Statistical Methods in Medical Research 4ed

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Table 13.1 (cont.) Variable 10 11 12 13 14 15 16 17 18 19 1 Physical health good 2 Optimistic about future 3 Never breathless 4 Breathlessness does not distress me 5 Rarely cough 6 Coughing does not trouble me 7 Never wheezy 8 Hardly ever feel ill 9 Condition has improved 10 Never worry about future 11 Confident could cope 0 71 12 Health depends on me 0 26 0 46 13 Worth trying anything 0 32 0 21 0 02 14 Wife happy with my condition 0 01 0 11 0 20 0 11 15 Feel like going out 0 12 0 02 0 20 0 31 0 29 16 Relaxing with other people 0 24 0 15 0 01 0 59 0 07 0 50 17 Support the family 0 03 0 04 0 03 0 03 0 43 0 13 0 09 18 Making a useful contribution 0 21 0 63 0 50 0 09 0 05 0 18 0 05 0 09 19 Accept my condition 0 52 0 27 0 17 0 08 0 30 0 26 0 22 0 25 0 23 20 Feel happy 0 28 0 18 0 04 0 03 0 23 0 20 0 07 0 11 0 18 0 27 13.2 Principal components 461
462 Multivariate methods eigenvalues exceeding 1, they lie in the tail of the scree plot. Most importantly, when three components were fitted, there was a clear interpretation, but adding another component did not give a fourth interpretable component. Accordingly, three components were retained. In Table 13.2 the first three components are given. The variables have been reordered, and component correlations exceeding 0 5 are given in bold type, to show the main features of each component. The first component is correlated more with variables 1, 3, 4, 5, 6, 7, 8, 9, 14 and 17, and may be interpreted as `physical health'. The second component is correlated with variables 2, 10, 11, 12, 18, 19 and 20, and may be interpreted as `optimism'. The third component is correlated with variables 13, 15 and 16, and may be interpreted as `socializing'. The identification of the components in terms of the original variables is clearer for the rotated components. These three components accounted for 57% of the total variation and, since no clear interpretation was made of the next component, attention was restricted to these three. In the above example the dimensionality of the data was reduced from 20 to 3 by the use of principal component analysis. It would appear that the method was highly effective. However, the original questions were chosen to represent a few characteristics and, before the data were collected, groupings of the questions Table 13.2 Component correlations (loadings) for the first three principal components. Component Rotated component Variable 1 2 3 1 2 3 1 Physical health good 0 67 0 02 0 01 0 59 0 32 0 07 3 Never breathless 0 63 0 02 0 08 0 55 0 28 0 14 4 Breathlessness does not distress me 0 69 0 28 0 10 0 53 0 51 0 13 5 Rarely cough 0 76 0 31 0 24 0 86 0 00 0 04 6 Coughing does not trouble me 0 77 0 23 0 26 0 84 0 07 0 08 7 Never wheezy 0 77 0 29 0 12 0 77 0 13 0 29 8 Hardly ever feel ill 0 81 0 08 0 08 0 67 0 45 0 12 9 Condition has improved 0 68 0 47 0 30 0 86 0 19 0 04 14 Wife happy with my condition 0 66 0 29 0 04 0 69 0 06 0 21 17 Support the family 0 59 0 19 0 13 0 63 0 06 0 00 2 Optimistic about future 0 22 0 66 0 08 0 07 0 68 0 15 10 Never worry about future 0 23 0 74 0 14 0 04 0 69 0 38 11 Confident could cope 0 43 0 64 0 04 0 13 0 75 0 16 12 Health depends on me 0 29 0 41 0 47 0 01 0 61 0 31 18 Making a useful contribution 0 43 0 49 0 32 0 12 0 70 0 15 19 Accept my condition 0 52 0 44 0 13 0 27 0 64 0 10 20 Feel happy 0 14 0 61 0 15 0 40 0 50 0 00 13 Worth trying anything 0 09 0 37 0 68 0 10 0 15 0 76 15 Feel like going out 0 33 0 27 0 68 0 23 0 12 0 76 16 Relaxing with other people 0 01 0 43 0 64 0 00 0 18 0 75
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To J.O. Irwin Mentor and friend
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# 1971, 1987, 1994, 2002 by Blackwe
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vi Contents 9.3 Factorial designs,
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Preface to the fourth edition In th
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Preface to the fourth edition xi Ho
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2 The scope of statistics other pat
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4 The scope of statistics groups is
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6 The scope of statistics pressure
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2 Describing data 2.1 Diagrams One
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10 Describing data 1- 4 weeks Under
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12 Describing data Table 2.1 Outcom
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14 Describing data Your height: ...
