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help for ^studysi^
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Usage
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^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 [^;^llist^;^... llist]^)^
^re^crt^(^rlist^) wg(^#[#...#]^) wd^f^(^wlist [^;^wlist^;^... wlist]^)^
^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
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^alpha^ specifies the significance level. The default is ^alpha(0.05)^.
^aratio^ specifies the allocation ratio. ^aratio(^#1 #2...#r^)^ means that allocation
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 end
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 and
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 specifies
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 has
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 are
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 hazard
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 hazard
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
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Manual: ^[R] sampsi^