###INDEPENDENT GROUPS: COMPARISONS OF TWO MEANS

# Minimum sample size for comparing two independent means
# Compare mean SBP in treatment vs control group
# We want to detect a difference of 5 mmHg, assuming:
# SD=12 mmHg (from previous studies)
# alpha=0.05
# power=0.80

library(Epi)

epi.sscompc(
  n = NA,             # sample size for each group (to be estimated)
  treat = 130,        # expected mean in treatment group
  control = 135,      # expected mean in control group
  sigma = 12,         # assumed common standard deviation
  power = 0.80,       # desired statistical power
  r = 1,              # equal sample size in the two groups
  design = 1,         # simple random sampling
  sided.test = 2,     # two-sided test
  conf.level = 0.95   # significance level alpha = 0.05
)


##########################################################################

###DEPENDENT GROUPS: COMPARISONS OF TWO MEANS

# Minimum sample size for comparing the mean of two dependent groups
# Compare mean FPG in the same patients before a dietary intervention and after 3 months
# We want to detect a difference of 8 mg/dL, assuming:
# SD of the paired differences=20 mg/dL (from previous studies)
# alpha=0.05
# power=0.80

library(pwr)

pwr.t.test(
  d = 8/20,           # standardized effect size = mean difference / SD of paired differences
  power = 0.80,       # desired statistical power
  sig.level = 0.05,   # significance level
  type = "paired",    # paired data
  alternative = "two.sided")

#What if type="two.sample"?
#The more similar the paired observations are, 
#the easier it is to detect a difference.
#So fewer subjects are needed.

##########################################################################

###INDEPENDENT GROUPS: COMPARISONS OF TWO PROPORTIONS

# Minimum sample size for comparing the proportions in two independent groups
# Compare smoking cessation rates in two groups:
# group 1 received standard counseling; group 2 counseling + a mobile app
# We expect the following proportions:
# 20% in the control group; 35% in the intervention group
# We assume:
# alpha=0.05
# power=0.80

library(pwrss)

power.z.twoprops(
  prob1 = 0.20,             # expected proportion in control group
  prob2 = 0.35,             # expected proportion in intervention group
  power = 0.80,             # desired statistical power
  alpha = 0.05,             # significance level
  alternative = "two.sided",
  paired = FALSE            # independent groups
)


##########################################################################

###DEPENDENT GROUPS: COMPARISONS OF TWO PROPORTIONS

# Minimum sample size for comparing the proportions in two dependent groups
# We want to evaluate whether an SMS reminder improves vaccination uptake in the same patients
# Expected willingness was 50% before and 65% after the SMS reminder
# We assume:
# alpha=0.05
# power=0.80
# moderate correlation between paired responses (r=0.5)

library(pwrss)

power.z.twoprops(
  prob1 = 0.50,             # expected proportion before intervention
  prob2 = 0.65,             # expected proportion after intervention
  power = 0.80,             # desired statistical power
  alpha = 0.05,             # significance level
  alternative = "two.sided",
  paired = TRUE,            # paired/matched data
  rho.paired = 0.50         # assumed correlation within pairs
)



###########################################################################

###SAMPLE SIZE FOR A CHI-SQUARE TEST
# We want to test whether obesity status is associated with the presence of hypertension
# We assume:
# alpha=0.05
# power=0.8
# small-to-moderate effect size

library(pwr)

pwr.chisq.test(
  w = 0.3,            # Cohen's effect size (0.1 small, 0.3 medium, 0.5 large)
  df = 1,             # degrees of freedom for a 2x2 table
  sig.level = 0.05,   # significance level
  power = 0.80        # desired statistical power
)




###########################################################################

###SAMPLE SIZE FOR A CORRELATION TEST
# We want to test whether BMI is associated with fasting insulin
# We assume:
# alpha=0.05
# power=0.8
# expected r=0.3


# Sample size for testing a correlation coefficient
# Example: correlation between BMI and fasting insulin

library(pwr)

pwr.r.test(
  r = 0.3,           # expected correlation coefficient
  sig.level = 0.05,   # significance level
  power = 0.80,       # desired statistical power
  alternative = "two.sided"
)


#######################################################################

###SAMPLE SIZE FOR AN ODDS RATIO

# A case-control study of the relationship between smoking and CHD is planned. 
# A sample of men with newly diagnosed CHD will be compared for smoking status with a sample of controls. 
# Assuming an equal number of cases and controls, how many study subject are required to detect an OR of 2.0 
# with 0.90 power using a two-sided 0.05 test? 
# Previous surveys have shown that around 30% of males without CHD are smokers.

library(epiR)

epi.sscc(OR = 2.0, p0 = 0.30, n = NA, power = 0.90, r = 1, phi.coef = 0, 
         design = 1, sided.test = 2, conf.level = 0.95, method = "unmatched")


# p0: prevalence of the disease among the controls
# phi.coef: correlation between case and control exposures for matched pairs. Set to null if unmatched.
# design: design effect, used to take into account the possible presence of clustering in the random sampling of the data.