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16 Describing data be transferred f
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18 Describing data extracted from t
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20 Describing data many variables a
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22 Describing data cannot be less t
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24 Describing data Bufotenin (nmol/
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26 Describing data Frequency 20 18
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28 Describing data The number of as
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30 Describing data Frequency Measur
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32 Describing data may be abbreviat
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34 Describing data variables follow
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36 Describing data 107 01. The geom
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38 Describing data If the number of
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40 Describing data Therefore the me
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42 Describing data xi x will then n
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44 Describing data taking the antil
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46 Describing data against their ef
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48 Probability example, is sometime
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50 Probability It will appear in du
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52 Probability In general, pairs of
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54 Probability the five types be cl
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56 Probability converted to a ratio
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58 Probability Correct Equivocal In
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60 Probability Probability 1 . 0 0
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62 Probability Probability density
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64 Probability As a second example,
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66 Probability coefficient. In the
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68 Probability n r pr …1 p† n r
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70 Probability π = 0 Probability .
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72 Probability 0 } — T n Fig. 3.8
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74 Probability Probability 0 . 4 0
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76 Probability Table 3.4 Binomial a
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78 Probability where exp(z) is a co
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80 Probability approaches the shape
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82 Probability Probabililty density
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84 Analysing means and proportions
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148 Analysing variances Probability
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150 Analysing variances headings 0
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152 Analysing variances Method AB N
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154 Analysing variances Example 5.2
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156 Analysing variances Comparison
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158 Analysing variances With contin
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160 Analysing variances Let y ˆ x1
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162 Analysing variances p … log x
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164 Analysing variances as expected
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166 Bayesian methods This argument
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168 Bayesian methods nothing of the
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170 Bayesian methods in this way. F
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172 Bayesian methods In some situat
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174 Bayesian methods difference bet
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176 Bayesian methods the distributi
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178 Bayesian methods In the unpaire
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180 Bayesian methods The examples d
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182 Bayesian methods difference bet
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184 Bayesian methods variation may
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186 Bayesian methods The resulting
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188 Regression and correlation Infa
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190 Regression and correlation y x
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192 Regression and correlation on s
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194 Regression and correlation y ,
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196 Regression and correlation y (a
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198 Regression and correlation incr
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200 Regression and correlation From
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202 Regression and correlation y ,
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204 Regression and correlation Valu
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206 Regression and correlation disc
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8 Comparison of several groups 8.1
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210 Comparison of several groups P
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212 Comparison of several groups s
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214 Comparison of several groups to
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216 Comparison of several groups sh
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218 Comparison of several groups s
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220 Comparison of several groups su
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222 Comparison of several groups No
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224 Comparison of several groups yc
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226 Comparison of several groups Q
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228 Comparison of several groups te
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230 Comparison of several groups Ta
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232 Comparison of several groups Ta
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234 Comparison of several groups th
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9 Experimental design 9.1 General r
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238 Experimental design the estimat
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240 Experimental design Table 9.1 N
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242 Experimental design Similarly,
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244 Experimental design The sum of
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246 Experimental design If, in a tw
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248 Experimental design Table 9.5 S
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250 Experimental design interaction
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252 Experimental design difference
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254 Experimental design Table 9.7 C
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256 Experimental design interaction
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258 Experimental design litters and
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260 Experimental design randomizati
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262 Experimental design rows, colum
