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标题: [讨论]医学数据处理——一道建模题的matlab实现 [打印本页]

作者: liwenhui 时间: 2008-8-12 11:53
标题: [讨论]医学数据处理——一道建模题的matlab实现

原题如附件所示：

[attach]5637[/attach]
题目要求判别病人的方法，以及确定主要的因素。

首先对题目给出的数据进行处理，将表一前面30个数据每种元素求平均值得到病人体内各种元素的平均含量。

再对表一后面30个元素求平均值，得到健康人体内个元素的平均含量，结果如下：

[attach]5640[/attach]

将ca k作为自变量，sorh作为因变量，进行回归。（得到的模型为线性概率模型，见《经计量学精要》，古亚拉提）

回归的代码如附件里的m文件所示：

[attach]5641[/attach]
运行的结果：

b =

0.85943269933448
-0.00026521067844
0.00045376919071

bint =

0.68868335685722 1.03018204181175
-0.00033716969449 -0.00019325166239
-0.00002536250203 0.00093290088345

r =

   0.24499009043804
   0.24298645516293
   0.22596382129192
   0.26974523197013
   0.26938499769464
   0.20134048077000
   0.26428218646615
   0.24546068238966
   0.24204749612136
   0.26329869754702
-0.30239364378778
   0.22418882468333
   0.36151397969142
   0.27800877719166
   0.22562971091175
   0.25817997058727
   0.34088284102996
   0.47584435732540
   0.39924147789994
   0.10818014268404
   0.03268403910683
   0.23266006146459
   0.42213189599121
   0.15295625201459
   0.32936275116498
   0.23035596133112
   0.27508838782562
   0.19186969392530
-0.04387393419007
   0.37180169649244
-0.28881576082096
-0.54037252177113
-0.47247370212743
-0.49482518478078
-0.27629228737278
-0.08212896037942
-0.34347303417696
-0.60782985983678
-0.50802211576599
   0.82648437263390
-0.60023746186573
-0.21743324654913
-0.59323300437026
-0.32095218604696
   0.10204363196572
-0.41168153438852
-0.22705964801276
-0.40337580412737
   0.50019536866747
   0.05178812516079
-0.08624980592198
-0.28795869072225
-0.34221336479873
-0.47546878418730
   0.13032287365765
-0.06744638245026
   0.12456342765303
-0.33184299743823
-0.32238525982281
-0.46743958519949

rint =

-0.45268049797649   0.94266067885257
-0.45471901948541   0.94069192981128
-0.47070402952424   0.92263167210809
-0.42749772755413   0.96698819149440
-0.42530394206593   0.96407393745521
-0.49119576109825   0.89387672263825
-0.42929291658125   0.95785728951356
-0.45189766754183   0.94281903232114
-0.45372849228423   0.93782348452696
-0.43273992792445   0.95933732301849
-0.72468928783798   0.11990200026242
-0.47284729549112   0.92122494485777
-0.33268274520904   1.05571070459188
-0.41631507827795   0.97233263266126
-0.47200984810697   0.92326926993047
-0.43768034176985   0.95404028294440
-0.35542375701992   1.03718943907983
-0.21577903322429   1.16746774787510
-0.29583373430114   1.09431669010102
-0.57933084093047   0.79569112629854
-0.65245595836408   0.71782403657773
-0.46476517082366   0.93008529375283
-0.26956573150114   1.11382952348357
-0.53878440595437   0.84469690998355
-0.36446419214936   1.02318969447933
-0.46717750756131   0.92788943022355
-0.41904949253371   0.96922626818495
-0.50456761920479   0.88830700705539
-0.68119689782050   0.59344902944035
-0.32210495077523   1.06570834376012
-0.98555305629226   0.40792153465034
-1.22681878775805   0.14607374421580
-1.16263827940142   0.21769087514656
-1.18559446484527   0.19594409528372
-0.97334318994612   0.42075861520057
-0.77754513466812   0.61328721390927
-1.03962716392182   0.35268109556790
-1.28897250636556   0.07331278669200
-1.19830502970058   0.18226079816860
   0.27837161793377   1.37459712733402
-1.28240289420555   0.08192797047410
-0.91514787090337   0.48028137780510
-1.27825077913241   0.09178477039189
-1.01775836842798   0.37585399633405
-0.58172439829518   0.78581166222663
-1.10573438258273   0.28237131380568
-0.92471005188033   0.47059075585482
-1.09775532080452   0.29100371254977
-0.13489900871102   1.13528974604595
-0.63713063617393   0.74070688649551
-0.78029430110123   0.60779468925727
-0.98542624488175   0.40950886343724
-1.03853703868559   0.35411030908814
-1.16731658432257   0.21637901594796
-0.55440318902529   0.81504893634058
-0.76249963681796   0.62760687191744
-0.55996646809892   0.80909332340498
-1.02839058696323   0.36470459208677
-1.01901501263124   0.37424449298562
-1.15831993205002   0.22344076165104

s =

0.53107910778697 32.27784221875193 0.00000000042300 0.12340023479290

得到回归方程：

sorh=0.85943269933448-0.00026521067844.*ca+0.00045376919071.*k

这就是我们需要的模型。

然后判断表二中的30个病例。

matlab代码如下：

ca=[323 542 1332 503 547 790 417 943 318 1969 1208 328 265 2220 1606 672 1521 1544 1062 2278 2993 2056 1025 1633 1068 2554 1211 2157 3870 1806];
k=[179 184 128 238 71 45.8 49.5 155 99.4 103 1314 264 73 62 40 47 36.2 98.9 47.3 36.5 65.5 44.8 180 228 53 77.5 134 74 143 68.9];
sorh=0.85943269933448-0.00026521067844.*ca+0.00045376919071.*k

运行结果如下：

sorh =

Columns 1 through 5

0.85499433533545 0.79918204271064 0.56425453206328 0.83402879546814 0.74658007076821

Columns 6 through 10

0.67069889230140 0.77130142136514 0.67967325412561 0.82020036114713 0.38397110012925

Columns 11 through 15

1.13531091637190 0.89223866315360 0.82227702046971 0.29879868302170 0.45165511738824

Columns 16 through 20

0.70253827538617 0.47247370213094 0.49482518478434 0.59924224155178 0.27184534930907

Columns 21 through 25

0.09537902075506 0.33448840420565 0.66927020826128 0.52980303692384 0.60023746186819