Multi criteria decision analysis

Conduct a multi criteria decision analysis (MCDA) and compute scores for competing treatment strategies using output from a probabilistic sensitivity analysis (PSA).

mcda(x, sample, strategy, criteria, criteria_min = NULL,
  criteria_max = NULL, optimal = NULL, weights, score_min = 0,
  score_max = 100)

Arguments

x	A data.frame or data.table of simulation output characterizing the probability distribution of model outcomes.
sample	Character name of column from x denoting a randomly sampled parameter set from the PSA.
strategy	Character name of column from x denoting treatment strategy.
criteria	A vector of character names of columns from x denoting the criteria to use in the MCDA.
criteria_min	A vector of minimum values for each criterion. If NULL, then the minimum value is computed automatically.
criteria_max	A vector of maximum values for each criterion. If NULL, then the maximum value is computed automatically.
optimal	A character vector denoting whether the optimal value of each criteria is "low" or "high". If an element is "low", then lower performance on that criterion is better, and, if an element is "high", then higher performance on that criterion is better. Must be specified if either criteria_min or criteria_min is NULL.
weights	Weights to apply to each criteria. Internally normalized to sum to 1.
score_min	Minimum of total value score. Default is 0.
score_max	Maximum of total value score. Default is 100.

See also

performance_matrix, lpvf_plot_data

Examples

n_samples <- 5
strategies <- c("Strategy 1", "Strategy 2")
outcome1 <- c(rnorm(n_samples, mean = 10, sd = 5),
              rnorm(n_samples, mean = 8, sd = 4))
outcome2 <- c(rnorm(n_samples, mean = 1500, sd = 90),
              rnorm(n_samples, mean = 1000, sd = 100))
outcomes <- data.frame(sample = rep(1:n_samples, length(strategies)),
                       strategy_id = rep(strategies, each = n_samples),
                       criteria1 = outcome1,
                       criteria2 = outcome2)

# Performance matrix
performance_mat <- performance_matrix(outcomes,
                                      strategy = "strategy_id",
                                      criteria = c("criteria1", "criteria2"),
                                      rownames = c("Criteria 1", "Criteria 2"),
                                      colnames = strategies)
print(performance_mat)
#>            Strategy 1             Strategy 2         
#> Criteria 1 "8.82 (1.14, 15.55)"   "3.77 (0.99, 6.83)"
#> Criteria 2 "1,447 (1,316, 1,574)" "974 (822, 1,181)" 

# MCDA                        
weights <- c(.7, .3)
mcda <- mcda(outcomes, sample = "sample", strategy = "strategy_id",
             criteria = c("criteria1", "criteria2"),
             weights = weights,
             optimal = c("low", "high"))
names(mcda)
#> [1] "scores"          "weighted_scores" "total_value"     "prob_rank"      

# Scores on common scale
print(mcda$scores)
#>     sample strategy_id criteria1 criteria2
#>  1:      1  Strategy 1  34.92297  79.33347
#>  2:      2  Strategy 1 100.00000 100.00000
#>  3:      3  Strategy 1  69.20929  81.52684
#>  4:      4  Strategy 1   0.00000  63.60754
#>  5:      5  Strategy 1  30.51387  86.45465
#>  6:      1  Strategy 2  99.16234  31.71191
#>  7:      2  Strategy 2  86.55179  49.55827
#>  8:      3  Strategy 2  58.46559  11.85367
#>  9:      4  Strategy 2  82.03813   0.00000
#> 10:      5  Strategy 2  72.69201  11.65839

# "Total value"
print(mcda$total_value)
#>     sample strategy_id     score rank
#>  1:      1  Strategy 1  48.24612    2
#>  2:      2  Strategy 1 100.00000    1
#>  3:      3  Strategy 1  72.90455    1
#>  4:      4  Strategy 1  19.08226    2
#>  5:      5  Strategy 1  47.29610    2
#>  6:      1  Strategy 2  78.92721    1
#>  7:      2  Strategy 2  75.45374    2
#>  8:      3  Strategy 2  44.48201    2
#>  9:      4  Strategy 2  57.42669    1
#> 10:      5  Strategy 2  54.38192    1

# "Total value" decomposed by criteria
print(mcda$weighted_scores)
#>     sample strategy_id  criteria weighted_score
#>  1:      1  Strategy 1 criteria1      24.446082
#>  2:      2  Strategy 1 criteria1      70.000000
#>  3:      3  Strategy 1 criteria1      48.446501
#>  4:      4  Strategy 1 criteria1       0.000000
#>  5:      5  Strategy 1 criteria1      21.359708
#>  6:      1  Strategy 2 criteria1      69.413638
#>  7:      2  Strategy 2 criteria1      60.586255
#>  8:      3  Strategy 2 criteria1      40.925914
#>  9:      4  Strategy 2 criteria1      57.426691
#> 10:      5  Strategy 2 criteria1      50.884407
#> 11:      1  Strategy 1 criteria2      23.800041
#> 12:      2  Strategy 1 criteria2      30.000000
#> 13:      3  Strategy 1 criteria2      24.458051
#> 14:      4  Strategy 1 criteria2      19.082263
#> 15:      5  Strategy 1 criteria2      25.936395
#> 16:      1  Strategy 2 criteria2       9.513574
#> 17:      2  Strategy 2 criteria2      14.867482
#> 18:      3  Strategy 2 criteria2       3.556100
#> 19:      4  Strategy 2 criteria2       0.000000
#> 20:      5  Strategy 2 criteria2       3.497517

# Probability of ranking
print(mcda$prob_rank)
#>    strategy_id rank N prob
#> 1:  Strategy 1    1 2  0.4
#> 2:  Strategy 1    2 3  0.6
#> 3:  Strategy 2    1 3  0.6
#> 4:  Strategy 2    2 2  0.4