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264 Experimental design type of des
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266 Experimental design Main unit S
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268 Experimental design categories
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270 Experimental design Example 9.6
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10 Analysing non-normal data 10.1 D
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274 Analysing non-normal data The s
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276 Analysing non-normal data Estim
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278 Analysing non-normal data betwe
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Table 10.1 Some properties of three
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282 Analysing non-normal data This
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284 Analysing non-normal data High
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286 Analysing non-normal data which
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288 Analysing non-normal data Table
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290 Analysing non-normal data 1 It
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292 Analysing non-normal data It is
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294 Analysing non-normal data proba
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296 Analysing non-normal data Fract
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298 Analysing non-normal data h=…
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300 Analysing non-normal data This
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302 Analysing non-normal data Boots
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304 Analysing non-normal data more
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306 Analysing non-normal data Sampl
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308 Analysing non-normal data 3 squ
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310 Analysing non-normal data mG ˆ
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11 Modelling continuous data 11.1 A
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314 Modelling continuous data Examp
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316 Modelling continuous data n k i
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318 Modelling continuous data consi
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320 Modelling continuous data basis
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322 Modelling continuous data 11.4
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324 Modelling continuous data var
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326 Modelling continuous data Table
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328 Modelling continuous data Again
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330 Modelling continuous data SSq D
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332 Modelling continuous data Two g
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334 Modelling continuous data which
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336 Modelling continuous data the i
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338 Modelling continuous data predi
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340 Modelling continuous data equat
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344 Modelling continuous data Somet
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346 Modelling continuous data multi
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348 Modelling continuous data (i) D
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350 Modelling continuous data The r
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352 Modelling continuous data In th
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354 Modelling continuous data The c
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356 Modelling continuous data If th
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358 Modelling continuous data at th
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360 Modelling continuous data about
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362 Modelling continuous data y −
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364 Modelling continuous data y −
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366 Modelling continuous data outli
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370 Modelling continuous data Patie
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372 Modelling continuous data Norma
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374 Modelling continuous data Cumul
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12 Further regression models for a
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380 Further regression models Table
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382 Further regression models repre
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384 Further regression models where
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386 Further regression models Popul
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388 Further regression models and S
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390 Further regression models s(x)
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392 Further regression models SS ˆ
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394 Further regression models A…a
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396 Further regression models and t
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398 Further regression models that
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400 Further regression models Regre
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402 Further regression models M…T
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404 Further regression models a0
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406 Further regression models Maxim
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408 Further regression models using
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Page 467 and 468: 456 Multivariate methods 13.2 Princ
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Page 495 and 496: 484 Multivariate methods explanator
Page 497 and 498: 486 Modelling categorical data In t
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512 Empirical methods for categoric
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16 Further Bayesian methods 16.1 Ba
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530 Further Bayesian methods Analyt
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532 Further Bayesian methods compli
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534 Further Bayesian methods One ap
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536 Further Bayesian methods result
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538 Further Bayesian methods (i) th
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540 Further Bayesian methods From (
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542 Further Bayesian methods A stra
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544 Further Bayesian methods the st
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546 Further Bayesian methods but ma
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548 Further Bayesian methods σ 30
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550 Further Bayesian methods practi
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552 Further Bayesian methods which
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554 Further Bayesian methods Densit
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556 Further Bayesian methods recurr
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558 Further Bayesian methods a ˆ m
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560 Further Bayesian methods values
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562 Further Bayesian methods distri
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564 Further Bayesian methods the se
