the following amounts: 1 = 25%, 2 = 50%, 3 = 75%, 4 = 100%.
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