Usage ----- ^studysi^ [method]^,edf0(^elist0^) hr^atio^(^hrlist^)^ [^np^eriod^(^#^) ng^roups^(^#^) n(^#^) po^wer^(^#^) al^pha^(^#^) > ar^atio^(^#[#...#]^)^ ^tr^end ^do^se^(^#[#...#]^) lg(^#[#...#]^) ld^f^(^llist [^;^llis > t^;^... llist]^)^ ^re^crt^(^rlist^) wg(^#[#...#]^) wd^f^(^wlist [^;^wlist^;^... wl > ist]^)^ ^cr^over^(^#[#...#]^) pw^ehr^(^hrlist^) nolo^cal ^de^tail ]
Description -----------
^studysi^ calculates sample size and power for comparative studies with either binary or time-to-event outcome. ^studysi^ has the following flexible features: > - 1. An arbitrary number K (>=2) groups. 2. Global or linear trend tests with arbitrary dose levels. 3. Logrank (unweighted or weighted (Tarone-Ware or Harrington-Fleming with any index)) and binomial (conditonal and unconditional) tests. 4. Time dependent rates of event, loss to follow-up and withdrawal from allocated treatment (treatment change). 5. Staggered entry
method: The method of comparison with the format l|t|h [I]|b [c|u] where l = unweighted logrank (default test) t = Tarone-Ware test (logrank with weights proportional to the square root of the total number at risk at event times. h = Harrington-Fleming (logrank with weights proportional to S**I, where S is the estimated pooled survival function at event times. I = Index for Harrington-Fleming weights. Default is I=1. b = Binomial test comparing the proportion of failure at the end of the study. c = Binomial test is conditional on the total number of observed events using Peto's approximation to the log odds ratio (default). u = Uncoditional binomial test.
Options -------
^alpha^ specifies the significance level. The default is ^alpha(0.05)^.
^aratio^ specifies the allocation ratio. ^aratio(^#1 #2...#r^)^ means that allo > cation ratio for group k is #k, k=1,...r. If r<^ngroups^, the allocation ratio for group k is #r, k=r+1,...,^ngroups^. The default is equal group size.
^crover^ (Only when wg is specified) is the target group number when crossing over. ^crover(^#1 #2...#r^)^ means that the kth group withdrawing from allocated treatment (specified by ^wg^) crosses over to recieve the allocated treatment of group #k, k=1,...r. The default is that when individuals in group 1 change treatment, they receive the treatment assigned to those in group 2. Individuals in group k (k > 1) crossover to recieve the treatment assined to group 1.
^detail^ requests more detailed output including expected proportion of failure > , withdrawal from allocated treatment and loss to follow-up by the end of the study.
^dose^ specifies doses for dose-respone (linear trend) test. ^dose(^#1 #2...#r^ > )^ assigns dose for groups 1,...,r. If r < ngroups, #r is taken as the dose for groups r+1,...ngroups. The default is dose(1 2...ngroups) which is only used when ^trend^ is specified but not ^dose^.
^edf0^ is required and gives the Control event distribution function. This need not be one of the distributions to be compared unless hratio = 1 for some of the groups. The format is ^edf0(^elist0^)^, where string "elist0 > " is "#1 [#2 ...#r^,^#1 #2 ...#r]". Thus, ^edf0(^p1 p2 ...pr^,^t1 t2 ...tr > ^)^ gives the value pi for the cumulative distribution function for the event time at the end of time period ti, i=1,...,r. Instantaneous event rates are assumed constant within time periods ( time-to-event is piecewise exponential). If r < ^nperiod^, the instantaneous event rates > in periods r+1,...,nperiod are taken to be the same as in period r. If only one value of ^edf0^ is specified, this is taken to be the value at the e > nd of the study and the instantaneous event rate is constant thoughout follow-up. Thus if the number of periods ^nperiod = 6^ then ^edf0(0.5)^ > is equivalent to ^edf0(0.5,6)^ and gives 50% cumulative failure at the end of period ^nperiod^ and an exponential distribution for the control failure time. ^edf0(0.2 0.4,1 5)^ gives expected cumulative proportions of failure ^0.2^ at the end of the first period and ^0.4^ at the end of > the fifth period. The instantaneous event rate during the first period is ^-log(1-0.2)=0.223^. The instantaneous event rate during periods 2,3,4 a > nd 5 is ^-log((1-0.4)/(1-0.2))/4 = 0.072^ which is also the default rate during period 6. This gives cumulative failure probability of 0.55 at the end of period 6.