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566 Further Bayesian methods probab
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17 Survival analysis 17.1 Introduct
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570 Survival analysis Table 17.1 Cu
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572 Survival analysis Table 17.2 Li
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574 Survival analysis otherwise the
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576 Survival analysis qtj ˆ dj=n 0
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578 Survival analysis quantities in
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580 Survival analysis Survival % 10
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582 Survival analysis logrank test
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584 Survival analysis the mean surv
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586 Survival analysis the death rat
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588 Survival analysis McGilchrist a
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590 Survival analysis The martingal
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592 Clinical trials trials. In drug
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594 Clinical trials first type of e
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596 Clinical trials . Proposed numb
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598 Clinical trials If the response
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600 Clinical trials methods of Baye
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602 Clinical trials represented by
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604 Clinical trials physicians find
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606 Clinical trials very minor proc
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608 Clinical trials each patient's
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610 Clinical trials Table 18.1 Resu
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612 Clinical trials solution is ava
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614 Clinical trials Administrative
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616 Clinical trials non-sequential
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618 Clinical trials Table 18.3 Maxi
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620 Clinical trials Standardized de
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622 Clinical trials A somewhat diff
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624 Clinical trials A trial showing
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626 Clinical trials Publication bia
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628 Clinical trials on different oc
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630 Clinical trials Table 18.5 Numb
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632 Clinical trials Treatment perio
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634 Clinical trials in cases where
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636 Clinical trials independent, an
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638 Clinical trials Sample size The
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640 Clinical trials and the restric
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642 Clinical trials original data.
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644 Clinical trials if the odds rat
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646 Clinical trials 3 2 1 0 -1 -2 -
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19 Statistical methods in epidemiol
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650 Statistical methods in epidemio
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Table 19.1 Death rate for two popul
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718 Laboratory assays such cases, t
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720 Laboratory assays and YT ˆ yT
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722 Laboratory assays significant a
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724 Laboratory assays The general p
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726 Laboratory assays This relation
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728 Laboratory assays Proportion po
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730 Laboratory assays P contribute
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732 Laboratory assays transformatio
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734 Laboratory assays Table 20.1 Es
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736 Laboratory assays P m iˆ1 ri l
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738 Laboratory assays synthesize hi
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740 Laboratory assays estimate of a
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Appendix tables 743
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2 0 0 02275 0 02222 0 02169 0 02118
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16 6 91 93 1 11 91 153 4 19 3 7 23
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16 0 128 0 258 0 392 0 535 0 690 0
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5 0 05 6 61 5 79 5 41 5 19 5 05 4 9
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3 0 0 05 4 17 3 32 2 92 2 69 2 53 2
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14 0.05 3 03 3 70 4 11 4 41 4 64 4
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Table A7 Percentage points for the
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Table A9 Sample size for detecting
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Bailey N.T.J. (1975) The Mathematic
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Buyse M.E., Staquet M.J. and Sylves
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eceptor interactions. J. Ster. Bioc
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Etzioni R.D. and Weiss N.S. (1998)
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Goetghebeur E. and Lapp K. (1997) T
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sample data in randomized block and
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Lehmann E.L. (1975) Nonparametrics:
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Mehta C.R. (1994) The exact analysi
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Peto R., Pike M., Day N. et al. (19
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Scott J.E.S., Hunter E.W., Lee R.E.
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Thompson S.G. and Barber J.A. (2000
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Zhang H., Crowley J., Sox H.C. and
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786 Author Index Brooks, S.P. 549,
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788 Author Index Gart, J.J. 127, 67
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790 Author Index Laurence, D.R. 519
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792 Author Index RamoÂn, J.M. 536
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794 Author Index Westley-Wise, V.J.
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796 Subject Index Assays (cont.) ra
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798 Subject Index Chronic obstructi
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800 Subject Index Continuous variab
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802 Subject Index Dot diagram 23, 2
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804 Subject Index Growth curves 409
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806 Subject Index McNemar's test 12
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808 Subject Index Normal (cont.) st
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810 Subject Index Proportions Bayes
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812 Subject Index Roughness penalty
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814 Subject Index Standard (cont.)
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816 Subject Index Tumour (cont.) in
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