Analysis of Table 1 from two (or three) articles by Cadegiani et al.

Cadegiani-Table1s.R

# Code to analyse Table 1 from some articles about the use of anti-androgens to treat Covid-19.
# By Nick Brown, October 2021.
# Licence: CC-0.
# See https://steamtraen.blogspot.com/2021/10/applying-john-carlisles-table-1.html

# Compute the chi-square p value for a given analysis modality (see the blog post).
mychi <- function (s1, s2, n1, n2, analysis)
{
  mat <- matrix(c(s1, (n1 - s1), s2, (n2 - s2)), ncol=2)

  no.zeroes <- substr(analysis, 2, 2) == "a"
  if (no.zeroes && any(mat < 1)) {
    return(NULL)
  }

  min.3 <- substr(analysis, 2, 2) == "c"
  if (min.3 && any(mat < 3)) {
    return(NULL)
  }

  analysis <- as.integer(substr(analysis, 1, 1))
  use.fisher <- if (analysis == 1) 5 else if (analysis == 2) 0 else 9999999

  func <- chisq.test
  if (any(mat < use.fisher)) {
    func <- fisher.test
  }

  p <- func(mat)$p.value
  if (is.nan(p)) {    # If two cells are zero, chisq.test() will return NaN as the p value (fisher.test gives 1.0).
    p <- 1.0          # In that case, we force a p value of 1.0 (which we will later discard anyway by the 0.98 test).
  }

  return(p)
}

# Calculate the p value from a t test.
# we use rounding to make it the most favourable possible for the authors.
mytt <- function (m1, sd1, n1, m2, sd2, n2, dp=1)
{
  if (dp > 0) {
    sign <- if (m1 < m2) 1 else -1
    delta <- (10 ^ (-dp -1)) * 5
    m1 <- m1 + (delta * sign)
    m2 <- m2 - (delta * sign)
    sd1 <- sd1 + delta
    sd2 <- sd2 + delta
  }

  se <- sqrt(
    (
      (   ((n1 - 1) * (sd1 ^ 2))
        + ((n2 - 1) * (sd2 ^ 2))
      )
      / (n1 + n2 - 2)
    )
    * ((1 / n1) + (1 / n2))
  )

  t <- (m1 - m2) / se
  p <- 2 * (pt(abs(t), (n1 + n2 - 2), lower.tail=FALSE))

  return (p)
}

# Set this to TRUE to see the tables of the first digits of the p values.
show.p.deciles <- FALSE

for (analysis in c("1a", "1b", "1c", "2a", "2b", "2c", "3a", "3b", "3c")) {
  cat("Analysis ", analysis, "\n", sep="")
### Proxalutamide Significantly Accelerates Viral Clearance and Reduces Time to Clinical Remission in Patients with Mild to Moderate COVID-19 (10.7759/cureus.13492)
  pv1 <- c()
  
#Gender
  pv1 <- c(pv1, mychi(100, 71, 128, 108, analysis))
  
#Age (y/o)
  pv1 <- c(pv1, mytt(44.5, 13.1, 171, 46.1, 12.7, 65))
#Time-to-treat
  pv1 <- c(pv1, mytt(4.2, 1.8, 171, 4.0, 1.6, 65))
  
