# SURVIVAL ANALYSIS: KAPLAN MEYER METHOD/LOG RANK TEST

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## Multidimensional analysis: Clustering et classification

Clustering is a multidimensional and descriptive analysis. To represent the multimorbid population: Patients with similar characteristics were classified into homogeneous groups irrespective of their status at 21 months. Subsequently, a measure of dissimilarity with the calculation of the Euclidean distance and a hierarchical grouping using the Ward method was practiced. Then, these results led to the creation of a classification tree called cluster dendrogram to examine the hierarchy of groups.
Subsequently, for each group, carrying out a multiple correspondence analysis (MCA) allowed the identification of the discriminating variables. Finally, clustering and their projection on factorial designs was possible through the use of hierarchical clustering on the principal components (HCPC). Qualitative and quantitative variables were applied for each group.

### Survival analysis

The patients did not all decompensate at the same time. Thus, time had to be taken into account for the survival analysis. The evaluation of the additional risk brought by the exposure to a risk factor while studying the probability of decompensation at any time of the follow-up was possible by a regression following the model of Cox. Survival curves for groups « D » and « NTR » were performed using the Kaplan-Meir method, a non-parametric estimate evaluating the survival function. A univariate analysis with a log-rank test with a p-value of 0.05 was performed in order to know if the two groups were significantly different. Then, the undefined risk ratios (HR) and their 95% confidence intervals (CI) (univariate analysis) were calculated by a semi-parametric evaluation using the Cox method). They were defined by the association between a variable and the risk factor of decompensation, taking into account the time. Subsequently, to produce the adjusted HR (multivariate analysis) and their 95% CI, a second model of Cox was produced. The association between a variable and the decompensation risk factor after adjustment for other variables represents adjusted HR. The goal was to dodge the confounding factors. At the end, the verification of the proportional hazards hypothesis defined by the Cox model was carried out by a Chi 2 test allowing, thus, a control of the final model.

#### Cleaning and recording data:

Data cleaning was performed, using the dictionary (Appendix No. 3), to find and delete some non-discriminating variables. The deletion concerned the following variables: pharmacological treatment (yes), stress at work (no), human help (yes), equipment for the patient at home (yes).Birth has been changed in age. The deletion also involved some unnecessary variables: inclusion date and patient identification number. Then, the variables related to the quality of the management of multimorbidity and the self-evaluation (intuition, good communication with other caregivers, coordination procedures, etc.) of the GP were removed (questions 26, 29, 30, 34, 45-52). The challenge was to confront groups with characteristics.

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Clustering and Classification :

The ascending hierarchical classification began the multidimensional analysis. Each patient was initially singularly taken. The patients were grouped by some characteristics, using the measure of dissimilarity, according to the Euclidean distances. Then, hierarchical groups were realized thanks to the integration of the distance between each patient for each characteristic. This led to a cluster dendrogram or cluster dendrogram (Figure 1).

I- INTRODUCTION
II- MATERIEL AND METHOD
1- STUDY DESIGN
2- STUDY POPULATION
A- INCLUSION CRITERIA
B- EXCLUSION CRITERIA
C- FP’S RECRUITMENT:
3- STUDY PROCESS
4- JUDGMENT CRITERIA
5- PATIENTS’ STATUS COLLECTION
6- DATA CLEANING
7- STATISTICAL ANALYSIS
A- CLEANING AND RECODING DATA
B- MULTIDIMENSIONAL ANALYSIS: CLUSTERING ET CLASSIFICATION
C- SURVIVAL ANALYSIS
8- ETHICS
III- RESULTS:
1- STUDY POPULATION:
2- STATUS AT TWENTY-ONE MONTHS :
3- CLEANING AND RECORDING DATA:
4- CLUSTERING AND CLASSIFICATION :
A- CLUSTER 1
B- CLUSTER 2
C- CLUSTER 3
5- SURVIVAL ANALYSIS:
A- SURVIVAL ANALYSIS: KAPLAN MEYER METHOD/LOG RANK TEST
B- UNI AND MULTIVARIATE ANALYSIS: REGRESSION FOLLOWING COX’S MODEL
C- COX’S MODEL VALIDITY:
VI- DISCUSSION
1- INTERPRETATION OF RESULTS:
2- ANALYSIS OF THE DIFFICULTIES ENCOUNTERED :
A- LOW NUMBER OF PATIENTS INCLUDED:
B- RELEVANCE OF CERTAIN ITEMS OF THE QUESTIONNAIRE:
C- SUBJECTIVITY OF THE QUESTION « EXPERTISE OF THE GP »:
D- CLASSIFICATION OF CHRONIC DISEASES
E- STATISTICAL ANALYSIS :
F- DATA TRANSMISSION
3- LIMITS OF STUDY :
A- SELECTION BIAS :
B- INFORMATION BIAS :
C- CONFUSION BIAS :
4- FUTURE PROSPECTS:
IV- CONCLUSION
BIBLIOGRAPHIE

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