qualint: Test for qualitative interactions from complete data

Description

Test for qualitative interactions between treatment effects and patient subgroups. Perform the testing based on the estimated treatment effects and their standard errors. Output all the results related with qualitative interaction tests as a "qualint" object, which includes all the results related with the testing. Two common tests for qualitative interactions are included: IBGA and LRT, among which IBGA is the default. Useful for three types of responses: continuous, binary and survival data. Complete data is needed as input.

Usage

qualint(y, trtment, subgrp, type = c("continuous", "binary", "survival"), scale = c("MD", "RD", "RR", "OR", "HR"), test = c("IBGA", "LRT"), alpha = 0.05, plotout = FALSE)

Arguments

response variable. A numeric vector for type = "continuous". A numeric vector with values equal to either 1 or 0 for type = "binary". A "Surv" object for type = "survival" (The function Surv() in package survival produces such a matrix).

trtment

treatment variable. A vector with different values representing different treatment groups. Each element corresponds to the treatment the patient received. Should have the same length as y.

subgrp

patient subgroup variable. A vector with the same length as y and trtment, with different values representing different patient subgroups. Each element corresponds to the patient subgroup the patient belongs to.

type

response type (see above). Three types of responses are included right now: continuous, binary, survival. By default, it assumes the response variable is continuous.

scale

the scale type for treatment effects. When type = "continuous", scale = "MD" by default (mean difference). When type = "binary", three types of scales are available, which are scale = "RD" (risk difference), "RR" (relative risk) or "OR" (odds ratio). When type = "survival", scale = "HR" (hazard ratio).

test

testing method. Choose either "IBGA" (interval based graphical approach) or "LRT" (Gail Simon likelihood ratio test).

alpha

significance level. The type I error for qualitative interaction tesing. The default is 0.05.

plotout

whether output the plot or not for test = "IBGA". There is no plot output for test = "LRT".

Value

call: the call that produces this object.
n: the sample size for each treatment in each subgroup.
type: response type.
alpha: significance level for the test.
treatment: treatment factors.
reference: reference treatment used for the comparison.
nsbp: the number of patient subgroups.
subgroup: subgroup factors.
scale: the scale type for treatment effects (see above).
effect: estimated treatment effects.
se: standard error of treatment effects estimators.
LowerCI: the lower limit of the confidence interval.
UpperCI: the upper limit of the confidence interval.
test: testing method used here, either "IBGA" or "LRT".
index: the testing index used only for test = "IBGA".
cvalue: the critical value used only for test = "LRT".
LowerTI: the lower limit of the testing interval used when test = "IBGA".
UpperTI: the upper limit of the testing interval used when test = "IBGA".
pvalue: the pvalue for qualitative interactions.
power: the power based on the observed data.
nobs: the number of subjects.
missing: the indexes of subjects with missing values.

Details

In order to test for qualitative interactions between treatment effects and patient subgoups, estimated treatment effects and their standard errors are necessary. For continuous responses, mean difference is derived as the meansure of treatment effects with with its standard error equal to $\sqrt{sd_1^2/n_1+sd_2^2/n_2}$. For binary responses, three different scales are available to measure the treatment effects: risk difference, log relative risk and log odds ratio. Their standard errors could easily obtained according to formulas. For survival responses, the log hazard ratio is used to evaluate the treatment effects. The cox regression model is used in this function to estimate the log hazard ratio and also its standard error.

For the IBGA graph, however, we plot it according to common measures of treatment effects instead of the one used in the calculation. For continuous responses, mean difference is used since it is the common treament effect scale. For binary responses, the function plots risk difference, relative risk, and odds ratio directly. For survival responses, hazard ratios are plotted instead of log hazard ratios.

In the power calculation, this function assumes the estimated treatment effect scale and its standard errors are equal to the true values. For IBGA method, an explicit formula is available, so it is very easy to calculate the power. For LRT, a simulation is used to assess the power since no explicit formula is available.

References

Gail and Simon (1985), Testing for qualitative interactions between treatment effects and patient subsets, Biometrics, 41, 361-372.

Pan and Wolfe (1993), Tests for generalized problems of detecting qualitative interaction, Technical Report No. 526, Department of Statistics, The Ohio State University.

Pan and Wolfe (1997), Test for qualitative interaction of clinical significance, Statistics in Medicine, 16, 1645-1652.

Examples

Run this code

#### Continuous ####
ynorm <- rnorm(300)
trtment <- sample(c(0, 1), 300, prob = c(0.4, 0.6),
                 replace = TRUE)
subgrp <- sample(c(0, 1, 2), 300, prob = c(1/3, 1/3, 1/3),
                 replace = TRUE)
test1 <- qualint(ynorm, trtment, subgrp)
plot(test1)
print(test1)
coef(test1)
test2 <- qualint(ynorm, trtment, subgrp, plotout = TRUE)
test3 <- qualint(ynorm, trtment, subgrp, test = "LRT")

#### Binary ####
ybin <- sample(c(0, 1), 300, prob = c(0.3, 0.7),
               replace = TRUE)
test4 <- qualint(ybin, trtment, subgrp, type = "binary")
test5 <- qualint(ybin, trtment, subgrp, type = "binary",
                 scale = "RR", test = "LRT")

#### Survival ####
time <- rpois(300, 200)
censor <- sample(c(0, 1), 300, prob = c(0.7, 0.3),
                 replace = TRUE)
test6 <- qualint(Surv(time, censor), trtment, subgrp)
test7 <- qualint(Surv(time, censor), trtment, subgrp,
                 type = "survival", test = "LRT")
test8 <- qualint(Surv(time, censor), trtment, subgrp,
                 test = "IBGA", plotout = TRUE)

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