Compute frequencies from (3 essential) probabilities.

comp_freq_prob computes frequency information from a sufficient and valid set of 3 essential probabilities (prev, and sens or its complement mirt, and spec or its complement fart). It returns a list of 11 key frequencies (freq) as its output.

Usage

comp_freq_prob(
  prev = prob$prev,
  sens = prob$sens,
  mirt = NA,
  spec = prob$spec,
  fart = NA,
  tol = 0.01,
  N = freq$N,
  round = TRUE,
  sample = FALSE
)

Arguments

prev

The condition's prevalence prev (i.e., the probability of condition being TRUE).

sens

The decision's sensitivity sens (i.e., the conditional probability of a positive decision provided that the condition is TRUE). sens is optional when its complement mirt is provided.

mirt

The decision's miss rate mirt (i.e., the conditional probability of a negative decision provided that the condition is TRUE). mirt is optional when its complement sens is provided.

spec

The decision's specificity value spec (i.e., the conditional probability of a negative decision provided that the condition is FALSE). spec is optional when its complement fart is provided.

fart

The decision's false alarm rate fart (i.e., the conditional probability of a positive decision provided that the condition is FALSE). fart is optional when its complement spec is provided.

tol

A numeric tolerance value for is_complement. Default: tol = .01.

N

The number of individuals in the population. If N is unknown (NA), a suitable minimum value is computed by comp_min_N.

round

A Boolean value that determines whether frequencies are rounded to the nearest integer. Default: round = TRUE.

sample

Boolean value that determines whether frequency values are sampled from N, given the probability values of prev, sens, and spec. Default: sample = FALSE.

Note: Sampling uses sample() and returns integer values.

Value

A list freq containing 11 key frequency values.

Details

comp_freq_prob is a wrapper function for the more basic function comp_freq, which only accepts 3 essential probabilities (i.e., prev, sens, and spec) as inputs.

Defaults and constraints:

• Initial values:

  By default, the values of prev, sens, and spec are initialized to the probability information currently contained in prob.

  Similarly, the population size N uses the frequency information currently contained in freq as its default. If N is unknown (NA), a suitable minimum value is computed by comp_min_N.

• Constraints:

  When using comp_freq_prob with the arguments mirt and fart, their complements sens and spec must either be valid complements (as in is_complement) or set to NA.

  In addition to prev, both sens and spec are necessary arguments. If only their complements mirt or fart are known, first use comp_complement, comp_comp_pair, or comp_complete_prob_set to compute the 3 essential probabilities.

• Rounding:

  By default, comp_freq_prob and its basic function comp_freq round frequencies to nearest integers to avoid decimal values in freq (i.e., round = TRUE by default).

  When frequencies are rounded, probabilities computed from freq may differ from exact probabilities.

  Using the option round = FALSE turns off rounding.

Key relationships between frequencies and probabilities (see documentation of comp_freq or comp_prob for details):

• Three perspectives on a population:

  by condition / by decision / by accuracy.

• Defining probabilities in terms of frequencies:

  Probabilities can be computed as ratios between frequencies, but beware of rounding and sampling issues!

Functions translating between representational formats: comp_prob_prob, comp_prob_freq, comp_freq_prob, comp_freq_freq (see documentation of comp_prob_prob for details).

See also

comp_freq_freq computes current frequency information from (4 essential) frequencies; comp_prob_freq computes current probability information from (4 essential) frequencies; comp_prob_prob computes current probability information from (3 essential) probabilities; num contains basic numeric variables; init_num initializes basic numeric variables; freq contains current frequency information; comp_freq computes current frequency information; prob contains current probability information; comp_prob computes current probability information; comp_complement computes a probability's complement; comp_comp_pair computes pairs of complements; comp_complete_prob_set completes valid sets of probabilities; comp_min_N computes a suitable population size N (if missing).

