上海中医药大学研究生医学统计学作业.doc

医学统计学作业目录I.统计图 1II.双变量回归与相关 2III.多因素试验资料的方差分析4IV.重复测量设计的方差分析6V.协方差分析 12VI.多元线性回归分析15VII.Logistic回归分析16VIII.生存分析 20I.统计图例2-8 正态分布图21II.双变量回归与相关例9-1某地方病研究所调查了8名正常儿童的尿肌酐含量（mmol/24h）如书中表9-1，估计尿肌酐含量(Y)对其年龄(X)的直线回归方程。1.2.例9-2检验例9-1数据得到的直线回归方程是否成立答：建立假设检验，确立检验水准H0：0，尿肌酐含量与年龄之间无直线关系H1：0，尿肌酐含量与年龄之间存在直线关系=0.05ANOVAaModelSum of SquaresdfMean SquareFSig.1Regression.8131.81320.968.004bResidual.2336.039Total1.0467a. Dependent Variable: 尿肌酐含量b. Predictors: (Constant), 年龄P=0.004，按照=0.05水准，拒绝H0 ，接受H1 ，尿肌酐含量与年龄之间存在直线关系；直线回归方程成立III. 多因素试验资料的方差分析例11-1 将20只家兔随机等分4组，每组5只，进行神经损伤后的缝合试验。处理由A、B两因素组合而成，因素A为缝合方法，有两水平，一为外膜缝合，记作a1，二为束膜缝合，记作a2；因素B为缝合后的时间，亦有两水平，一为缝合后1月，记作b1，二为缝合后2月，记作b2。试验结果为家兔神经缝合后的轴突通过率(%)（注：测量指标，视为计量资料），见书中表11-1。欲用析因分析比较不同缝合方法及缝合后时间对轴突通过率的影响。Tests of Between-Subjects EffectsDependent Variable:轴突通过率 SourceType III Sum of SquaresdfMean SquareFSig.Partial Eta SquaredNoncent. ParameterObserved PowerbCorrected Model2620.000a3873.3332.911.067.3538.733.580Intercept27380.000127380.00091.267.000.85191.2671.000缝合后的时间2420.00012420.0008.067.012.3358.067.760缝合方法180.0001180.000.600.450.036.600.113缝合后的时间*缝合方法20.000120.000.067.800.004.067.057Error4800.00016300.000Total34800.00020Corrected Total7420.00019a. R Squared = .353 (Adjusted R Squared = .232)b. Computed using alpha = .05A因素主效应所对应的检验假设为H0：A因素主效应=0， H1：A因素主效应0，=0.05；B因素主效应所对应的检验假设为H0：B因素主效应=0，H1：A因素主效应0，=0.05；AB交互作用所对应的检验假设为H0：AB交互作用=0，H1：A因素主效应0，=0.05。方差分析的检验界值为，统计学结论：模型Corrected Model检验F=2.911，P=0.0670.05，模型不具备统计学意义；A（缝合方法）F=0.600，P=0.450.05，不具备统计学意义；按照=0.05水准，不拒绝H0，拒绝H1；B（缝合后的时间）F=8.067，P=0.0120.05，不具备统计学意义；按照=0.05水准，接受H0，拒绝H1。专业结论：尚不能认为两种缝合方法对神经轴突通过率有影响；可以认为缝合后2月与缝合后1月相比，神经轴突通过率提高了。IV.重复测量设计的方差分析例12-3 将手术要求基本相同的15名患者随机分3组，在手术过程中分别采用A，B，C三种麻醉诱导方法，在T0（诱导前）、T1、T2、T3、T4 ， 五个时相测量患者的收缩压，数据记录见表12-17。试进行方差分析。1. 建立假设检验，确立检验水准H0:三种麻醉诱导方法在五个时相时测得的收缩压均值无差别H1:三种麻醉诱导方法在五个时相时测得的收缩压均值有差别=0.052. 正态性检验、方差齐性检验：Tests of NormalitygroupKolmogorov-SmirnovaShapiro-WilkStatisticdfSig.StatisticdfSig.t0方法A.3005.161.8365.154方法B.2275.200*.9165.503方法C.2295.200*.8675.254t1方法A.3315.077.8345.148方法B.2205.200*.9135.485方法C.1845.200*.9785.921t2方法A.2585.200*.9405.666方法B.2275.200*.9695.869方法C.2215.200*.9535.758t3方法A.2835.200*.9375.647方法B.2415.200*.9025.421方法C.2515.200*.9415.672t4方法A.1865.200*.9435.687方法B.2925.189.8925.367方法C.1645.200*.9845.955*. This is a lower bound of the true significance.a. Lilliefors Significance Correction符合正态分布，P值均大于0.05Test of Homogeneity of VarianceLevene Statisticdf1df2Sig.t0Based on Mean.145212.866Based on Median.127212.882Based on Median and with adjusted df.127211.675.882Based on trimmed mean.144212.868t1Based on Mean.440212.654Based on Median.385212.689Based on Median and with adjusted df.385210.205.690Based on trimmed mean.438212.655t2Based on Mean.950212.414Based