#Obesity
  pv1 <- c(pv1, mychi(28, 9, 171, 65, analysis))
#Hypertension
  pv1 <- c(pv1, mychi(39, 14, 171, 65, analysis))
#Myocardial infarction
  pv1 <- c(pv1, mychi(2, 0, 171, 65, analysis))
#Stroke
  pv1 <- c(pv1, mychi(2, 0, 171, 65, analysis))
#Congestive heart failure
  pv1 <- c(pv1, mychi(1, 1, 171, 65, analysis))
#Lipid disorders
  pv1 <- c(pv1, mychi(30, 16, 171, 65, analysis))
#DM (type 1 and 2)
  pv1 <- c(pv1, mychi(15, 6, 171, 65, analysis))
#Prediabetes
  pv1 <- c(pv1, mychi(18, 5, 171, 65, analysis))
#Dysglycemia
  pv1 <- c(pv1, mychi(33, 11, 171, 65, analysis))
#Asthma
  pv1 <- c(pv1, mychi(8, 4, 171, 65, analysis))
#COPD
  pv1 <- c(pv1, mychi(0, 0, 171, 65, analysis))
#Chronic kidney disease
  pv1 <- c(pv1, mychi(1, 0, 171, 65, analysis))
#Liver fibrosis/cirrhosis
  pv1 <- c(pv1, mychi(0, 0, 171, 65, analysis))
#Clinical depression
  pv1 <- c(pv1, mychi(11, 3, 171, 65, analysis))
#Anxiety
  pv1 <- c(pv1, mychi(29, 7, 171, 65, analysis))
#Hypothyroidism
  pv1 <- c(pv1, mychi(18, 7, 171, 65, analysis))
#Autoimmune disorders
  pv1 <- c(pv1, mychi(1, 0, 171, 65, analysis))
#Cancer
  pv1 <- c(pv1, mychi(3, 1, 171, 65, analysis))
#Beta-blocker
  pv1 <- c(pv1, mychi(7, 3, 171, 65, analysis))
#ACEi
  pv1 <- c(pv1, mychi(1, 0, 171, 65, analysis))
#ARB
  pv1 <- c(pv1, mychi(25, 5, 171, 65, analysis))
#Loop diuretics
  pv1 <- c(pv1, mychi(2, 0, 171, 65, analysis))
#Thiazide diuretics
  pv1 <- c(pv1, mychi(7, 2, 171, 65, analysis))
#CCB
  pv1 <- c(pv1, mychi(15, 3, 171, 65, analysis))
#Statins
  pv1 <- c(pv1, mychi(13, 4, 171, 65, analysis))
#Others
  pv1 <- c(pv1, mychi(2, 0, 171, 65, analysis))
#Aspirin
  pv1 <- c(pv1, mychi(5, 1, 171, 65, analysis))
#Clopidogrel
  pv1 <- c(pv1, mychi(0, 1 , 171, 65, analysis))
#Warfarin
  pv1 <- c(pv1, mychi(0, 0, 171, 65, analysis))
#Xa factor inhibitors
  pv1 <- c(pv1, mychi(1, 0, 171, 65, analysis))
#Direct thrombin inhibitors
  pv1 <- c(pv1, mychi(0, 0, 171, 65, analysis))
#Heparin
  pv1 <- c(pv1, mychi(0, 0, 171, 65, analysis))
#Metformin
  pv1 <- c(pv1, mychi(16, 5, 171, 65, analysis))
#GLP1R analogs
  pv1 <- c(pv1, mychi(10, 3, 171, 65, analysis))
#SGLT2 inhibitors
  pv1 <- c(pv1, mychi(16, 3, 171, 65, analysis))
#DPP4 inhibitors
  pv1 <- c(pv1, mychi(2, 1, 171, 65, analysis))
#Sulfonylureas
  pv1 <- c(pv1, mychi(3, 0, 171, 65, analysis))
#Glitazones
  pv1 <- c(pv1, mychi(0, 0, 171, 65, analysis))
#Acarbose
  pv1 <- c(pv1, mychi(0, 0, 171, 65, analysis))
#Insulin
  pv1 <- c(pv1, mychi(2, 0, 171, 65, analysis))
#Orlistat
  pv1 <- c(pv1, mychi(3, 2, 171, 65, analysis))
#Levothyroxine
  pv1 <- c(pv1, mychi(18, 7, 171, 65, analysis))
#Hypnotics
  pv1 <- c(pv1, mychi(6, 1, 171, 65, analysis))
#SSRI
  pv1 <- c(pv1, mychi(17, 4, 171, 65, analysis))
#Other antidepressants and mood stabilizers
  pv1 <- c(pv1, mychi(8, 3, 171, 65, analysis))
#Benzodiazepines
  pv1 <- c(pv1, mychi(4, 0, 171, 65, analysis))
#Atypical antipsychotics
  pv1 <- c(pv1, mychi(8, 2, 171, 65, analysis))
#Omega-3
  pv1 <- c(pv1, mychi(3, 0, 171, 65, analysis))
#Vitamin D
  pv1 <- c(pv1, mychi(20, 5, 171, 65, analysis))
#Zinc
  pv1 <- c(pv1, mychi(9, 2, 171, 65, analysis))
#Vitamin C
  pv1 <- c(pv1, mychi(14, 5, 171, 65, analysis))
#Multivitamin
  pv1 <- c(pv1, mychi(12, 4, 171, 65, analysis))
  
