1. Case introduction
Fifteen patients with basically the same surgical requirements were randomly divided into 3 groups, and three anesthesia induction methods A, B, and C were used during the operation, and the patients were measured at T0 (before induction), T1, T2, T3, and T4. systolic blood pressure, try analysis of variance.
2. Problem Analysis
It can be obtained from the case that the data includes both the group, the measurement time, and the intersection of the group and the measurement time, so consider using the repeated measurement variance for two-factor multi-level analysis. For the variance analysis of the repeated measurement experimental data, two factors need to be considered Influence, one is the treatment group, which is generally experimented by random grouping, and the other is the measurement time, which needs to be determined by researchers based on professional knowledge and research cases. The case is analyzed next.
3. Software operation and result interpretation
(1) Data import
1. Data format
The special feature of repeated measurement variance data is that ID numbers, such as case numbers, etc., and time point data are required. The same ID (case) will have multiple data at different time points, such as 15 samples with 5 identical measurements At the time point, if there are 5 samples in one sample, then there will be 15*5=75 rows of data. The data format is as follows:
2. Import data
Upload the organized data to the SPSSAU system as follows:
The upload results are as follows:
(2) Judgment of applicable conditions
Like most analyses, some tests are generally required before the analysis. Repeated measurement variance needs to check whether the data has outliers and whether the dependent variable satisfies a normal distribution.
1. Outliers
Outliers analyze abnormal values in data, also known as outliers. There are many methods for testing outliers, such as descriptive statistics (generally considered to be data outside 3 times the standard deviation), or box plots, etc. Descriptive statistics are used here for judgment. Using SPSSAU to describe the analysis, the results are as follows:
From the above results, we can see that there are 75 samples in total, the minimum value is 108, the maximum value is 148, the average value is 124.12, and the standard deviation is 8.46. It can be roughly judged that there are no outliers. Next check to see if the dependent variable satisfies a normal distribution.
2. Normal distribution
There are many ways to judge whether the data conform to the normal distribution, such as normality test (the most stringent), descriptive statistics (check skewness and kurtosis), and graphical methods, etc. Here, the descriptive statistics method is used for judgment.
Generally, the absolute value of kurtosis is less than 10 and the absolute value of skewness is less than 3, which means that although the data is not absolutely normal, it is basically acceptable as a normal distribution. [References: Kline R , Kline RB , Kline R . Principles and Practice of Structural Equation Modeling[J]. Journal of the American Statistical Association, 2011, 101(12).】
From the results, the kurtosis is 0.37, and the skewness is 0.677. It can be judged that the data can be accepted as a normal distribution.
(3) Repeated measures analysis of variance
- Software operation
The analysis path of repeated measurement variance is to click [Experimental Medicine/Research] → [Repeated measurement variance] and then analyze:
- Interpretation of results
The data satisfies the analysis conditions, and then the repeated measurement variance is performed, and the sphericity test is explained first.
It can be seen from the sphericity test that the p value is less than 0.05, so the p value needs to be corrected if it fails the sphericity test. Next, check the sphericity W value. If the W value is less than 0.75, use GG correction, otherwise use HF correction, so use GG correction. [Special reminder: If the p value of the sphericity test is greater than 0.05, the p value does not need to be corrected if the test is passed. If the p value is less than 0.05, the p value needs to be corrected if the sphericity test is not passed. Next, look at the sphericity W value. If the w value If it is less than 0.75, use GG correction, otherwise use HF correction].
Analysis of within-group effects
According to the sphericity test, it is found that the p-value does not need to be corrected. From the above table, it can be seen that there are two effects, the main effect (time point) and the second-order effect (interaction effect, drug type-time point), and the p-value of the main effect is found If it is less than 0.05, it is significant at the 0.05 level, and the second-order effect is also significant, which can be further analyzed in the analysis, such as post-hoc multiple comparisons and simple effects. Not explained here. The final result is as follows:
1. Mean square (effect)
square sum SS (effect)/df (effect), for example: 1155433.080/1=1155433.08;
2. Mean square (error)
square sum SS (error)/df (error), for example: 946.480/12=78.873;
3. F
F value = mean square (effect) / mean square (error), for example: 1155433.080/78.873=14649.223;
4. P
The P value is obtained from the F value.
5. ges (generalized eta-squared)
square sum SS (effect)/[square sum SS (effect) + square sum SS (within error group) + square sum SS (error group)], for example: 1155433.08/(1155433.08+ 946.48+263.12)=0.999;
6. Partial Eta side
Partial Eta square = square sum SS (effect)/[square sum SS (effect) + square sum SS (error)], for example: 1155433.080/(1155433.080+946.480)=0.999;
4. Conclusion
Repeated measures analysis of variance was performed on the case data. Firstly, it was sorted into the correct data format, and then the data was checked to see whether the relevant test was met before analysis. Then, the data was analyzed. The analysis results showed that the data met the sphericity test and found that there was no need to correct the p value, and the two The two effects are the main effect (time point) and the second-order effect (interaction effect, drug type-time point), and the p-value of the main effect is found to be less than 0.05, which is significant at the 0.5 level, and the second-order effect is also significant. It shows that different time points and anesthesia induction methods have a significant impact on systolic blood pressure.
5. Knowledge Tips
1. What if there are missing data?
Repeated measurement variance requires balanced data, that is, there can be no missing data. For example, if there are 12 subjects and each subject repeats 3 times, there must be 12*3=36 rows of data; if there is missing data for a subject, Then the subject can be screened out; the data can also be filled first (usually using the average value) and then analyzed.
2. What does the ID value of the repeated measurement variance mean?
The ID of the repeated measurement variance refers to the ID of the research object. For example, if there are 100 patients and the measurement is repeated 4 times, then the data has a total of 400 rows, but the ID is from 1 to 100, and each ID needs to be repeated 4 times.
3. How to analyze the unbalanced data if the repeated measurement variance is unbalanced?
If the data is unbalanced during the repeated measurement analysis of variance, then the remaining two analysis methods can be selected for research, namely the HLM model (HLM in medical research) and the generalized estimating matrix GEE (generalized estimating equation in medical research).