antibiotic outbreak prediction with excel 861


figure 1. Linear regression of piperacillin-tazobactam consumption (DOT/1000 PD) in the medical intensive care unit as the y-axis from the period from January 2012 to December 2015 as sequential months from 1 to 48 (x-axis). Dashed lines represent upper and lower bounds of the 95% confidence interval. Solid lines represent upper and lower bounds of the 80% prediction interval. The latter is suggested to predict periods of potential under- and overuse.


table 1. Derivations of Equation From the Supplemental Materiala Equation Set 1 1.1b Linear prediction value obtained from regression


1.2c Standard error of the mean for the given month


1.3 Standard error of the predicted y value for each x in the regression


1.4 Standard deviation for the given month 1.5d,e Upper bound 95% confidence interval 1.6 Lower bound 95% confidence interval


Equation Set 2 2.1 Standard error of prediction


2.2 Upper bound 80% prediction interval 2.3 Lower bound 80% prediction interval


ŷ=FORECAST(month,antibiotic_DOT_1000_PD,T)


SEM=steyx_drug*SQRT(1/COUNT(Analysis_period)+((month-AVERAGE (MonthsTotal))^2/devsq_ Analysis_period))


steyx_drug =STEYX(antibiotic_DOT_1000_PD, Analysis_period) devsq_ Analysis_period =DEVSQ(Analysis_period)


95% CI_UB =ŷ+TINV(0.05,COUNT(Analysis_period)-2)*SEM at that month 95% CI_LB=ŷ - TINV(0.05,COUNT(Analysis_period)-2)* SEM at that month


SE of Prediction =steyx_drug*SQRT(1+(1/COUNT(analysis_period))+((month- AVERAGE(analysis_period))^2/devsq_analysis_period))


80% PI_UB =ŷ+TINV(0.2,COUNT(analysis_period)-2)* SE of Prediction 80% PI_LB=ŷ - TINV(0.2,COUNT(analysis_period)-2)* SE of Prediction


NOTE. DOT, days of therapy; PD, patient days; T, time; SEM, standard error of the mean; SQRT, square root; DEVSQ, squared deviation of the sample mean; TINV, inverse of the two-tailed Student t distribution; PI_UB; upper bound 80% prediction interval PI_LB, lower bound 80%


prediction interval; SE, standard error. aEquation set 1 includes the formulae needed to construct a simple linear regression model using the FORECAST function with DOT/1,000 DP as the dependent variable and time as the independent variable. This calculates mean linear predictions for consumption data across ordered time months, with variability quantified as standard error of the mean (SEM) and attendant 95% confidence intervals at each time point. Equation set 2 includes the formulae needed to calculate standard errors of predictions and attendant 80% prediction intervals at each


time point. bMonth is a single numeric value when months are numbered sequentially. cAnalysis_period is the total time of analysis. dTINV is the 2-tailed inverse of the Student t distribution: the first number following TINV is the probability associated with the 2-tailed Student


t distribution and the second number following it is the degrees of freedom. eThe COUNT -2 function is used to determine the needed degrees of freedom.


confidence interval for the mean (rather than any individual single prediction).7 Values above or below the prediction interval serve as a decision support tool for the investigation of


antibiotic over- or underuse. Upper and lower bounds of these predictive intervals were calculated using standard errors of predictions (see Table 1, equation set 2).8,9


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