nPV {bdpv}

Asymptotic sample size calculation for inference on negative and positive predictive values in case-control designs.

Description

Functions to compute sample size (to reach a pre-specified power) and optimal allocation of true positives and true negatives in case-control designs (Steinberg et al., 2008) for binary diagnostic tests (Mercaldo et al. 2007).

Usage

nPV(se, sp, prev, NPV0, PPV0,
 NPVpower = 0.8, PPVpower = 0.8,
 rangeP = c(0.05, 0.95), nsteps = 20,
 alpha = 0.05, setnames = NULL)

Arguments

se

a (vector of) numeric value(s), specifying the expected sensitivity

sp

a (vector of) numeric value(s), specifying the expected specificity

prev

a (vector of) numeric value(s), specifying the prevalence

NPV0

a (vector of) numeric value(s), specifying the negative predictive value to be rejected under H0: NPV>=NPV0

PPV0

a (vector of) numeric value(s), specifying the positive predictive value to be rejected under H0: PPV>=PPV0

NPVpower

a (vector of) numeric value(s), the power that is to be obtained for the test H0: NPV>=NPV0

PPVpower

a (vector of) numeric value(s), the power that is to be obtained for the test H0: PPV>=PV0

rangeP

a vector of two numeric values, giving the range of the proportion of truely positives to be considered in experimental design

nsteps

a single (integer) value, the number of steps in rangeP to be considered

alpha

a single numeric value, the type I error of the test (1-confidence level)

setnames

an optional vector of names for the parameter sets

Details

The function uses nNPVPPV and implement the methods described in section 3.2 of Steinberg et al.(2009). The results for NPV are the smallest integers fulfilling Eq.(3.6) and NA if necesarry conditions mentioned before are not met, the results for PPV are the smallest integers fulfilling Eq.(3.8) and NA if necesarry conditions mentioned before are not met.

The arguments se, sp, prev, NPV0, PPV0, NPVpower, PPVpower can be given as vectors or single values, where shorter values are recycled to the length of the longest. The proportion of true positives is varied over nstep equidistant values over the range specified in argument rangeP. On each resulting parameter set, the asymptotic sample size formulas of Steinberg et al.(2009) are applied.

The result of those calculations may be plot using plotnPV and plotnPV2.

Warnings are returned by the internal function nNPV and nPPV if the validity of asymptotic formulas under binomial sampling may be doubtable, namely when the asymptotic formulas return a total sample size n for given propP, se, sp, such that min(n*propP*se, n*propP*(1-se))<5 or min(n*(1-propP)*sp, n*(1-propP)*(1-sp))<5. That is, a warning is returned if the proposed design of the case-control study (n1, n0) = (n*propP, n*(1-propP)) leads to expected counts < 5 for any cell of the 2x2 table.

Value

A list with elements

outDAT

a data.frame showing the parameter settings (in rows) and the input parameters se, sp, prev, NPV0, PPV0, NPVpower, PPVpower, trueNPV, truePPV

nlist

a list with an element for each parameter setting in OUTDAT, listing the results of nNPV, and nPPV

NSETS

a single (integer), the number of parameter sets

nsteps

a single (integer), the number of steps in the range of proportions of true positives

rangeP

the input range of the proportion of true positives

propP

the resulting sequence of proportions of true positives considered

Author(s)

Frank Schaarschmidt

References

Steinberg DM, Fine J, Chappell R (2009). Sample size for positive and negative predictive value in diagnostic research using case-control designs. Biostatistics 10,1, 94-105.

See Also

plotnPV for showing the results in one graphic, and plotnPV for showing the results in a set of subgraphics,

Examples

#Reproducing illustration in Section 3.4 and 4.2 of
#Steinberg et al. (2009)

FIG1<-nPV(se=0.8, sp=0.95, prev=1/16, NPV0=0.98, PPV0=0.4,
 NPVpower = 0.8, PPVpower = 0.8,
 rangeP = c(0.01, 0.99), nsteps = 100, alpha = 0.05)

FIG1

DFIG1<-as.data.frame(FIG1)

plot(x=DFIG1$propP, y=DFIG1[,2], ylim=c(0,2000), lty=1,  type="l",
 ylab="total sample size", xlab="proportion of true positives")
lines(x=DFIG1$propP, y=DFIG1[,3], lty=2 )