Other functions computing frequencies: comp_freq(), comp_freq_freq(), comp_min_N(), comp_prob_prob()

Other format conversion functions: comp_freq_freq(), comp_prob_freq(), comp_prob_prob()

Examples

# Basics:
comp_freq_prob(prev = .1, sens = .9, spec = .8, N = 100)  # ok: hi = 9, ... cr = 72.
#> $N
#> [1] 100
#> 
#> $cond_true
#> [1] 10
#> 
#> $cond_false
#> [1] 90
#> 
#> $dec_pos
#> [1] 27
#> 
#> $dec_neg
#> [1] 73
#> 
#> $dec_cor
#> [1] 81
#> 
#> $dec_err
#> [1] 19
#> 
#> $hi
#> [1] 9
#> 
#> $mi
#> [1] 1
#> 
#> $fa
#> [1] 18
#> 
#> $cr
#> [1] 72
#> 
# Same case with complements (using NAs to prevent defaults):
comp_freq_prob(prev = .1, sens = NA, mirt = .1, spec = NA, fart = .2, N = 100)  # same result
#> $N
#> [1] 100
#> 
#> $cond_true
#> [1] 10
#> 
#> $cond_false
#> [1] 90
#> 
#> $dec_pos
#> [1] 27
#> 
#> $dec_neg
#> [1] 73
#> 
#> $dec_cor
#> [1] 81
#> 
#> $dec_err
#> [1] 19
#> 
#> $hi
#> [1] 9
#> 
#> $mi
#> [1] 1
#> 
#> $fa
#> [1] 18
#> 
#> $cr
#> [1] 72
#> 

comp_freq_prob()                   # ok, using probability info currently contained in prob
#> $N
#> [1] 1000
#> 
#> $cond_true
#> [1] 250
#> 
#> $cond_false
#> [1] 750
#> 
#> $dec_pos
#> [1] 400
#> 
#> $dec_neg
#> [1] 600
#> 
#> $dec_cor
#> [1] 774
#> 
#> $dec_err
#> [1] 226
#> 
#> $hi
#> [1] 212
#> 
#> $mi
#> [1] 38
#> 
#> $fa
#> [1] 188
#> 
#> $cr
#> [1] 562
#> 
length(comp_freq_prob())           # list of 11 key frequencies
#> [1] 11
all.equal(freq, comp_freq_prob())  # TRUE, unless prob has been changed after computing freq
#> [1] TRUE
freq <- comp_freq_prob()           # computes frequencies and stores them in freq

# Ways to work:
comp_freq_prob(prev = 1, sens = 1, spec = 1, N = 101)  # ok + warning: N hits (TP)
#> Warning: Extreme case (prev = 1 & sens = 1):
#>   N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.
#> $N
#> [1] 101
#> 
#> $cond_true
#> [1] 101
#> 
#> $cond_false
#> [1] 0
#> 
#> $dec_pos
#> [1] 101
#> 
#> $dec_neg
#> [1] 0
#> 
#> $dec_cor
#> [1] 101
#> 
#> $dec_err
#> [1] 0
#> 
#> $hi
#> [1] 101
#> 
#> $mi
#> [1] 0
#> 
#> $fa
#> [1] 0
#> 
#> $cr
#> [1] 0
#> 

# Same case with complements (note NAs to prevent default arguments):
comp_freq_prob(prev = 1, sens = NA, mirt = 0, spec = NA, fart = 0, N = 101)
#> Warning: Extreme case (prev = 1 & sens = 1):
#>   N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.
#> $N
#> [1] 101
#> 
#> $cond_true
#> [1] 101
#> 
#> $cond_false
#> [1] 0
#> 
#> $dec_pos
#> [1] 101
#> 
#> $dec_neg
#> [1] 0
#> 
#> $dec_cor
#> [1] 101
#> 
#> $dec_err
#> [1] 0
#> 
#> $hi
#> [1] 101
#> 
#> $mi
#> [1] 0
#> 
#> $fa
#> [1] 0
#> 
#> $cr
#> [1] 0
#> 

