pwr2n.NPH: Sample Size Calculation with Combination Test
In nphPower: Sample Size Calculation under Non-Proportional Hazards

Description Usage Arguments Details Value References See Also Examples

View source: R/pwr2n.NPH.R View source: R/oxy-pwr2n.NPH.R

pwr2n.NPH calculates the number of events and subjects required to achieve pre-specified power in the setup of two groups. The method extends the calculation in the framework of the Markov model by Lakatos, allowing for using the maximum weighted logrank tests or projection test with an arbitrary number of weight functions. For maximum weighted logrank type test, if only one weight function is provided, the test is essentially the classic (weighted) logrank test.

pwr2n.NPH(
  method = "MaxLR",
  entry = 1,
  fup = 1,
  CtrlHaz,
  hazR,
  transP1 = c(0, 0),
  transP0 = c(0, 0),
  Wlist = list(function(x) {     x^0 }),
  entry_pdf0 = function(x) {     (1/entry) * (x >= 0 & x <= entry) },
  entry_pdf1 = entry_pdf0,
  ratio = 1,
  alpha = 0.05,
  beta = 0.1,
  alternative = c("two.sided"),
  criteria = 500,
  k = 100,
  summary = TRUE
)

`method`	a text specifying the calculation method, either `"MaxLR"` or `"Projection"`. Maximum weighted logrank test is used if `"MaxLR"` is specified; otherwise, projection test is used.
`entry`	a numeric value indicating the enrollment time, Default: 1
`fup`	a numeric value indicating the minimum follow-up time for subjects. , Default: 1
`CtrlHaz`	a function, specifying the hazard function for control group.
`hazR`	a function, specifying the hazard ratio function between treatment and control group
`transP1`	a numeric vector of length 2, consisting of the transition probability from receiving treatment to drop-out (drop-out rate) and from receiving treatment to receiving control (drop-in rate) per time unit.
`transP0`	a numeric vector of length 2, consisting of the transition probability from receiving control to drop-out (drop-out rate) and from receiving control to receiving treatment (drop-in rate) per time unit.
`Wlist`	a list, consisting of weight functions applied to the test. The element of the list must be functions. Default is a list of one constant function, corresponding to the logrank test.
`entry_pdf0`	a function, indicating the probability density function (pdf) of enrollment time for control group. The default assumes a uniform distribution corresponding to the constant enrollment rate. Default: function(x) (1/entry) * (x >= 0 & x <= entry)
`entry_pdf1`	a pdf of enrollment time for treatment group. See `entry_pdf0`, Default: assume same pdf as control group.
`ratio`	an integer, indicating the randomization ratio between treatment and control group, Default: 1
`alpha`	type I error rate, Default: 0.05
`beta`	type II error rate, Default: 0.1
`alternative`	a character string specifying the alternative hypothesis, must be one of "`two.sided`", "`greater`","`less`". See details. For `"Projection"` method, only `"two-sided"` alternative is supported. Default: c("`two.sided`")
`criteria`	an integer indicating the maximum iteration allowed in obtaining the number of events. See details , Default: 500
`k`	an integer, indicating number of sub-intervals per time unit, Default: 100
`summary`	a logical value, controlling whether to print the summary of calculation, Default: TRUE

The detailed methods can be found in the reference papers. The number of subjects is determined by several factors, including the control hazard function, hazard ratio function, entry time distribution, follow-up time, etc. Under proportional hazard assumption, the number of events is mainly determined by the hazard ratio besides type i/ii error rates. However, under nonproportional hazards, all the above design parameters may have an impact on the number of events. The study design assumes entry time units of enrollment and at least fup time units of follow-up. If enrollment time entry is set to zero, all subjects are enrolled simultaneously, so there is no staggered entry. Otherwise, if entry is greater than 0, administrative censoring is considered. The user-defined enrollment time function, hazard function for the control group and hazard ratio function can be either discrete or continuous. Various non-proportional hazards types are accommodated. See examples below. If multiple weight functions are provided in Wlist, a maximum weighted logrank test or combination test is implemented. An iterative procedure is used to obtain the event number based on the multivariate normal distribution. Package mvtnorm is used to calculate the quantiles. Because the algorithm is slightly seed dependent, the quantiles are mean values of ten replicates.

The "alternative" option supports both two-sided and one-sided test. Let Λ_1 and Λ_0 denote the cumulative hazard of treatment and control group. The less option tests H_0: Λ_1 > Λ_0 against H_a: Λ_1 <= Λ_0. The greater option tests H_0: Λ_1 < Λ_0 against H_a: Λ_1 >= Λ_0.

An object of class "NPHpwr" with corresponding plot function. The object is a list containing the following components:

`eventN`	total number of events
`totalN`	total number of subjects
`pwr`	actual power given the number of events
`prob_event`	event probability at the end of trial
`L_trans`	a list, consisting of transition matrix at each interval
`pdat`	a dataframe including all the intermediate variables in the calculation. see Details.
`studytime`	a vector of length 2, including the entry and follow-up time as input
`RandomizationRatio`	as input
`eventlist`	a vector containing the number of events using each weight function alone
`inputfun`	a list containing all the input functions specified by users

Brendel, M., Janssen, A., Mayer, C. D., & Pauly, M. (2014). Weighted logrank permutation tests for randomly right censored life science data. Scandinavian Journal of Statistics, 41(3), 742-761.

Cheng, H., & He, J. (2021). A Maximum Weighted Logrank Test in Detecting Crossing Hazards. arXiv preprint arXiv:2110.03833.

Cheng, H., & He, J. (2021). Sample size calculation for the maximum weighted logrank test under non-proportional hazards (to submit)

pwr2n.LR gen.wgt, evalfup

 #------------------------------------------------------------
 ## Delayed treatment effects using maxcombo test
 ## generate a list of weight functions for maxcombot test
 wmax <- gen.wgt(method = "Maxcombo" )
 t_enrl <- 12; t_fup <- 18; lmd0 <- log(2)/12
 ## delayed treatment effects
 f_hr_delay <- function(x){(x<=6)+(x>6)*0.75}
 f_haz0 <- function(x){lmd0*x^0}
 ##  The following code takes more than 5 seconds to run
 
 snph1 <- pwr2n.NPH(entry = t_enrl, fup = t_fup, Wlist = wmax,
                    k = 100, ratio = 2, CtrlHaz = f_haz0, hazR = f_hr_delay)
 
 #-------------------------------------------------------------
 # same setting using projection test
 snph2 <- pwr2n.NPH(method = "Projection", entry = t_enrl,
  fup = t_fup, Wlist = wmax, k = 10, ratio = 2, CtrlHaz = f_haz0,
  hazR = f_hr_delay)

 #-------------------------------------------------------------
 #proportional hazards with weibull survival for control group
 #logrank test
 wlr <- gen.wgt(method = "LR" )
 b0 <- 3
 th0 <- 10/(-log(0.2))^(1/b0)
 #Weibull hazard function
 f_hz_weibull <- function(x){b0/th0^b0*x^(b0-1)}
 #hazard ratio function
 f_hr <- function(x){0.5*x^0}
 # define entry and follow-up time
 t_enrl <- 5; t_fup <- 5
 exph1 <- pwr2n.NPH(entry = t_enrl, fup = t_fup, k = 100,
 Wlist = wlr,  CtrlHaz = f_hz_weibull, hazR = f_hr, summary = FALSE)
 summary(exph1)