upmplot: Graphical plot of Unit Probability MASS

In anirban0451/tpidesigns: R-Package to generate Toxicity Probability Interval Dose Escalation Design Results (TPI, mTPI, mTPI - 2)

Description

upmplot Produces a graphical plot of Unit Probability Mass for a given set of parameters.

Usage

upmplot(x, n, pt, e1 = 0.05, e2 = 0.05, design = c("mtpi", "mmtpi"),
  w, a1 = NULL, b1 = NULL, a2 = NULL, b2 = NULL)

Arguments

x	Total Number of events (In Dose Escalation Oncology Trials, this may be defined as number of people who have experienced Dose Limiting Toxicities through administration of current Dose Level)
n	Trial size (In Dose Escalation Oncology Trials, this may be defined as total number of people who have been administered current Dose Level (missing responses will be excluded). Necessarily n will be greater than or equal to x
pt	Target toxicity proportion to achieve in current Dose Level (Less Toxicity means under- dosing, where as more toxicity means over - dosing)
e1	Amount of variation that can be allowed to the left of the pt value to conclude that target toxicity has been achieved. Default value is 0.05. This means, that if a Posterior Toxicity (DLT) mean takes a value within the range (pt - e1, pt), toxicity for the cohort (of size >= 3) will be achieved.
e2	Amount of variation that can be allowed to the right of the pt value to conclude that target toxicity has been achieved. Default value is 0.05. This means, that if a Posterior Toxicity (DLT) mean takes a value within the range (pt, pt + e2), toxicity for the cohort (of size >= 3) will be achieved.
design	The Design that is implemented in the trials. This arguement includes values "mtpi" and "mmtpi"
w	Weight on the first Beta distribution of the mixture Prior
a1	alpha parameter ( > 0) for 1st Beta distribution, must be input properly when w = 0 or 1
b1	beta parameter ( > 0) for 1st Beta distribution, must be input properly properly when w = 0 or 1
a2	alpha parameter ( > 0) for 2nd Beta distribution, will not be used if w = 0 or 1
b2	beta parameter ( > 0) for 2nd Beta distribution, will not be used if w = 0 or 1

Details

Unit Probability MASS or UPM(a,b) = (F(b) - F(a))/(b - a), defined for an interval (a,b), when X~F(). In this function, F() is assumed to be Cumulative Beta distribution function or mixture of two cumulative Beta distribution functions.

Hence, F(x) = w * pbeta(x, a1, b1) + (1 - w) * pbeta(x, a2, b2), pbeta is cumulative Beta distribution.

If F() consists of a single Beta distribution, and not a mixture, then the convention here assumed is to input w = 1 and a1, b1 , or w = 0 and a2,b2

Value

A graph that includes Probability Distributions of the Dose Limiting Toxocity Rate and value of Unit Probability Mass at corresponding intervals.

Decision Making Based on UPM values

For modified Toxicity Probability Interval (mTPI) Design, the toxicity range (0,1) is divided into three ranges, (1) Under-Dosing Interval [0, pt - e1), (2) Target-Toxicity Interval [pt - e1, pt - e2], (3) Over-Dosing Interval (pt + e2, 1]. UPM is calculated for the the above intervals and Decision is taking accordingly,
if the UPM is maximum for interval (1), then the strength of the current Dosage is escalated,
if its maximum for Interval (2), then more patients are administered with current dose,
if the UPM is maximum in interval (3), then strength of the current Dose is de-escalated.
For Modified Toxicity Interval Design-2 (mTPI -2, encoded as "mmtpi") the intervals (1) and (3) are again divided into another sub- intervals and same steps are followed.
But, before that, we must ensure that the Dose is not severely toxic and hence it is advised to run the decisiontpi function to know about the severity of current Dose.The graphical display will be meaningful only if decisiontpi does not return the value "DU"

See Also

UPM, weights_formulate

Examples

require(ggplot2)
n = 13 #must be a value >= 3
x = sample.int(n, 1)
upmplot(x = 5, n = 7, pt = 0.3, design = "mmtpi", w = 0.1, a1 = 1, a2 = 1, b1 = 4, b2 = 6)

anirban0451/tpidesigns documentation built on Dec. 7, 2019, 5:35 p.m.