comp_freq_prob(prev = 1, sens = 1, spec = 0, N = 102)  # ok + warning: N hits (TP)
#> Warning: Extreme case (prev = 1 & sens = 1):
#>   N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.
#> $N
#> [1] 102
#> 
#> $cond_true
#> [1] 102
#> 
#> $cond_false
#> [1] 0
#> 
#> $dec_pos
#> [1] 102
#> 
#> $dec_neg
#> [1] 0
#> 
#> $dec_cor
#> [1] 102
#> 
#> $dec_err
#> [1] 0
#> 
#> $hi
#> [1] 102
#> 
#> $mi
#> [1] 0
#> 
#> $fa
#> [1] 0
#> 
#> $cr
#> [1] 0
#> 
comp_freq_prob(prev = 1, sens = 0, spec = 1, N = 103)  # ok + warning: N misses (FN)
#> Warning: Extreme case (prev = 1 & sens = 0):
#>   N mi (FN) cases; 0 cond_false or dec_true cases; PPV = NaN.
#> $N
#> [1] 103
#> 
#> $cond_true
#> [1] 103
#> 
#> $cond_false
#> [1] 0
#> 
#> $dec_pos
#> [1] 0
#> 
#> $dec_neg
#> [1] 103
#> 
#> $dec_cor
#> [1] 0
#> 
#> $dec_err
#> [1] 103
#> 
#> $hi
#> [1] 0
#> 
#> $mi
#> [1] 103
#> 
#> $fa
#> [1] 0
#> 
#> $cr
#> [1] 0
#> 
comp_freq_prob(prev = 1, sens = 0, spec = 0, N = 104)  # ok + warning: N misses (FN)
#> Warning: Extreme case (prev = 1 & sens = 0):
#>   N mi (FN) cases; 0 cond_false or dec_true cases; PPV = NaN.
#> $N
#> [1] 104
#> 
#> $cond_true
#> [1] 104
#> 
#> $cond_false
#> [1] 0
#> 
#> $dec_pos
#> [1] 0
#> 
#> $dec_neg
#> [1] 104
#> 
#> $dec_cor
#> [1] 0
#> 
#> $dec_err
#> [1] 104
#> 
#> $hi
#> [1] 0
#> 
#> $mi
#> [1] 104
#> 
#> $fa
#> [1] 0
#> 
#> $cr
#> [1] 0
#> 
comp_freq_prob(prev = 0, sens = 1, spec = 1, N = 105)  # ok + warning: N correct rejections (TN)
#> Warning: Extreme case (prev = 0 & spec = 1):
#>   N cr (TN) cases; 0 cond_true or dec_false cases; NPV = NaN.
#> $N
#> [1] 105
#> 
#> $cond_true
#> [1] 0
#> 
#> $cond_false
#> [1] 105
#> 
#> $dec_pos
#> [1] 0
#> 
#> $dec_neg
#> [1] 105
#> 
#> $dec_cor
#> [1] 105
#> 
#> $dec_err
#> [1] 0
#> 
#> $hi
#> [1] 0
#> 
#> $mi
#> [1] 0
#> 
#> $fa
#> [1] 0
#> 
#> $cr
#> [1] 105
#> 