# Limit p values to a maximum of 0.98, to prevent "infinity" errors.
  pv1[pv1 > 0.98] <- 0.98
  
# Now compute the overall probability by Stouffer's formula. 
  overall.pv1 <- 1 - pnorm(sum(sapply(pv1, qnorm))/sqrt(length(pv1)))
  cat("Overall p value from \"Proxalutamide Significantly Accelerates Viral Clearance\" = ", overall.pv1, "\n", sep="")

  if (show.p.deciles) {
    cat("Table of first digits of p values\n")
    cat(0:9, "\n", sep="  ")
    cat(tabulate(floor(pv1 * 10) + 1), "\n", sep="  ")
  }
  
  cat("\n")
### Early Antiandrogen Therapy With Dutasteride Reduces Viral Shedding, Inflammatory Responses, and Time-to-Remission in Males With COVID-19 (10.7759/cureus.13047)
### Note: In the preprint (10.21203/rs.3.rs-135815/v1), the number of people in each condition was reversed (43 placebo, 44 treatment).
  pv2 <- c()

#AGE (y/o)
  pv2 <- c(pv2, mytt(43.8, 14.1, 44, 40, 10.8, 43))
#BMI (Kg/m2)
  pv2 <- c(pv2, mytt(26.1, 2.2, 44, 26.0, 3.2, 43))
#Time-to-treat
  pv2 <- c(pv2, mytt(4.4, 1.4, 44, 4.3, 1.4, 43))
  
