powerConLogistic.con {powerSurvEpi}

Sample Size Calculation for Conditional Logistic Regression with Continuous Covariate

Description

Sample Size Calculation for Conditional Logistic Regression with Continuous Covariate, such as matched logistic regression or nested case-control study.

Usage

powerConLogistic.con(
  N = NULL, 
  power = 0.8, 
  OR, 
  sigma, 
  nD, 
  nH, 
  R2 = 0, 
  alpha = 0.05, 
  nTests = 1,
  OR.low = 1.01,
  OR.upp = 100
)

Arguments

N

integer. Number of sets. Each set contains nD cases and nH controls.

power

numeric. Power of the test for if the exposure variable is associated with the risk of diseases

OR

numeric. Odds ratio =exp(\theta), where \theta is the regression coefficient of the exposure variable.

sigma

numeric. Standard deviation of the continuous exposure variable.

nD

integer. Number of cases per set.

nH

integer. Number of controls per set.

R2

numeric. Coefficient of determination of the exposure variable and other covariates

alpha

numeric. family-wise type I error rate.

nTests

integer. Number of tests.

OR.low

numeric. Lower bound of odds ratio. Only used when OR=NULL and power and N are not equal to NULL.

OR.upp

numeric. Upper bound of odds ratio. Only used when OR=NULL and power and N are not equal to NULL.

Details

The power and sample size calculation formulas are provided by Lachin (2008, Section 3.1, Formulas (24) and (25))

power = \Phi\left( \sqrt{N c} - z_{\alpha/(2 nTests)}\right)

and

N = (z_{power} + z_{\alpha/(2 nTests)})^2/ c

where \Phi is the cumulative distribution function of the standard normal distribution N(0, 1), z_{a} is the upper 100 a-th percentile of N(0, 1),

c = \theta^2 \sigma^2 nD (1-1/b) (1-R^2)

and b is the Binomial coefficient (n chooses nD), n = nD + nH, and R^2 is the coefficient of determination for linear regression linking the exposure with other covariates.

Value

If the inputs is.null(N) = TRUE and is.null(power) = FALSE, then the function returns the number N of sets.

If the inputs is.null(N) = FALSE and is.null(power) = TRUE, then the function returns the power.

Otherwise, an error message is output.

References

Lachin, JM Sample Size Evaluation for a Multiply Matched Case-Control Study Using the Score Test From a Conditional Logistic (Discrete Cox PH) Regression Model. Stat Med. 2008 27(14): 2509-2523

Examples

library(pracma)

# Section 4.1 in Lachin (2008) 

# estimate number of sets 
N = powerConLogistic.con(N = NULL,
                                power = 0.85,
                                OR = 1.39,
                                sigma = 1,
                                nD = 1,
                                nH = 2,
                                R2 = 0,
                                alpha = 0.05,
                                nTests = 1)
print(ceiling(N)) # 125

# estimate power 
power = powerConLogistic.con(N = 125,
                                power = NULL,
                                OR = 1.39,
                                sigma = 1,
                                nD = 1,
                                nH = 2,
                                R2 = 0,
                                alpha = 0.05,
                                nTests = 1)
print(power) # 0.85

# estimate OR 
OR = powerConLogistic.con(N = 125,
                                power = 0.85,
                                OR = NULL,
                                sigma = 1,
                                nD = 1,
                                nH = 2,
                                R2 = 0,
                                alpha = 0.05,
                                nTests = 1)
print(OR) # 1.39