R: Simulate Power for Adjusted Ordinal Regression Two-Sample...

simRegOrd {Hmisc} | R Documentation

## Simulate Power for Adjusted Ordinal Regression Two-Sample Test

### Description

This function simulates the power of a two-sample test from a proportional odds ordinal logistic model for a continuous response variable- a generalization of the Wilcoxon test. The continuous data model is normal with equal variance. Nonlinear covariate adjustment is allowed, and the user can optionally specify discrete ordinal level overrides to the continuous response. For example, if the main response is systolic blood pressure, one can add two ordinal categories higher than the highest observed blood pressure to capture heart attack or death.

### Usage

    simRegOrd(n, nsim=1000, delta=0, odds.ratio=1, sigma,
              p=NULL, x=NULL, X=x, Eyx, alpha=0.05, pr=FALSE)

### Arguments

`n` | combined sample size (both groups combined)
`nsim` | number of simulations to run
`delta` | difference in means to detect, for continuous portion of response variable
`odds.ratio` | odds ratio to detect for ordinal overrides of continuous portion
`sigma` | standard deviation for continuous portion of response
`p` | a vector of marginal cell probabilities which must add up to one. The `i`th element specifies the probability that a patient will be in response level `i` for the control arm for the discrete ordinal overrides.
`x` | optional covariate to adjust for - a vector of length `n`
`X` | a design matrix for the adjustment covariate `x` if present. This could represent for example `x` and `x^2` or cubic spline components.
`Eyx` | a function of `x` that provides the mean response for the control arm treatment
`alpha` | type I error
`pr` | set to `TRUE` to see iteration progress

### Value

a list containing `n, delta, sigma, power, betas, se, pvals` where `power` is the estimated power (scalar), and `betas, se, pvals` are `nsim`-vectors containing, respectively, the ordinal model treatment effect estimate, standard errors, and 2-tailed p-values. When a model fit failed, the corresponding entries in `betas, se, pvals` are `NA` and `power` is the proportion of non-failed iterations for which the treatment p-value is significant at the `alpha` level.

### Author(s)

Frank Harrell
Department of Biostatistics
Vanderbilt University School of Medicine
fh@fharrell.com

### See Also

`popower`

### Examples

    ## Not run:
    ## First use no ordinal high-end category overrides, and compare power
    ## to t-test when there is no covariate

    n <- 100
    delta <- .5
    sd <- 1
    require(pwr)
    power.t.test(n = n / 2, delta=delta, sd=sd, type='two.sample')  # 0.70
    set.seed(1)
    w <- simRegOrd(n, delta=delta, sigma=sd, pr=TRUE)     # 0.686

    ## Now do ANCOVA with a quadratic effect of a covariate
    n <- 100
    x <- rnorm(n)
    w <- simRegOrd(n, nsim=400, delta=delta, sigma=sd, x=x,
                   X=cbind(x, x^2),
                   Eyx=function(x) x + x^2, pr=TRUE)
    w$power  # 0.68

    ## Fit a cubic spline to some simulated pilot data and use the fitted
    ## function as the true equation in the power simulation
    require(rms)
    N <- 1000
    set.seed(2)
    x <- rnorm(N)
    y <- x + x^2 + rnorm(N, 0, sd=sd)
    f <- ols(y ~ rcs(x, 4), x=TRUE)

    n <- 100
    j <- sample(1 : N, n, replace=n > N)
    x <-   x[j]
    X <- f$x[j,]
    w <- simRegOrd(n, nsim=400, delta=delta, sigma=sd, x=x,
                   X=X,
                   Eyx=Function(f), pr=TRUE)
    w$power  ## 0.70

    ## Finally, add discrete ordinal category overrides and high end of y
    ## Start with no effect of treatment on these ordinal event levels (OR=1.0)

    w <- simRegOrd(n, nsim=400, delta=delta, odds.ratio=1, sigma=sd,
                   x=x, X=X, Eyx=Function(f),
                   p=c(.98, .01, .01),
                   pr=TRUE)
    w$power  ## 0.61   (0.3 if p=.8 .1 .1, 0.37 for .9 .05 .05, 0.50 for .95 .025 .025)

    ## Now assume that odds ratio for treatment is 2.5
    ## First compute power for clinical endpoint portion of Y alone
    or <- 2.5
    p <- c(.9, .05, .05)
    popower(p, odds.ratio=or, n=100)   # 0.275
    ## Compute power of t-test on continuous part of Y alone
    power.t.test(n = 100 / 2, delta=delta, sd=sd, type='two.sample')  # 0.70
    ## Note this is the same as the p.o. model power from simulation above
    ## Solve for OR that gives the same power estimate from popower
    popower(rep(.01, 100), odds.ratio=2.4, n=100)   # 0.706
    ## Compute power for continuous Y with ordinal override
    w <- simRegOrd(n, nsim=400, delta=delta, odds.ratio=or, sigma=sd,
                   x=x, X=X, Eyx=Function(f),
                   p=c(.9, .05, .05),
                   pr=TRUE)
    w$power  ## 0.72

    ## End(Not run)

[Package Hmisc version 4.7-0 Index]