#Obesity
  pv2 <- c(pv2, mychi(4, 5, 44, 43, analysis))
#Hypertension
  pv2 <- c(pv2, mychi(12, 7, 44, 43, analysis))
#Mi
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Stroke
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Hf
  pv2 <- c(pv2, mychi(0, 1, 44, 43, analysis))
#Lipid disorders
  pv2 <- c(pv2, mychi(9, 9, 44, 43, analysis))
#Other cardiac dysfunctions
  pv2 <- c(pv2, mychi(0, 1, 44, 43, analysis))
#T1DM and T2DM
  pv2 <- c(pv2, mychi(4, 4, 44, 43, analysis))
#Prediabetes
  pv2 <- c(pv2, mychi(8, 5, 44, 43, analysis))
#Dysglycemia
  pv2 <- c(pv2, mychi(12, 9, 44, 43, analysis))
#Asthma
  pv2 <- c(pv2, mychi(1, 0, 44, 43, analysis))
#COPD
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#CKD
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Liver fibrosis/cirrhosis
  pv2 <- c(pv2, mychi(1, 0, 44, 43, analysis))
#Clinical depression
  pv2 <- c(pv2, mychi(2, 3, 44, 43, analysis))
#Anxiety
  pv2 <- c(pv2, mychi(6, 8, 44, 43, analysis))
#ADHD
  pv2 <- c(pv2, mychi(5, 3, 44, 43, analysis))
#Insomnia
  pv2 <- c(pv2, mychi(4, 1, 44, 43, analysis))
#Hypothyroidism
  pv2 <- c(pv2, mychi(1, 4, 44, 43, analysis))
#Autoimmune disorders
  pv2 <- c(pv2, mychi(1, 1, 44, 43, analysis))
#Cancer
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Erectile dysfunction
  pv2 <- c(pv2, mychi(2, 1, 44, 43, analysis))
#Hypogonadism
  pv2 <- c(pv2, mychi(8, 8, 44, 43, analysis))
#BPH
  pv2 <- c(pv2, mychi(2, 2, 44, 43, analysis))
#Beta-blocker
  pv2 <- c(pv2, mychi(2, 1, 44, 43, analysis))
#ECAi
  pv2 <- c(pv2, mychi(1, 0, 44, 43, analysis))
#ARB
  pv2 <- c(pv2, mychi(11, 7, 44, 43, analysis))
#Loop diuretics
  pv2 <- c(pv2, mychi(1, 0, 44, 43, analysis))
#Thiazide diuretics
  pv2 <- c(pv2, mychi(4, 1, 44, 43, analysis))
#CCB
  pv2 <- c(pv2, mychi(2, 2, 44, 43, analysis))
#Statins
  pv2 <- c(pv2, mychi(8, 8, 44, 43, analysis))
#Others
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Aspirin
  pv2 <- c(pv2, mychi(0, 1, 44, 43, analysis))
#Clopidogrel
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Warfarin
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Xa factor inhibitors
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Direct thrombin inhibitors
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Heparin
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Metformin
  pv2 <- c(pv2, mychi(10, 6, 44, 43, analysis))
#GLP1R analogues
  pv2 <- c(pv2, mychi(2, 3, 44, 43, analysis))
#SGLT2 inhibitors
  pv2 <- c(pv2, mychi(7, 3, 44, 43, analysis))
#DPP4 inhibitors
  pv2 <- c(pv2, mychi(2, 1, 44, 43, analysis))
#Sylfonylureas
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Glitazone
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Acarbose
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Insulin
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Orlistat
  pv2 <- c(pv2, mychi(2, 2, 44, 43, analysis))
#Levothyroxine
  pv2 <- c(pv2, mychi(1, 4, 44, 43, analysis))
#Liothyronine
  pv2 <- c(pv2, mychi(1, 0, 44, 43, analysis))
#Testosterone
  pv2 <- c(pv2, mychi(7, 6, 44, 43, analysis))
#Aromatase inhibitors or SERMs
  pv2 <- c(pv2, mychi(2, 2, 44, 43, analysis))
#Hypnotics
  pv2 <- c(pv2, mychi(3, 1, 44, 43, analysis))
#Selective serotonin reuptaker inhibitors (SSRI)
  pv2 <- c(pv2, mychi(3, 6, 44, 43, analysis))
#Other antidepressants and humor stabilizers
  pv2 <- c(pv2, mychi(4, 4, 44, 43, analysis))
#Benzodiazepines
  pv2 <- c(pv2, mychi(1, 0, 44, 43, analysis))
#Atypical antipsychotics
  pv2 <- c(pv2, mychi(3, 2, 44, 43, analysis))
#CNS stimulants
  pv2 <- c(pv2, mychi(5, 5, 44, 43, analysis))
#Alpha-1 adrenaline blockers
  pv2 <- c(pv2, mychi(2, 2, 44, 43, analysis))
#GnRH analogues and inhibitors, NSAA and others antiandrogens
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Omega-3
  pv2 <- c(pv2, mychi(3, 1, 44, 43, analysis))
#Vitamin D
  pv2 <- c(pv2, mychi(13, 15, 44, 43, analysis))
#Zinc
  pv2 <- c(pv2, mychi(6, 7, 44, 43, analysis))
#Biotin
  pv2 <- c(pv2, mychi(1, 0, 44, 43, analysis))
#Vitamin C
  pv2 <- c(pv2, mychi(8, 7, 44, 43, analysis))
#Multivitamin
  pv2 <- c(pv2, mychi(1, 2, 44, 43, analysis))
#BCG vaccine
  pv2 <- c(pv2, mychi(44, 43, 44, 43, analysis))  #corrected, as paper has too many people in the treatment group!
#Influeza vaccine (in 2020)
  pv2 <- c(pv2, mychi(14, 14, 44, 43, analysis))
#Pneumococcal vaccine (since 2017)
  pv2 <- c(pv2, mychi(3, 5, 44, 43, analysis))
#Current smoking
  pv2 <- c(pv2, mychi(2, 2, 44, 43, analysis))
#Regular physical activity
  pv2 <- c(pv2, mychi(28, 32, 44, 43, analysis))
#Ivermectin
  pv2 <- c(pv2, mychi(6, 6, 44, 43, analysis))
#Hydroxychloroquine
  pv2 <- c(pv2, mychi(4, 3, 44, 43, analysis))
#Xa factor inhibitors
  pv2 <- c(pv2, mychi(8, 3, 44, 43, analysis))
#Enoxaparin
  pv2 <- c(pv2, mychi(3, 3, 44, 43, analysis))
#Glucocorticoids
  pv2 <- c(pv2, mychi(6, 7, 44, 43, analysis))
#Vitamin C
  pv2 <- c(pv2, mychi(4, 4, 44, 43, analysis))
#Zinc
  pv2 <- c(pv2, mychi(3, 3, 44, 43, analysis))
#Vitamin D
  pv2 <- c(pv2, mychi(1, 2, 44, 43, analysis))
#Colchicine
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#Bromexhine
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
#N-acetylcysteine
  pv2 <- c(pv2, mychi(0, 0, 44, 43, analysis))
  
# Limit p values to a maximum of 0.98, to prevent "infinity" errors.
  pv2[pv2 > 0.98] <- 0.98
  
# Now compute the overall probability by Stouffer's formula. 
  overall.pv2 <- 1 - pnorm(sum(sapply(pv2, qnorm))/sqrt(length(pv2)))
  cat("Overall p value from \"Early Antiandrogen Therapy With Dutasteride\" = ", overall.pv2, "\n", sep="")

  if (show.p.deciles) {
    cat("Table of first digits of p values\n")
    cat(0:9, "\n", sep="  ")
    cat(tabulate(floor(pv2 * 10) + 1), "\n", sep="  ")
  }

  cat("\n")
### 5-Alpha-Reductase Inhibitors Reduce Remission Time of COVID-19 (10.1101/2020.11.16.20232512)
  pv3 <- c()
  
