planMod {DoseFinding}

Evaluate performance metrics for fitting dose-response models

Description

This function evaluates, the performance metrics for fitting dose-response models (using asymptotic approximations or simulations). Note that some metrics are available via the print method and others only via the summary method applied to planMod objects. The implemented metrics are

• Root of the mean-squared error to estimate the placebo-adjusted dose-response averaged over the used dose-levels, i.e. a rather discrete set (dRMSE). Available via the print method of planMod objects.

• Root of the mean-squared error to estimate the placebo-adjusted dose-response (cRMSE) averaged over fine (almost continuous) grid at 101 equally spaced values between placebo and the maximum dose. NOTE: Available via the summary method applied to planMod objects.

• Ratio of the placebo-adjusted mean-squared error (at the observed doses) of model-based vs ANOVA approach (Eff-vs-ANOVA). This can be interpreted on the sample size scale. NOTE: Available via the summary method applied to planMod objects.

• Power that the (unadjusted) one-sided ‘⁠1-alpha⁠’ confidence interval comparing the dose with maximum effect vs placebo is larger than ‘⁠tau⁠’. By default ‘⁠alpha = 0.025⁠’ and ‘⁠tau = 0⁠’ (Pow(maxDose)). Available via the print method of planMod objects.

• Probability that the EDp estimate is within the true [EDpLB, EDpUB] (by default ‘⁠p=0.5⁠’, ‘⁠pLB=0.25⁠’ and ‘⁠pUB=0.75⁠’). This metric gives an idea on the ability to characterize the increasing part of the dose-response curve (P(EDp)). Available via the print method of planMod objects.

• Length of the quantile range for a target dose (TD or EDp). This is calculated by taking the difference of the dUB and dLB quantile of the empirical distribution of the dose estimates. (lengthTDCI and lengthEDpCI). It is NOT calculated by calculating confidence interval lengths in each simulated data-set and taking the mean. NOTE: Available via the summary method of planMod objects.

A plot method exists to summarize dose-response and dose estimations graphically.

Usage

planMod(model, altModels, n, sigma, S, doses, asyApprox = TRUE,
        simulation = FALSE, alpha = 0.025, tau = 0, p = 0.5,
        pLB = 0.25, pUB = 0.75, nSim = 100, cores = 1,
        showSimProgress = TRUE, bnds, addArgs = NULL)

## S3 method for class 'planMod'
plot(x, type = c("dose-response", "ED", "TD"),
     p, Delta, placAdj = FALSE, xlab, ylab, ...)

## S3 method for class 'planMod'
summary(object, digits = 3, len = 101,
        Delta, p, dLB = 0.05, dUB = 0.95, ...)

Arguments

model

Character vector determining the dose-response model(s) to be used for fitting the data. When more than one dose-response model is provided the best fitting model is chosen using the AIC. Built-in models are "linlog", "linear", "quadratic", "emax", "exponential", "sigEmax", "betaMod" and "logistic" (see drmodels).

altModels

An object of class ‘⁠Mods⁠’, defining the true mean vectors under which operating characteristics should be calculated.

n, sigma, S

Either a vector ‘⁠n⁠’ and ‘⁠sigma⁠’ or ‘⁠S⁠’ need to be specified. When ‘⁠n⁠’ and ‘⁠sigma⁠’ are specified it is assumed computations are made for a normal homoscedastic ANOVA model with group sample sizes given by ‘⁠n⁠’ and residual standard deviation ‘⁠sigma⁠’, i.e. the covariance matrix used for the estimates is thus sigma^2*diag(1/n) and the degrees of freedom are calculated as sum(n)-nrow(contMat). When a single number is specified for ‘⁠n⁠’ it is assumed this is the sample size per group and balanced allocations are used.

When ‘⁠S⁠’ is specified this will be used as covariance matrix for the estimates.

doses

Doses to use

asyApprox, simulation

Logicals determining, whether asymptotic approximations or simulations should be calculated. If multiple models are specified in ‘⁠model⁠’ asymptotic approximations are not available.

alpha, tau

Significance level for the one-sided confidence interval for model-based contrast of best dose vs placebo. Tau is the threshold to compare the confidence interval limit to. CI(MaxDCont) gives the percentage that the bound of the confidence interval was larger than tau.

p, pLB, pUB

p determines the type of EDp to estimate. pLB and pUB define the bounds for the EDp estimate. The performance metric Pr(Id-ED) gives the percentage that the estimated EDp was within the true EDpLB and EDpUB.

nSim

Number of simulations

cores

Number of cores to use for simulations. By default 1 cores is used, note that cores > 1 will have no effect Windows, as the mclapply function is used internally.

showSimProgress

In case of simulations show the progress using a progress-bar.

bnds

Bounds for non-linear parameters. This needs to be a list with list entries corresponding to the selected bounds. The names of the list entries need to correspond to the model names. The defBnds function provides the default selection.

addArgs

See the corresponding argument in function fitMod. This argument is directly passed to fitMod.

x

An object of class planMod

type

Type of plot to produce

Delta

Additional arguments determining what dose estimate to plot, when ‘⁠type = "ED"⁠’ or ‘⁠type = "TD"⁠’

placAdj

When ‘⁠type = "dose-response"⁠’, this determines whether dose-response estimates are shown on placebo-adjusted or original scale

xlab, ylab

Labels for the plot (ylab only applies for ‘⁠type = "dose-response"⁠’)

len

Number of equally spaced points to determine the mean-squared error on a grid (cRMSE).

dLB, dUB

Which quantiles to use for calculation of lengthTDCI and lengthEDpCI. By default dLB = 0.05 and dUB = 0.95, so that this corresponds to a 90% interval.

object, digits

object: A planMod object. digits: Digits in summary output

...

Additional arguments (currently ignored)

Author(s)

Bjoern Bornkamp

References

TBD

See Also

fitMod

Examples

## Not run: 
doses <- c(0,10,25,50,100,150)
fmodels <- Mods(linear = NULL, emax = 25,
                logistic = c(50, 10.88111), exponential= 85,
                betaMod=rbind(c(0.33,2.31),c(1.39,1.39)),
                doses = doses, addArgs=list(scal = 200),
                placEff = 0, maxEff = 0.4)
sigma <- 1
n <- rep(62, 6)*2

model <- "quadratic"
pObj <- planMod(model, fmodels, n, sigma, doses=doses,
               simulation = TRUE, 
               alpha = 0.025, nSim = 200, 
               p = 0.5, pLB = 0.25, pUB = 0.75)
print(pObj)
## to get additional metrics (e.g. Eff-vs-ANOVA, cRMSE, lengthTDCI, ...)
summary(pObj, p = 0.5, Delta = 0.3)
plot(pObj)
plot(pObj, type = "TD", Delta=0.3)
plot(pObj, type = "ED", p = 0.5)

## End(Not run)