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Variance estimation in the analysis of microarray data

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  • Yuedong Wang
  • Yanyuan Ma
  • Raymond J. Carroll

Abstract

Microarrays are one of the most widely used high throughput technologies. One of the main problems in the area is that conventional estimates of the variances that are required in the "t"-statistic and other statistics are unreliable owing to the small number of replications. Various methods have been proposed in the literature to overcome this lack of degrees of freedom problem. In this context, it is commonly observed that the variance increases proportionally with the intensity level, which has led many researchers to assume that the variance is a function of the mean. Here we concentrate on estimation of the variance as a function of an unknown mean in two models: the constant coefficient of variation model and the quadratic variance-mean model. Because the means are unknown and estimated with few degrees of freedom, naive methods that use the sample mean in place of the true mean are generally biased because of the errors-in-variables phenomenon. We propose three methods for overcoming this bias. The first two are variations on the theme of the so-called heteroscedastic simulation-extrapolation estimator, modified to estimate the variance function consistently. The third class of estimators is entirely different, being based on semiparametric information calculations. Simulations show the power of our methods and their lack of bias compared with the naive method that ignores the measurement error. The methodology is illustrated by using microarray data from leukaemia patients. Copyright (c) 2009 Royal Statistical Society.

Suggested Citation

  • Yuedong Wang & Yanyuan Ma & Raymond J. Carroll, 2009. "Variance estimation in the analysis of microarray data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 425-445.
  • Handle: RePEc:bla:jorssb:v:71:y:2009:i:2:p:425-445
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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9868.2008.00690.x
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    References listed on IDEAS

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    1. Devanarayan, Viswanath & Stefanski, Leonard A., 2002. "Empirical simulation extrapolation for measurement error models with replicate measurements," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 219-225, October.
    2. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    3. Danh V. Nguyen & A. Bulak Arpat & Naisyin Wang & Raymond J. Carroll, 2002. "DNA Microarray Experiments: Biological and Technological Aspects," Biometrics, The International Biometric Society, vol. 58(4), pages 701-717, December.
    4. Anastasios A. Tsiatis & Yanyuan Ma, 2004. "Locally efficient semiparametric estimators for functional measurement error models," Biometrika, Biometrika Trust, vol. 91(4), pages 835-848, December.
    5. Ma, Yanyuan & Genton, Marc G. & Tsiatis, Anastasios A., 2005. "Locally Efficient Semiparametric Estimators for Generalized Skew-Elliptical Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 980-989, September.
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    Cited by:

    1. Dazard, Jean-Eudes & Sunil Rao, J., 2012. "Joint adaptive mean–variance regularization and variance stabilization of high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2317-2333.
    2. Michela Battauz & Ruggero Bellio, 2011. "Structural Modeling of Measurement Error in Generalized Linear Models with Rasch Measures as Covariates," Psychometrika, Springer;The Psychometric Society, vol. 76(1), pages 40-56, January.
    3. Aurore Delaigle & Peter Hall, 2016. "Methodology for non-parametric deconvolution when the error distribution is unknown," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 231-252, January.
    4. Yun Fang & Li-Xing Zhu, 2012. "Asymptotics of SIMEX-based variance estimation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 329-345, April.
    5. repec:eee:econom:v:200:y:2017:i:2:p:194-206 is not listed on IDEAS
    6. repec:bla:jorssb:v:79:y:2017:i:5:p:1601-1618 is not listed on IDEAS
    7. repec:spr:psycho:v:82:y:2017:i:3:d:10.1007_s11336-017-9556-y is not listed on IDEAS

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