#age
  pv3 <- c(pv3, mytt(42.0, 11.5, 66, 42.0, 12.6, 64))
#weight
  pv3 <- c(pv3, mytt(85.5, 11.6, 66, 85.5, 9.8, 64))
#height
  pv3 <- c(pv3, mytt(1.8, 0.1, 66, 1.8, 0.1, 64))
#BMI - not included here because it's redundant with height and weight.
# (If we use BMI instead of height/weight the result is to the authors' disadvantage.)
#pv3 <- c(pv3, mytt(26.5, 2.8, 66, 26.5, 3.2, 64))
  
#obesity
  pv3 <- c(pv3, mychi(8, 10, 66, 64, analysis))
#Married?
  pv3 <- c(pv3, mychi(47, 43, 66, 64, analysis))
#Live alone?
  pv3 <- c(pv3, mychi(12, 13, 66, 64, analysis))
#Hypertension
  pv3 <- c(pv3, mychi(18, 15, 66, 64, analysis))
#Mi
  pv3 <- c(pv3, mychi(1, 0, 66, 64, analysis))
#Stroke
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Hf
  pv3 <- c(pv3, mychi(0, 1, 66, 64, analysis))
#Lipid disorders
  pv3 <- c(pv3, mychi(14, 16, 66, 64, analysis))
#Other cardiac dysfunctions
  pv3 <- c(pv3, mychi(0, 3, 66, 64, analysis))
#Diabetes
  pv3 <- c(pv3, mychi(7, 7, 66, 64, analysis))
#Pré-dm2
  pv3 <- c(pv3, mychi(11, 9, 66, 64, analysis))
#Asthma
  pv3 <- c(pv3, mychi(1, 0, 66, 64, analysis))
#COPD
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Chronic renal dis.
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Liver fibrosis/chirrosis
  pv3 <- c(pv3, mychi(1, 0, 66, 64, analysis))
#Clinical depression
  pv3 <- c(pv3, mychi(5, 4, 66, 64, analysis))
#Anxiety
  pv3 <- c(pv3, mychi(13, 12, 66, 64, analysis))
#ADHD
  pv3 <- c(pv3, mychi(5, 6, 66, 64, analysis))
#Insomnia
  pv3 <- c(pv3, mychi(4, 6, 66, 64, analysis))
#Hypothyroidism
  pv3 <- c(pv3, mychi(3, 4, 66, 64, analysis))
#Autoimmune disorders
  pv3 <- c(pv3, mychi(1, 0, 66, 64, analysis))
#Cancer
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Hypogonadism
  pv3 <- c(pv3, mychi(13, 11, 66, 64, analysis))
#BPH
  pv3 <- c(pv3, mychi(2, 3, 66, 64, analysis))
#Beta-blocker
  pv3 <- c(pv3, mychi(3, 3, 66, 64, analysis))
#ECAi
  pv3 <- c(pv3, mychi(4, 1, 66, 64, analysis))
#ARB
  pv3 <- c(pv3, mychi(14, 14, 66, 64, analysis))
#Loop diur.
  pv3 <- c(pv3, mychi(3, 0, 66, 64, analysis))
#Thiazide diuretics
  pv3 <- c(pv3, mychi(4, 5, 66, 64, analysis))
#CCB
  pv3 <- c(pv3, mychi(2, 4, 66, 64, analysis))
#Statins
  pv3 <- c(pv3, mychi(14, 15, 66, 64, analysis))
#Others
  pv3 <- c(pv3, mychi(0, 1, 66, 64, analysis))
#Aspirin
  pv3 <- c(pv3, mychi(0, 2, 66, 64, analysis))
#Clopidogrel
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Warfarin
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Xa factor inhibitors
  pv3 <- c(pv3, mychi(0, 1, 66, 64, analysis))
#Direct thrombin inhibitors
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Heparins
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Metformin
  pv3 <- c(pv3, mychi(16, 14, 66, 64, analysis))
#GLP1R analogue
  pv3 <- c(pv3, mychi(4, 8, 66, 64, analysis))
#SGLT2 inhibitors
  pv3 <- c(pv3, mychi(8, 7, 66, 64, analysis))
#DPP4 inhibitors