comp_freq_prob(prev = 0, sens = 1, spec = 0, N = 106)  # ok + warning: N false alarms (FP)
#> Warning: Extreme case (prev = 0 & spec = 0):
#>   N fa (FP) cases; 0 cond_true or dec_true cases; PPV = NaN.
#> $N
#> [1] 106
#> 
#> $cond_true
#> [1] 0
#> 
#> $cond_false
#> [1] 106
#> 
#> $dec_pos
#> [1] 106
#> 
#> $dec_neg
#> [1] 0
#> 
#> $dec_cor
#> [1] 0
#> 
#> $dec_err
#> [1] 106
#> 
#> $hi
#> [1] 0
#> 
#> $mi
#> [1] 0
#> 
#> $fa
#> [1] 106
#> 
#> $cr
#> [1] 0
#> 
# Same case with complements (using NAs to prevent defaults):
comp_freq_prob(prev = 0, sens = NA, mirt = 0,
               spec = NA, fart = 1, N = 106)  # ok + warning: N false alarms (FP)
#> Warning: Extreme case (prev = 0 & spec = 0):
#>   N fa (FP) cases; 0 cond_true or dec_true cases; PPV = NaN.
#> $N
#> [1] 106
#> 
#> $cond_true
#> [1] 0
#> 
#> $cond_false
#> [1] 106
#> 
#> $dec_pos
#> [1] 106
#> 
#> $dec_neg
#> [1] 0
#> 
#> $dec_cor
#> [1] 0
#> 
#> $dec_err
#> [1] 106
#> 
#> $hi
#> [1] 0
#> 
#> $mi
#> [1] 0
#> 
#> $fa
#> [1] 106
#> 
#> $cr
#> [1] 0
#> 

# Rounding:
comp_freq_prob(prev = .5, sens = .5, spec = .5, N = 1)   # yields fa = 1 (see ?round for reason)
#> $N
#> [1] 1
#> 
#> $cond_true
#> [1] 0
#> 
#> $cond_false
#> [1] 1
#> 
#> $dec_pos
#> [1] 1
#> 
#> $dec_neg
#> [1] 0
#> 
#> $dec_cor
#> [1] 0
#> 
#> $dec_err
#> [1] 1
#> 
#> $hi
#> [1] 0
#> 
#> $mi
#> [1] 0
#> 
#> $fa
#> [1] 1
#> 
#> $cr
#> [1] 0
#> 
comp_freq_prob(prev = .1, sens = .9, spec = .8, N = 10)  # 1 hit (TP, rounded)
#> $N
#> [1] 10
#> 
#> $cond_true
#> [1] 1
#> 
#> $cond_false
#> [1] 9
#> 
#> $dec_pos
#> [1] 3
#> 
#> $dec_neg
#> [1] 7
#> 
#> $dec_cor
#> [1] 8
#> 
#> $dec_err
#> [1] 2
#> 
#> $hi
#> [1] 1
#> 
#> $mi
#> [1] 0
#> 
#> $fa
#> [1] 2
#> 
#> $cr
#> [1] 7
#> 
comp_freq_prob(prev = .1, sens = .9, spec = .8, N = 10, round = FALSE)  # hi = .9
#> $N
#> [1] 10
#> 
#> $cond_true
#> [1] 1
#> 
#> $cond_false
#> [1] 9
#> 
#> $dec_pos
#> [1] 2.7
#> 
#> $dec_neg
#> [1] 7.3
#> 
#> $dec_cor
#> [1] 8.1
#> 
#> $dec_err
#> [1] 1.9
#> 
#> $hi
#> [1] 0.9
#> 
#> $mi
#> [1] 0.1
#> 
#> $fa
#> [1] 1.8
#> 
#> $cr
#> [1] 7.2
#> 

# Sampling (from probabilistic description):
comp_freq_prob(prev = .5, sens = .5, spec = .5, N = 100, sample = TRUE)  # freq values vary
#> $N
#> [1] 100
#> 
#> $cond_true
#> [1] 55
#> 
#> $cond_false
#> [1] 45
#> 
#> $dec_pos
#> [1] 58
#> 
#> $dec_neg
#> [1] 42
#> 
#> $dec_cor
#> [1] 53
#> 
#> $dec_err
#> [1] 47
#> 
#> $hi
#> [1] 33
#> 
#> $mi
#> [1] 22
#> 
#> $fa
#> [1] 25
#> 
#> $cr
#> [1] 20
#> 

