**Introduction:**

The purpose of this section is to critically appraise the data analysis methods used by 5 quantitative studies and to determine how statistical tests have been used to analyze the data. The subject matter of the five quantitative research papers under study is to establish a relationship between the extended work durations or shifts and medical error risks.

**Discussion:**

Griffiths et al (2014) conducted a study to investigate nurses care quality and undone work or errors are associated with working length beyond contracted hours. The data analysis method used by the authors was Intraclass correlation coefficients (ICC 1) to measure variance for shift length within-country, with-in hospital and with-in unit. The authors computed ICC1 from unconditional random intercept models to measure the degree of similarity between participants within a group and to measure proportion of variance in the outcome to be accredited to difference between groups.

On one hand, to measure the link between shift length and overtime with the outcome measures, Griffiths and his team used a binomial generalized linear mixed model whereas a generalized mixed model with a Poisson distribution was used to measure the association between shift length and care left undone. A generalized linear model is a model linking responses (variables “Subsidiaries”) with other “independent” or “explanatory” variables.

A log Poisson generalized estimating equation model is used by Tanaka et al (2010) to determine the frequencies of perceived medical errors by nurses or adverse events among three-shift and two-shift system over 6 months.

The Poisson regression is a type of generalized linear model in which the response variable has a Poisson distribution and the logarithm of its expected value can be modeled by a linear combination of parameters unknown. Poisson model is appropriate when the dependent variable is a count, such as the number of adverse events in this study, which depend on other variables such as the two-shift or three-shift and shorter intervals between night shifts etc. The events must be independent.

A study by Olds & Clarks conducted secondary analysis of 11,516 registered nurses using bivariate and multivariate logistic regression to observe the links between nurse characteristics, shift hours, and the medical errors or adverse events. Logistic regression is a group of statistical techniques that aim to test hypotheses or causal relationships when the dependent variable is nominal.

The primary benefit of using multivariate and bivariate analyses is it enables the researcher to identify associations between variables and to measure the link among those variables. Initially bivariate analysis was used because the researchers had to examine relationship among two variables. Later they used multivariate because of more than one dependent variable or outcome.

Two such studies conducted by Stimpfel & Aiken (2013) and Scott et al (2006) calculated descriptive and inferential statistics to examine shift length by individual nurses involved in the study followed by hospital specialty unit and state. Descriptive Statistics procedures used to organize and summarize sets of observations quantitatively. The summary can be done using tables, graphs or numerical values. Data sets containing observations of more than one variable allow studying the relationship or association between them. Statistical Inference methods used to infer something about a population based on data obtained from a sample. The statistical data are arithmetic calculations on the values obtained in a portion of the population, selected according to strict criteria.

Sometimes analysts investigate the variability of a population, rather than its mean or proportion as done by Stimpfel and Aiken. Excessive variability is the worst enemy of high quality and hypothesis testing is designed to determine if the variance of a population is equal to a predetermined value. In the analysis of variance with a criterion, the measures of the dependent variable are made to each level of the factor that is thought to affect this variable.

The authors examine two important factors while in the process of ANOVA with two classification criteria, and study the effects of three or more factors on the dependent variable by more advanced procedures. Analysis of variance is a good example of a statistical technique that is very practical due to widespread use of computers. The volume of calculations is such that it is very difficult to design any useful size only with manual calculations.

Stimpfel and Aiken also used the generalized estimation equation models in which bivariate generalized estimating equation models were created preceding to multivariate generalized estimating equation models. The Generalized Estimating Equations procedure extends the generalized linear model to allow for analysis of repeated measurements and other correlated observations, such as data clusters.

Scott et al (2006) used univariate analyses with generalized estimating equation logistic regression models. In statistics, the logistic regression is a type of regression analysis used to predict the outcome of a categorical variable (a variable that can take a limited number of categories) based on independent or predictor variables. It is useful to model the probability of occurring as a function of other factors event. The logistic regression analysis is part of the set of generalized linear models which is used as link function logit. The odds that describe the possible outcome of a single test are modeled as a function of explanatory variables, using a logistic function.

The authors initially conducted univariate analyzes. Each explanatory variable was cross with the response variable and odds ratios (OR) with 95% confidence intervals were calculated to estimate the strength of association of each of the explanatory variables with the response variable. Only variables that had a P value less than or equal to 0.20 in the univariate analysis were included in multivariate analysis. To analyze the impact of shift hours or long working on the number of medical errors or adverse events, they performed a logistic regression type of analysis based on the method of generalized estimating equations (GEE), which enabled to take into account the correlation between data from repeated measurements over time.

**References**

Calhoun, A. W., Boone, M. C., Dauer, A. K., Campbell, D. R., & Montgomery, V. L. (2014). Using simulation to investigate the impact of hours worked on task performance in an intensive care unit. American Journal of Critical Care, 23(5), 387-395.

Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications.

Griffiths, P., Dall’Ora, C., Simon, M., Ball, J., Lindqvist, R., Rafferty, A. M., … & Aiken, L. H. (2014). Nurses’ shift length and overtime working in 12 European countries: the association with perceived quality of care and patient safety.*Medical care*, *52*(11), 975.

Little, R. J., & Rubin, D. B. (2014). Statistical analysis with missing data. John Wiley & Sons.

Mikulich-Gilbertson, S. K., Wagner, B. D., Riggs, P. D., & Zerbe, G. O. (2015). On estimating and testing associations between random coefficients from multivariate generalized linear mixed models of longitudinal outcomes. Statistical methods in medical research, 0962280214568522.

Olds, D. M., & Clarke, S. P. (2010). The effect of work hours on adverse events and errors in health care. *Journal of safety research*, *41*(2), 153-162.

Scott, L. D., Rogers, A. E., Hwang, W. T., & Zhang, Y. (2006). Effects of critical care nurses’ work hours on vigilance and patients’ safety. *American Journal of Critical Care*, *15*(1), 30-37.

Stimpfel, A. W., & Aiken, L. H. (2013). Hospital staff nurses’ shift length associated with safety and quality of care. *Journal of nursing care quality*,*28*(2), 122.

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