on Median.908212.429Based on Median and with adjusted df.90828.995.437Based on trimmed mean.976212.405t3Based on Mean.200212.821Based on Median.141212.870Based on Median and with adjusted df.141211.781.870Based on trimmed mean.207212.816t4Based on Mean.172212.844Based on Median.024212.976Based on Median and with adjusted df.02429.538.976Based on trimmed mean.157212.857方差齐性相等，P值均大于0.053. ANOVADescriptive StatisticsgroupMeanStd. DeviationNt0方法A121.003.5365方法B121.204.3245方法C126.203.6335Total122.804.34615t1方法A112.405.1285方法B119.805.9755方法C123.003.3915Total118.406.49015t2方法A118.405.6395方法B118.005.4315方法C118.601.9495Total118.334.32015t3 方法A125.804.7125方法B128.205.2155方法C142.604.8275Total132.208.93015t4 方法A120.803.7015方法B135.204.3825方法C130.603.7155Total128.877.21015描述统计分析结果Multivariate TestsaEffectValueFHypothesis dfError dfSig.factor1Pillais Trace.983126.659b4.0009.000.000Wilks Lambda.017126.659b4.0009.000.000Hotellings Trace56.293126.659b4.0009.000.000Roys Largest Root56.293126.659b4.0009.000.000factor1 * groupPillais Trace1.80923.6568.00020.000.000Wilks Lambda.00822.215b8.00018.000.000Hotellings Trace20.60020.6008.00016.000.000Roys Largest Root13.37633.440c4.00010.000.000a. Design: Intercept + group Within Subjects Design: factor1b. Exact statisticc. The statistic is an upper bound on F that yields a lower bound on the significance level.球形检验结果Tests of Between-Subjects EffectsMeasure: MEASURE_1 Transformed Variable: Average SourceType III Sum of SquaresdfMean SquareFSig.Intercept1155433.08011155433.08014649.223.000group912.2402456.1205.783.017Error946.4801278.873组间效应检验结果Pairwise ComparisonsMeasure: MEASURE_1 (I) group(J) groupMean Difference (I-J)Std. ErrorSig.b95% Confidence Interval for DifferencebLower BoundUpper Bound 方法A方法B-4.8002.512.080-10.273.673方法C-8.520*2.512.005-13.993-3.047方法B 方法A4.8002.512.080-.67310.273方法C-3.7202.512.164-9.1931.753方法C 方法A8.520*2.512.0053.04713.993方法B3.7202.512.164-1.7539.193Based on estimated marginal means*. The mean difference is significant at the .05 level.b. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).组间多重比较检验结果Pairwise ComparisonsMeasure: MEASURE_1 (I) factor1(J) factor1Mean Difference (I-J)Std. ErrorSig.b95% Confidence Interval for DifferencebLower BoundUpper Bound124.400*.860.0002.5266.27434.467*.764.0002.8016.1324-9.400*1.188.000-11.988-6.8125-6.067*.972.000-8.184-3.94921-4.400*.860.000-6.274-2.5263.067.527.901-1.0821.2154-13.800*.613.000-15.135-12.4655-10.467*.881.000-12.385-8.54831-4.467*.764.000-6.132-2.8012-.067.527.901-1.2151.0824-13.867*.843.000-15.704-12.0295-10.533*.775.000-12.221-8.846419.400*1.188.0006.81211.988213.800*.613.00012.46515.135313.867*.843.00012.02915.70453.333*.943.0041.2795.388516.067*.972.0003.9498.184210.467*.881.0008.54812.385310.533*.775.0008.84612.2214-3.333*.943.004-5.388-1.279Based on estimated marginal means*. The mean difference is significant at the .05 level.b. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).组内不同时间多重比较检验结果统计结论：球形检验结果：Mauchlys W=0.293，P=0.1780.05。组间效应检验结果F=14649.223，P0.05，说明三种麻醉诱导方法间差异有统计学意义；进一步作LSD法多重比较，方法A组、方法C组间差异具体统计学意义，P=0.005，方法B组与方法A组、方法C组间差异无统计学意义，P值分别为0.08、0.164；不同时相间比较，T2与T3间差异无统计学意义P=0.901，其余各时相间比较均有统计学意义。按照水平，拒绝H0，接受H1认为三种麻醉诱导方法在五个时相时测得的收缩压均值有差别。V.协方差分析例13-1 为研究某降糖药物的有效性及其合用二甲双胍片的有效性，选择收治90名2型糖尿病患者，并采用随机对照试验，分为三个治疗组，第一组为该降糖药组，第二组为二甲双胍片组，第三组为该降糖组+二甲双胍片组，每组30名患者，治疗3个月，主要有效性指标为糖化血红蛋白。测得每个患者入组前（X）和3个月后（Y）的糖化血红蛋白含量（%）见书中表13-3的上部，试分析三种治疗降糖化血红蛋白的效果是否不同。1. 设立假设检验，确立检验水准H0:各组降糖的总体修正均数相等H1:各组降糖的总体修正均数不全相等=0.052. 判断是否符合协方差分析条件：三个组的入组前（X）糖化和3个月后（Y）糖化间都有明显的直线趋势；三组的直线趋势相近。因此，本资料符合协方差分析的条件。3. 检验各组总体斜率是否相等：Tests of Between-Subjects EffectsDependent Variable: 3个月后 SourceType I Sum of SquaresdfMean SquareFSig.Corrected Model48.973a59.79556.618.000Intercept6230.01616230.01636013.278.000c18.72529.36254.120.000x30.183130.183174.476.000c * x.0652.033.188.829Error14.53184.173Total6293.52090Corrected Total63.50489a. R Squared = .771 (Adjusted R Squared = .758)I型方差分析模型的结果模型中交互作用无统计学意义P=0.829，说明三组患者3月后糖化降低随着入组前糖化变化的斜率是相同的，故可对资料进行协方差分析。4. 比较修正均数有无差异Tests of Between-Subjects EffectsDependent Variable: 3个月后 SourceType III Sum of SquaresdfMean SquareFSig.Corrected Model48.908a316.30396.053.000Intercept.3631.3632.140.147c19.85129.92558.480.000x30.183130.183177.835.000Error14.59686.170Total6293.52090Corrected Total63.50489a. R Squared = .770 (Adjusted R Squared = .762)修正均数比较的方差分析结果x的F=96.053，P0.01，说明入组前糖化血糖蛋白对3个月后的糖化血红蛋白含量的下降有影响EstimatesDependent Variable: 3个月后 组别MeanStd. Error95% Confidence IntervalLower BoundUpper Bound试验组8.356a.0768.2068.506盐酸二甲双胍8.877a.0758.7279.027试验药+盐酸二甲双胍7.728a.0757.5787.877a. Covariates appearing in the model are evaluated at the following values: 入组前 = 9.9700.修正均数及其可信区间结果试验药+二甲双胍组的糖化水平低于另外二组，同时提示修正均数是按照入组前糖化均值x为9.97%计算的。Pairwise ComparisonsDependent Variable: 3个月后 (I) 组别(J) 组别Mean Difference (I-J)Std. ErrorSig.b95% Confidence Interval for DifferencebLower BoundUpper Bound试验组盐酸二甲双胍-.521*.107.000-.734-.308试验药+盐酸二甲双胍.628*.107.000.416.840盐酸二甲双胍试验组.521*.107.000.308.734试验药+盐酸二甲双胍1.149*.106.000.9381.361试验药+盐酸二甲双胍试验组-.628*.107.000-.840-.416盐酸二甲双胍-1.149*.106.000-1.361-.938Based on estimated marginal means*. The mean difference is significant at the .05 level.b. Adjustment for multiple comparisons: Least Significant Difference (equivalent to no adjustments).各组修正均数是否相等的假设检验结果Univariate TestsDependent Variable: 3个月后 Sum of SquaresdfMean SquareFSig.Contrast19.85129.92558.480.000Error14.59686.170The F tests the effect of 组别. This test is based on the linearly independent pairwise comparisons among the estimated marginal means.