In triphosphate/AMS597: A method to deal paired sample with NA values

Introduction

This package is based on Professor Kuan's paper^[A Simple and Robust Method for Partially Matched Samples Using the P-Values Pooling Approach, 2013].

It provided a statistical analyses in scenarios where some samples from the matched pairs design are missing, resulting in partially matched samples.

Package Info

This package could process 5 procedures:

• modified t-statistic of Kim et al.;
• corrected Z-test of Looney and Jones;
• MLE based test of Ekbohm under homoscedasticity;
• MLE based test of Lin and Stivers under heteroscedasticity;
• weighted Z-test combination.

Arguments

x,y

$x,y$ are vector values. In our package, we assume $x$ is tumor data and $y$ is normal data. NA values for missing data.

alternative

alternative can be "two.sided", "less" or "greater".

Usage

1. modttest(x,y);
2. cor_Z(x,y);
3. homoMLE(x,y);
4. heteMLE(x,y);
5. weighted.z.test(x,y).

Theory & Formulas

Modified t-statistic of Kim et al.

The modified t-statistic $t_3$ of Kim et al.^[Kim B, Kim I, Lee S, Kim S, Rha S, Chung H. Statistical methods of translating microarray data into clinically relevant diagnostic information in colorectal cancer. Bioinformatics. 2004; 21(4): 517–528. [PubMed: 15374865]] takes the form $$ \begin{aligned} t_3=\frac{{n_1}\bar{D}+{n_H}(\bar{T}-\bar{N})}{\sqrt{{n_1}{S_D}^2+{n_H}^2(S_N^2/n_3+S_T^2/n_2)}} \end{aligned} $$ And the null distribution of $t_3$ is approcimated with a standard Gaussian distribution.

Corrected Z-test of Looney and Jones

The corrected Z-test of Looney and Jones^[ Looney S, Jones P. A method for comparing two normal means using combined samples of correlated and uncorrelated data. Statistics in Medicine. 2003; 22:1601–1610.] is based on a modified variance estimation of the standard Z-test by accounting for the correlation among the $n_1$ matched pairs, $$ \begin{aligned} Z_{corr}=\frac{\bar{T^}-\bar{N^}}{\sqrt{S_T^{2}/(n_1+n_2)+S_N^{2}/(n_1+n_3)-2n_1S_{TN_1}/(n_1+n_2)(n_1+n_3)}} \end{aligned} $$

MLE based test

There are two kinds of MLE based test. The first is proposed by Ekbohm^[ Ekbohm G. On comparing means in the paired case with incomplete data on both responses. Biometrika. 1976;63(2):299–304. ] and the second is proposed by Lin and Stivers^[ Lin P, Stivers L. On differences of means with incomplete data. Biometrika. 1974; 61(2):325–334. ].

Both MLE based test under homo- or heteroscedasticity have similar form like this: $$ \begin{aligned} Z_{LS}=\frac{f(\bar{T_1}-\bar{T})-g(\bar{N_1}-\bar{N})+\bar{T}-\bar{N}}{\sqrt{V_1}} \end{aligned} $$

Wighted Z-test Combination

The combined p-value by the weighted Z-test introduced by Liptak^[Liptak T. On the combination of independent tests. Magyar Tudom Aanyos Akad Aemia Matematikai Kutat Ao Intezetenek Kozlemenyei. 1958; 3:171–197. ] is: $$ \begin{aligned} p_{ci}=1-\Phi(\frac{w_1Z_{1i}+w_2Z_{2i}}{\sqrt{w_1^2+w_2^2}}) \end{aligned} $$

Notes

We assume the data set is big and missing value is relatively small.
Instead of call particular method, we call t.test() in extreme case.

• While tumor and normal have different dimension, the package call two sample t-test;
• While paired sample size is very small or 0, this package call two sample t-test;
• If the unpaired sample size is very small or 0, this package call Paired t-test;

triphosphate/AMS597 documentation built on May 5, 2019, 5:57 p.m.