Log rank test sample size required for the determination of: iterative non-central France
【Abstract】 Objective: To propose an iterative non-central
France, Log rank test for the determination of sample size required, and with the Lachin Foukes method were compared.
Methods: The pre-sample repeated sampling, calculation of Log rank test statistic and its average value. Adjust the pre-
sample repeated operation, when the average of the full booking non-center parameter approximation, the last preset
sample size was seen as a necessary sample size. RESULTS: The sample size obtained varies because of the survival distribution can be scheduled to meet the Log rank test efficacy. In contrast, Lachin Foukes France obtained sample
size too small, lack of efficacy for the Log rank test. Conclusion: The iterative non-central France is better than
Lachin Foukes method can be used for chronic diseases and cancer survival study design.
Key words censored Log rank test; Monte Carlo method of
sample size of non-central France
The Sample Size Determination in Log Rank Test:
the Iterative Non Central Procedure
Abstract Objective: This paper proposes an iterative non
central procedure for the sample size determination in log
rank test and compares it with the Lachin Foulkes
procedure. Methods: Samplings are performed with a prescribed size. The statistics of log rank test and their average are calculated. Such a course is repeated with adjusted sample sizes. When the average is converged to the interested value of non central parameter, the last adjusted sample size is
regarded as the required one. Results: The sample sizes determined by this procedure vary from distribution to distribution and are met with the prescribed power of log rank
test. By contrast, the sample sizes from Lachin Foulkes
procedure are biased to small and unable to meet with the power. Conclusion: The iterative non central procedure is
superior to the Lachin Foulles procedure and can be applied
in planning survival studies on chronic diseases and cancer.
Key words censorship; Log rank test; monte carlo method; non central procedure sample size
As we all know, survival study sample size required for the determination should be based on Log rank test [1], based on the survival data of the test is the standard method of comparison between the two groups. Over the years, it is against this objective has made unremitting efforts, however, has not been realized, this is because the test is a non-
parametric test, there is no analytic efficacy function.
Determination of the existing multi-exponential
distribution based on the assumption [2 ~ 8], which does not match the relationship between Log rank test. Lachin (1981) [9] pointed out that this is a last resort, but also his (1986) [7] that this is inaccurate. By ignoring the survival distribution of income variability and sample size too small, it can not be scheduled to meet the Log rank test of the effectiveness of [10]. On the other hand, in recent years, the survival rate based on the method of comparison is relatively conservative [11,12].
First, according to this study, clinical data analysis shows the actual design parameters and survival of research assignment based on determination of the principles of sample size requirements, and then make iterative non-central France,
that is, through repeated sampling to estimate the non-center
parameter, determined the required sample size, and with the exponential distribution based on the method were compared.
1 Principle
In each group t "" The survival rate of point estimates and t "" The survival rate of test match the conditions of each group at each time point the estimated probability of death match with the Log rank test. Pre-clinical happy to
accept a match, but the test is the effectiveness of low; effect after a match high, but it is estimated that less intuitive. In making clinical data analysis, usually do not care about matching relationship, such as the first for t ""
The survival rate of point estimate, and then Log rank test for comparison between groups. This has resulted in loss estimation and test matches, but there are advantages of an intuitive and efficient, not only recognized, and has been
agreed upon as vulgar. Keeping with this agreement, in the Survival Study design, each group should be t "" The survival rate of the main design parameters for the Log rank test was used for the determination of sample size.
r × 2 contingency table chi-square test required total
sample size N depends on the non-central parameter expression
[13]: λ (r-1, α, β) = Nτ (1) where, λ a non-central
parameter, r is the set number, r-1 is the degrees of freedom,
α is a type I error probability, β is a type II error
probability. τ non-central chi-square, depending on the
proportion (rate) πi, i = 1, ..., r. Given r, α, β, πi as
well as the set of samples points qi, through the equation (1) can be determined N. Then qi distribution, must sample size in each group.
Ruoqiang πi replaced by an estimate of i, equation (1) converted to r × 2 contingency table chi-square test: χ2 (r-
1) = N (2) That is to say, E (χ2 (r-1)) = λ (r-1, α, β).
Log rank test of special circumstances: each observation point in time be regarded as a layer, the point number at risk is seen as the layer of sample size. The total sample size N can not be separated from the equal right-hand side, that is
not written in equation (2) form, hence there is no corresponding non-central parameter expression. However, by N, and proceeds χ2 (r-1)-inverse = χ2 (r-1) / N. By equation
(1) can be seen, given πi, qi, τ fixed, then λ and N is
linear.
The use of multiple sampling so that the average asymptotic τ. When the number of sufficiently long time, and τ the Chake reduced to within the given errors, χ2 (r-1) on
average, λ (r-1, α, β) the difference between no exception. Therefore, instead of τ available approximation of the total sample size. With sampling, the number of errors decreases, the proceeds to become an acceptable sample size.
2 Methods
Here to two other samples of design as an example to illustrate the determination method. Given α, β, by Haynam
table [14] found λ (1, α, β). For example, λ (1,0.05,0.1)
= 10.507, λ (1,0.01,0.05) = 17.814. To take control group, t "" The survival rate was π2, treatment contrast difference
of μ = π1-π2, the test group t "" The survival rate was π1
= μ π2. To take the ratio of the final inspection b1 = b2 = b.
To achieve a given t "" The survival rate and a given percentage of the final inspection of the overall, more
convenient way is to set the overall distribution. The time of death using Weibull Distribution: Fi (t) = 1-exp (-θitγ), i
= 1,2. This distribution shape parameter generated by very different survival curves, the application is very wide. By π
i = exp (-θitγ) take t = 1 was θi =- lnπi. Take γ = 2 /
3, 1,3 / 2, representing the decline in constant, increased risk. Censored time to adopt the exponential distribution: Ei (t) = 1-exp (-φit), where, φi = θib / (1-b).
Set sample size of n1 = n2 = n, thus taking the patient (ij, j = 1, ..., n) the time of death and final inspection are: Xij = (-θi-1lnUij) 1 / γ, and Yij = (-- θi-1lnVij)
Here, Uij, Vij is (0,1) band pseudo-random number. If Xij ?
Yij, observing the survival time of Tij = Xij, δij = 1; if
Xij