Generating Distributions for Cost Effectiveness Analysis
(for beta testing purposes only, not for official use)
Data Entry Form - Enter Data in Yellow Boxes
  Option 1. Normal Uniform Distribution
(often applies to data like blood pressure, weight, etc)
  probabilistic deterministic
standard deviation  
Description: Enter mean and standard deviation to generate probabilistic values.
Excel function = NORMINV().
Calculated Normal Distribution Sample Values

  Option 2. Beta Distribution
(often applies to binomial data, like success vs failure)
    Success Fail  
  probabilistic deterministic
standard error alpha beta  
Description: Enter number of successes and failures to generate mean, std error and probabilistic values.
Excel function = BETAINV().
Calculated Beta Probability Sample Values

  Option 3. Gamma Distribution
(often applies to cost data)
  probabilistic deterministic
standard error alpha beta  
Description: Enter mean and standard error to generate alpha, beta and probablistic values.
Excel function = GAMMAINV().
  alpha = (mean * mean)/(std error*std error)___________ variance = s*s
  beta = (variance)/mean
Calculated Gamma Distribution Sample Values

You can modify the number of values generated after you press the "Submit" button.

Binomial Distribution and Proportions (Examples with Sample Size N = 100)
Mean proportion [from the sample] = p ::: example: 0.9, n= 100 (for 90 successes [alpha], 10 failures [beta]). Sometimes coded as 1 and 0 for patient level data. Variance [from the sample] = p*(1-p) = p*q ::: example: 0.9 * 0.1 = 0.09 Standard Deviation (SD) [from the sample] = sqrt (p*q) ::: example: sqrt (0.09) = 0.3
Variance [of the mean] = (p*q) / n ::: example: 0.09/100 = 0.0009 Standard Error (SE) [of the mean] = sqrt (p*q) / sqrt n ::: example: sqrt (0.9 * 0.1) / sqrt (100) = 0.03
Standard Error (of the mean) is often applied in probabilitistic analysis, where one is interested in estimating the "uncertainty" in the model parameters and model variables. Consider the standard error for the Beta weight for a predictor variable in a regression model. With randomized trial analysis, one is more likely to focus on the "standard deviation" and "variance" to describe the sample data.

-- Briggs A et al. Decision Modelling for Health Economic Evaluation. Oxford University Press, 2006.
-- Lewandowski A. Statistical Tables --