## Medical Applications of Finite Mixture ModelsPatients are not alike! This simple truth is often ignored in the analysis of me- cal data, since most of the time results are presented for the “average” patient. As a result, potential variability between patients is ignored when presenting, e.g., the results of a multiple linear regression model. In medicine there are more and more attempts to individualize therapy; thus, from the author’s point of view biostatis- cians should support these efforts. Therefore, one of the tasks of the statistician is to identify heterogeneity of patients and, if possible, to explain part of it with known explanatory covariates. Finite mixture models may be used to aid this purpose. This book tries to show that there are a large range of applications. They include the analysis of gene - pression data, pharmacokinetics, toxicology, and the determinants of beta-carotene plasma levels. Other examples include disease clustering, data from psychophysi- ogy, and meta-analysis of published studies. The book is intended as a resource for those interested in applying these methods. |

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### Contents

1 | |

II | 7 |

III | 11 |

IV | 13 |

V | 15 |

VI | 18 |

VII | 19 |

VIII | 20 |

LXII | 128 |

LXIII | 129 |

LXIV | 130 |

LXV | 132 |

LXVI | 133 |

LXVII | 134 |

LXVIII | 135 |

LXIX | 136 |

IX | 21 |

X | 22 |

XI | 28 |

XII | 29 |

XIII | 30 |

XIV | 33 |

XV | 34 |

XVII | 36 |

XVIII | 39 |

XIX | 41 |

XX | 42 |

XXI | 43 |

XXII | 47 |

XXIII | 49 |

XXIV | 51 |

XXV | 52 |

XXVI | 53 |

XXVII | 55 |

XXVIII | 56 |

XXIX | 61 |

XXX | 64 |

XXXII | 69 |

XXXIII | 70 |

XXXIV | 72 |

XXXV | 73 |

XXXVI | 74 |

XXXVII | 77 |

XXXVIII | 79 |

XXXIX | 80 |

XL | 82 |

XLII | 83 |

XLIII | 84 |

XLIV | 87 |

XLV | 91 |

XLVI | 93 |

XLVII | 95 |

XLVIII | 97 |

XLIX | 98 |

LI | 102 |

LII | 107 |

LIII | 109 |

LIV | 110 |

LV | 112 |

LVI | 117 |

LVII | 119 |

LIX | 121 |

LX | 124 |

LXX | 138 |

LXXI | 139 |

LXXII | 143 |

LXXIII | 144 |

LXXIV | 148 |

LXXV | 149 |

LXXVI | 153 |

LXXVII | 154 |

LXXVIII | 155 |

LXXX | 157 |

LXXXI | 160 |

LXXXII | 162 |

LXXXIII | 164 |

LXXXIV | 166 |

LXXXV | 168 |

LXXXVI | 169 |

LXXXVIII | 171 |

XC | 173 |

XCII | 176 |

XCIII | 177 |

XCIV | 180 |

XCV | 181 |

XCVII | 182 |

XCVIII | 183 |

XCIX | 184 |

CI | 185 |

CII | 186 |

CIV | 187 |

CV | 190 |

CVI | 191 |

CVII | 192 |

CVIII | 194 |

CIX | 196 |

CX | 197 |

CXI | 200 |

CXII | 202 |

CXIII | 206 |

CXIV | 209 |

CXV | 210 |

CXVI | 213 |

CXVII | 214 |

CXVIII | 215 |

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237 | |

243 | |

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### Common terms and phrases

absorption algorithm Ames test analysis applied approach Aspirin assumed Bšohning beta-carotene bootstrap breast cancer case-control studies childhood leukemia clustering cohort studies Computation conﬁdence interval convex set covariate-adjusted mixture model covariates data set deﬁned denotes density differentially expressed dose drug EM algorithm example ﬁnd ﬁnding ﬁnite mixture model Finite Mixture Models ﬁrst ﬁt ﬁxed effects model gene expression given heterogeneity variance homogenous model hypothesis individual Intercept investigated leads likelihood function likelihood ratio linear mixed effects linear models matrix maximize maximum likelihood estimate meta-analysis metaregression methods mixed effects model mixture density negative binomial negative binomial distribution normal distribution null number of components observed obtained overdispersion parameters patients periodogram pharmacokinetic plot Poisson distribution Poisson regression population publication bias random effects model regression model relative risk Residual result sample Schlattmann score test signiﬁcant simulation study starting values Step subpopulation Table test statistic variable vector