^hratio^ is required and specifies the event hazard ratio functions. The format is ^hratio(^hrlist^)^, where the string "hrlist" is "#1_1 [#1_2 ...#1_r1]^,^#2_1 [#2_2 ...#2_r2]^,^...^,^ #k_1 [#k_2 ...#k > _rk]". The event hazard ratio of group i (relative to the control distribution edf0) is #i_j during period j, j=1,...ri; i=1,...k, If ri < ^nperiod^ then the hazard ratio function during periods ri+1,... ^nperiod^ is assumed to be #i_ri. If k < ^ngroups^, the hazard ratio functions for groups k+1,...,ngroups are assumed equal to the geometric mean of the hazard ratio functions for groups 1,...k.
^ldf^ is required when lg, groups with loss to follow-up, is specified. ^ldf^ specifies the distribution function of time to loss-to-follow-up. The format is ^ld^f^(^llist [^;^llist^;^... llist]^)^, where each llist spec > ifies a cumulative distribution function for time to to loss from follow-up, one for each group specified by ^lg^ and in the same order. Each llist h > as the same form and interpretation as a distribution function as elist0 in ^edf0^. e. g. if ^nperiod^ = 6, then ^lg(1 3) ldf(0.2;.05 0.15,2 5)^ specifies that: (i) Groups 1 and 3 are subject to loss to follow-up. (ii) The cumulative probability of loss to follow-up is .2 by the end of the last period in group1, .05 at the end of the period 2 and .15 at the end of period 5 in group 3. (iii) Individuals in the other groups are not subject to loss to follow-up.
^lg^ specifies the groups subject to loss to follow-up. ^ldf^ must then be specified giving the cumulative distribution functions of time to loss- to-follow-up in the same order.
^local^ specifies local alternative for the unconditional binomial test of the null hypothesis of equal proportions. The default is ^nolocal^ if method is b u.
^n^ specifies that total sample size is calculated if ^n^ = 0. Otherwise power is calculated given total sample size = ^n^. The default is ^n = 0^.
^ngroup^ specifies the number of comparitive groups. The default is ^ngroups^ = > 2.
^nperiod^ is the number of time periods within which all instantaneous rates ar > e constant. The default is ^nperiod = 1^.
^power^ specifies the study power. the default is power = 0.8 if ^n > 0^.
^pwehr^ specifies the hazard ratio function post withdrawal from allocated treatment. The format is ^pw^ehr^(^hrlist^)^, where hrlist gives the ha > zard ratio functions (relative to the control event time distribution) after treatment change for the groups specified by ^wg^ and in the same order > . The format and interpretation of hrlist is the same as that of ^hratio^ except that the hazard ratio functions for the remaining groups, subject to treatment change (given in ^wg^) but not assigned to a hazar > d ratio function by ^pwehr^, is taken to be the same as the last hazard ratio function specified by ^pwehr^. When both ^pwehr^ and ^crover^ are specified, ^crover^ is ignored.
^recrt^ specifies the duration and rate of recruitment. If ^recrt^ is not specified, recruitment is assumed completed at the begining of the study. i.e. duration of recruitment = 0. When ^recrt^ is specified, its format is ^recrt(^[duration [recrpr0]]^,^[w1 w2...wk]^,^[s1 s2...sk]^)^ > ; where duration = the number of periods for the completion of recruitment. The default is duration = ^nperiods^. recrpr0 = the proportion recruited (instantaneously) at the start of the study. The default is recrpr0 = 0. w1...wk are the relative proportions recruited in periods 1 to k. The default specifies equal proportions. s1...sm specify the shape of recruitment time distribution within periods. si = 0 for uniform entry during period i, and si = L>0 for negative exponential with rate L. The default is uniform entry time within each period.
^wdf^ is required when wg, groups with treatment change (withdrawal from allocated treatment), is specified. ^wdf^ specifies the distribution function of time to withdrawal. The format is the same as that of ^ldf^.
^wg^ specifies the groups subject to loss to follow-up. ^wdf^ must then be specified giving the cumulative distribution functions of time to withdrawal from allocated treatment in the same order.
Examples --------
. ^studysi l, edf0(0.5) hr(1,0.75) np(3)^ (compares two exponential distributions using the logrank test)
. ^studysi h, edf0(0.5) hr(1,0.75,0.5) np(3) ng(3) recrt(2,,)^
. ^studysi l, edf0(0.5) hr(1,0.75,0.5) np(3) ng(3) recrt(2,,) tr^
. ^studysi , edf0(0.2 0.5,1 3) hr(1,0.6 0.6 0.75) np(3)^ (treatment effect changes over time)
. ^studysi l, edf0(0.5) hr(1,0.75) np(3) lg(1 2) ldf(.1;.1)^ (10% lost to follow-up by end of study)
. ^studysi l, edf0(0.5) hr(1,0.75) np(3) lg(1 2) ldf(.1;.1) /*^ ^*/ wg(1 2) wdf(.3;.1)^ (30% of group 1 and 10% og group 2 crossover by end of study)
Also see --------
Manual: ^[R] sampsi^