  pv3 <- c(pv3, mychi(3, 2, 66, 64, analysis))
#Sylfonylureas
  pv3 <- c(pv3, mychi(1, 0, 66, 64, analysis))
#Glitazone
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Acarbose
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Insulin
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Orlistat
  pv3 <- c(pv3, mychi(4, 5, 66, 64, analysis))
#Levothyroxine
  pv3 <- c(pv3, mychi(3, 4, 66, 64, analysis))
#Liothyronine
  pv3 <- c(pv3, mychi(1, 0, 66, 64, analysis))
#Testosterone
  pv3 <- c(pv3, mychi(11, 9, 66, 64, analysis))
#Aromatase inhibitors or SERMs
  pv3 <- c(pv3, mychi(2, 2, 66, 64, analysis))
#Hipnotics
  pv3 <- c(pv3, mychi(4, 5, 66, 64, analysis))
#Selective serotonin reuptaker inhibitors (SSRI)
  pv3 <- c(pv3, mychi(10, 9, 66, 64, analysis))
#Other antidepressants and humor stabilizers
  pv3 <- c(pv3, mychi(7, 6, 66, 64, analysis))
#Benzodiazepines
  pv3 <- c(pv3, mychi(2, 2, 66, 64, analysis))
#Atypical antipsychotics
  pv3 <- c(pv3, mychi(4, 3, 66, 64, analysis))
#CNS stimulants
  pv3 <- c(pv3, mychi(5, 8, 66, 64, analysis))
#Alpha-1 adren. Blockers
  pv3 <- c(pv3, mychi(2, 3, 66, 64, analysis))
#Gnrh analogues and inh., NSAA, others
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
#Erectile dysfunction
  pv3 <- c(pv3, mychi(2, 1, 66, 64, analysis))
#Omega-3
  pv3 <- c(pv3, mychi(3, 1, 66, 64, analysis))
#Vitamin D
  pv3 <- c(pv3, mychi(17, 17, 66, 64, analysis))
#Zinc
  pv3 <- c(pv3, mychi(6, 7, 66, 64, analysis))
#Biotin
  pv3 <- c(pv3, mychi(1, 0, 66, 64, analysis))
#Vitamin C
  pv3 <- c(pv3, mychi(8, 8, 66, 64, analysis))
#Multivitamin
  pv3 <- c(pv3, mychi(2, 2, 66, 64, analysis))
#BCG
  pv3 <- c(pv3, mychi(64, 63, 66, 64, analysis))
#INFLUENZA (in 2020)
  pv3 <- c(pv3, mychi(20, 21, 66, 64, analysis))
#PNEUMOCOCCAL (since 2017)
  pv3 <- c(pv3, mychi(4, 8, 66, 64, analysis))
#CURRENT SMOKING
  pv3 <- c(pv3, mychi(4, 6, 66, 64, analysis))
#Ivermectin
  pv3 <- c(pv3, mychi(7, 6, 66, 64, analysis))
#Hydroxychlorouquine
  pv3 <- c(pv3, mychi(4, 3, 66, 64, analysis))
#Xa FACTOR INHIBITORS
  pv3 <- c(pv3, mychi(9, 6, 66, 64, analysis))
#Enoxaparin
  pv3 <- c(pv3, mychi(4, 4, 66, 64, analysis))
#Glucocorticoids
  pv3 <- c(pv3, mychi(7, 8, 66, 64, analysis))
#Vitamin c
  pv3 <- c(pv3, mychi(4, 5, 66, 64, analysis))
#Zinc
  pv3 <- c(pv3, mychi(3, 4, 66, 64, analysis))
#Vitamin d
  pv3 <- c(pv3, mychi(1, 3, 66, 64, analysis))
#Colchicine
  pv3 <- c(pv3, mychi(0, 0, 66, 64, analysis))
  
# Limit p values to a maximum of 0.98, to prevent "infinity" errors.
  pv3[pv3 > 0.98] <- 0.98
  
# Now compute the overall probability by Stouffer's formula. 
  overall.pv3 <- 1 - pnorm(sum(sapply(pv3, qnorm))/sqrt(length(pv3)))
  cat("Overall p value from \"5-Alpha-Reductase Inhibitors\" = ", overall.pv3, "\n", sep="")

  if (show.p.deciles) {
    cat("Table of first digits of p values\n")
    cat(0:9, "\n", sep="  ")
    cat(tabulate(floor(pv3 * 10) + 1), "\n", sep="  ")
  }

  cat("\n")
}