修正均数按方差分析法进行的检验结果修正均数按方差分析法进行的检验结果，结论和修正均数比较的方差分析结果一致。各组间总体修正均数间差别均有统计学意义（P均0.05）。在=0.05水平上，拒绝H0，接受H1，各组降糖的总体修正均数不全相等。可以认为在扣除了入组前糖化水平的影响后，第三组治疗患者的平均降糖量最多，第一组治疗次之，第二组治疗最少。VI.多元线性回归分析PPT例题2：有学者认为糖尿病人的血糖变化可能受胰岛素、糖化血红蛋白、血清总胆固醇、甘油三脂等多种生化指标的影响，现测量了27名糖尿病人的相关指标，资料如下表所示，请对此作分析。1.建立假设检验H0：1=2=3=0H1：j（j=1,2,，m）不全为0Variables Entered/RemovedaModelVariables EnteredVariables RemovedMethod1x4, x2, x3, x1b.Entera. Dependent Variable: yb. All requested variables entered.Model SummaryModelRR SquareAdjusted R SquareStd. Error of the Estimate1.775a.601.5282.0095a. Predictors: (Constant), x4, x2, x3, x1回归方程模型摘要ANOVAaModelSum of SquaresdfMean SquareFSig.1Regression133.711433.4288.278.000bResidual88.841224.038Total222.55226a. Dependent Variable: yb. Predictors: (Constant), x4, x2, x3, x1回归方程的方差分析结果CoefficientsaModelUnstandardized CoefficientsStandardized CoefficientstSig.BStd. ErrorBeta1(Constant)5.9432.8292.101.047x1.142.366.078.390.701x2.351.204.3091.721.099x3-.271.121-.339-2.229.036x4.638.243.3982.623.016a. Dependent Variable: y多元回归方程的参数估计回归方程的方差分析得出，F=8.278，P0.001。拒绝H0：1=2=3=4=0，所以拟合的回归方程有统计学意义。1、2、3、4的估计值b1、b2、b3、b4分别为0.142、0.351、-0.271、0.638，据此写出多元回归方程：血糖的变化与甘油三酯、胰岛素和糖化血红蛋白有线性回归关系（总胆固醇的P=0.701，无统计学意义），且胰岛素与血糖的变化负相关，从标准化回归系数看出，糖化血红蛋白（=0.398）对空腹血糖影响最大。VII.Logistic回归分析PPT例16-2为了探讨冠心病发生的有关危险因素，对26例冠心病病人和28例对照者进行病例-对照研究，各因素的说明及资料见表16-2和表16-3。试用logistic 逐步回归分析方法筛选危险因素。(入=0.01，出=0.15)表16-2 冠心病8个可能的危险因素与赋值表16-3 冠心病危险因素的病例-对照调查资料Variables not in the EquationScoredfSig.Step 0Variablesx15.7891.016x25.9681.015x34.7471.029x44.3111.038x57.4601.006x610.1171.001x75.2441.022x86.8181.009Overall Statistics25.4188.001Variables in the EquationBS.E.WalddfSig.Exp(B)Step 1ax62.8261.0956.6571.01016.875Constant-.523.3152.7511.097.593Step 2bx51.828.6807.2271.0076.219x63.0591.1447.1431.00821.303Constant-1.281.4617.7151.005.278Step 3cx51.722.7145.8141.0165.597x63.0281.1766.6271.01020.656x81.663.7854.4931.0345.277Constant-2.359.7709.3781.002.095Step 4dx1.924.4773.7581.0532.519x51.496.7444.0441.0444.464x63.1351.2496.3031.01223.000x81.947.8475.2891.0217.008Constant-4.7051.5439.2951.002.009a. Variable(s) entered on step 1: x6.b. Variable(s) entered on step 2: x5.c. Variable(s) entered on step 3: x8.d. Variable(s) entered on step 4: x1.logitP=-4.705+0.924X1+1.495X5+3.135X6+1.947X8最终进入模型的危险因素有4个（P值均小于0.05），它们分别是年龄(X1)：OR=2.519，高血脂史（X5）：OR=4.464，动物脂肪摄入量（X6）：OR=23.000，A型性格（X8）：OR=7.008。VIII.生存分析例17-4据例17-1和例17-2的资料，问甲种手术方式后和乙种手术方式后病人的其生存率有无差别？1.建立假设检验，确立检验水准H0:S1(t)=S2(t)，两种手术方式的患者生存率相同H1:S1(t)S2(t)，两种手术方式的患者生存率不同=0.052. 运用Kaplan-Meler法进行log-rank检验，比较两组的生存率Case Processing SummarygroupTotal NN of EventsCensoredNPercent甲种手术1811738.9%乙种手术141400.0%Overall3225721.9%Survival TablegroupTimeStatusCumulative Proportion Surviving at the TimeN of Cumulative EventsN of Remai