# Watch out for:
comp_freq_prob(prev = 1, sens = 1, spec = 1, N = NA)  # ok + warning: N = 1 computed
#> Warning: Extreme case (prev = 1 & sens = 1):
#>   N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.
#> Warning: Extreme case (prev = 1 & sens = 1):
#>   N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.
#> Warning: Unknown population size N. A suitable minimum value of N = 1 was computed.
#> $N
#> [1] 1
#> 
#> $cond_true
#> [1] 1
#> 
#> $cond_false
#> [1] 0
#> 
#> $dec_pos
#> [1] 1
#> 
#> $dec_neg
#> [1] 0
#> 
#> $dec_cor
#> [1] 1
#> 
#> $dec_err
#> [1] 0
#> 
#> $hi
#> [1] 1
#> 
#> $mi
#> [1] 0
#> 
#> $fa
#> [1] 0
#> 
#> $cr
#> [1] 0
#> 
comp_freq_prob(prev = 1, sens = 1, spec = 1, N =  0)  # ok, but all 0 + warning (NPV = NaN)
#> Warning: Extreme case (prev = 1 & sens = 1):
#>   N hi (TP) cases; 0 cond_false or dec_false cases; NPV = NaN.
#> $N
#> [1] 0
#> 
#> $cond_true
#> [1] 0
#> 
#> $cond_false
#> [1] 0
#> 
#> $dec_pos
#> [1] 0
#> 
#> $dec_neg
#> [1] 0
#> 
#> $dec_cor
#> [1] 0
#> 
#> $dec_err
#> [1] 0
#> 
#> $hi
#> [1] 0
#> 
#> $mi
#> [1] 0
#> 
#> $fa
#> [1] 0
#> 
#> $cr
#> [1] 0
#> 
comp_freq_prob(prev = .5, sens = .5, spec = .5, N = 10, round = TRUE)  # ok, but all rounded
#> $N
#> [1] 10
#> 
#> $cond_true
#> [1] 5
#> 
#> $cond_false
#> [1] 5
#> 
#> $dec_pos
#> [1] 5
#> 
#> $dec_neg
#> [1] 5
#> 
#> $dec_cor
#> [1] 4
#> 
#> $dec_err
#> [1] 6
#> 
#> $hi
#> [1] 2
#> 
#> $mi
#> [1] 3
#> 
#> $fa
#> [1] 3
#> 
#> $cr
#> [1] 2
#> 
comp_freq_prob(prev = .5, sens = .5, spec = .5, N = 10, round = FALSE) # ok, but not rounded
#> $N
#> [1] 10
#> 
#> $cond_true
#> [1] 5
#> 
#> $cond_false
#> [1] 5
#> 
#> $dec_pos
#> [1] 5
#> 
#> $dec_neg
#> [1] 5
#> 
#> $dec_cor
#> [1] 5
#> 
#> $dec_err
#> [1] 5
#> 
#> $hi
#> [1] 2.5
#> 
#> $mi
#> [1] 2.5
#> 
#> $fa
#> [1] 2.5
#> 
#> $cr
#> [1] 2.5
#> 

# Ways to fail:
comp_freq_prob(prev = NA, sens = 1, spec = 1, 100)  # NAs + no warning (prev NA)
#> Warning: Please enter a valid set of essential probabilities.
comp_freq_prob(prev = 1, sens = NA, spec = 1, 100)  # NAs + no warning (sens NA)
#> Warning: Please enter a valid set of essential probabilities.
comp_freq_prob(prev = 1, sens = 1, spec = NA, 100)  # NAs + no warning (spec NA)
#> Warning: Please enter a valid set of essential probabilities.
comp_freq_prob(prev = 8, sens = 1, spec = 1,  100)  # NAs + warning (prev beyond range)
#> Warning: Please enter a valid set of essential probabilities.
comp_freq_prob(prev = 1, sens = 8, spec = 1,  100)  # NAs + warning (sens & spec beyond range)
#> Warning: Please enter a valid set of essential probabilities.