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How to solve the problem of repeated measurement in medical analysis

repeated measurements is a very common situation in the medical field. With tested products: Volume refers to the repeated measurement of the same measurement index or the same group of measurement indexes of the same research object at different time points, so as to analyze the change characteristics of measurement indexes with time. Such measurement data are common in clinical and epidemiological studies. For example, in order to study the therapeutic effect of various new drugs on patients with hypertension, it is necessary to measure the blood pressure of the subjects at the time points of one hour, two hours, four hours, six hours, etc. after taking the medicine, so as to analyze the changes of their blood pressure. Medical research is one of the most applied fields of statistical analysis methods, and statistical analysis methods can also help solve the above problems

at a glance, many people may think that using t-test or analysis of variance as the difference test at each measurement time point can better solve the above problems. But in fact, such a processing method is wrong, and it is likely to draw the conclusion that the error is the acquisition of the signal. The reason is that there is a prerequisite for the application of traditional t-test or analysis of variance, that is, the independence of data, while repeated measurement data in the medical field often have a high degree of correlation. For example, Zhang San's diastolic blood pressure is 90 two hours after taking the medicine, so his diastolic blood pressure is likely to be around 90 four hours later, which will not be too far away. This is the correlation between the data. If Li Si is tested at this time, his diastolic blood pressure may be any value between 70 and 110, because this value has nothing to do with Zhang San's diastolic blood pressure two hours later. Therefore, when the preconditions of t-test or ANOVA are destroyed, we must use a new statistical analysis method - repeated measurement ANOVA to correct the original results. At this time, we must rely on advanced statistical analysis software. In the following analysis, which is more intuitive, simple and safe, we will rely on the global high-end Six Sigma quality management software JMP. By the way, JMP software is a global high-end statistical analysis software specifically for Six Sigma and quality management. It is one of the professional statistical software designated by FDA (American food and Drug Administration). It has been used for quality improvement and drug research and development by most well-known pharmaceutical companies in the world. Its customers include Bayer, Roche, Lilly, Novo Nordisk, AstraZeneca, Pfizer, GlaxoSmithKline, Weicai pharmaceutical, Takeda pharmaceutical Sanofi Aventis, etc

generally speaking, the analysis of variance of repeated measurements can be divided into three main steps:

first, the sphericity test

the sphericity here refers to the sphericity of the covariance matrix, that is, the main diagonal elements (variance) of the matrix are equal, and the non main diagonal elements (covariance difference) are zero. The sphericity is usually tested by Mauchly's method. When the sphericity is not satisfied, the numerator and denominator degrees of freedom of time-dependent F statistics must be adjusted in order to reduce the probability of making the first kind of errors

second, variance decomposition and F-test

the concept of variance decomposition and F-test is believed to be understood by everyone. However, unlike traditional variance analysis, the error structure of repeated measurement data is divided into two levels: one level of error comes from measurements at different time points, and the other level of error comes from different observation objects. The error of each layer may be related to several explanatory variables, thus forming a relatively complex error structure. Generally, errors from different observation pairs are used to test inter group effects (such as different drugs), and errors from different time points are used to test intra group effects (such as different times) and the interaction between inter group effects and intra group effects

third, draw a contour map

in addition to quantitative analysis, you can also use visual methods (such as contour map) to draw the change curve of measurement indicators at different levels of inter group variables and different measurement time points (see the following for the specific form), so as to reflect the significance of inter group effects and the trend of indicators over time. The measurement interval can be equidistant or unequal

next, a typical biomedical example is used to explain the whole process of "repeated measurement analysis of variance". When specific statistical calculations are involved, JMP is used. The reason for adopting JMP is to ensure the authority of analysis on the one hand; On the other hand, the following functions are not available in other similar software; In addition, JMP has great advantages over similar software in terms of visualization and analysis ability of analysis results

case analysis

a pharmacokinetic study aimed at comparing the metabolic rate of different dosage forms of a drug in the body. The dosage forms are divided into capsule type and tablet type. 16 subjects were randomly divided into two groups, with 8 in each group. One group was given capsules and the other group was given tablets. The drug concentration in blood was measured 1 hour, 2 hours, 4 hours, 6 hours and 8 hours after taking the drug. The measurement results are shown in Figure 1 below. Try to choose an appropriate mathematical statistical method for analysis

figure I concentration of two different dosage forms of a drug in blood (ug/ml)

first, perform the spherical test of Mauchly's method. From the calculation results shown in Figure 2, the corresponding p value is only 0, Far less than 0.01, obviously dissatisfied with football symmetry. Therefore, in the following analysis of variance, the degree of freedom of intra group effects must be adjusted with the adjustment coefficient epsilon

results of sphericity test in Figure 2

secondly, variance decomposition and F test are carried out. Since the spherical symmetry is not satisfied, the inspection result should be subject to the corrected result, that is, the part marked with red box in Figure 3. Statistical inference: the difference between blood concentrations of different dosage forms of drugs is not significant (P value =0.0645), and the difference between blood concentrations at different times is significant (P value

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