506 Assignment 13 CT

Introduction

The data provided by clinical studies are expressed multiple times in terms of survival. This measure is not limited to the terms of life or death, but to situations in which the time elapsed until an event of interest occurs, such as recurrence time, duration of the effectiveness of an intervention, time of particular learning among others. Therefore, survival is a measure of time to a response, failure, death, relapse or development of a specific disease or event. The term survival is due to the fact that the death of a patient was used as an event in the first applications of this method of analysis. Survival analysis consists of a set of techniques to analyze the follow-up time until the occurrence of an event of interest. The null hypothesis of this is study states that H0 the risk of dying is not related to the patient treatment group, while the alternative hypothesis postulates that H1 the risk of dying is related to the patient treatment group.

Discussion

To carry out the Kaplan-Meier analysis, it is necessary to define the start and the date of completion of the follow-up, with which the times of patient survival. Thus, depending on the type of study and design, the date of commencement of monitoring is usually the diagnosis of illness, hospital admission, initiation of treatment, among others. The end date is predetermined by the researcher, depending on the type of data analyzed (Guyot et al., 2012). During this period, the follow-up -of the patients is individual, and he may die, continues alive on the date of completion of the study, or loses contact with him at a certain time. The last two situations represent what are called censored data (Miller Jr, 2011). The survival time is then defined as the time from the date of commencement of follow-up to date of the last contact with the patient, either because they died well-being censored. Different procedures allow estimating survival curves, although perhaps one of the most popular in clinical research is the Kaplan-Meier method. It is a non-parametric method, with very few restrictions (Lacny et al., 2015). The only thing that it supposes is that the censored subjects would have behaved in the same way as those followed until the event occurred (what is known as “non-informative censorship. To apply this method, all the observed survival times are ordered from lowest to highest, recording for each of them the number of deaths and censures produced (Goel, Khanna & Kishore, 2010). The probability of survival is calculated for each period, and the Kaplan-Meier function is “the probability of accumulated individual survival at overtime”. The statistical program automatically does these steps.

In the table above, the column on the left (Time) is the time during which the different individuals are being monitored, ordered by increasing times. The second column (Status) indicates whether the effect or outcome has been evaluated or not. The "censorship" value appears, which corresponds to the lost or withdrawn during the follow-up, and those who at the end of the study period still did not have the event, that is, we're alive. The next column (Cumulative survival) is cumulative survival or proportion of cases for which the event has not taken place at each time. The next column (Standard error) is the standard error corresponding to the Kaplan-Meier point estimate at each time. The fifth column (Cumulative events) are the cumulative outcomes, that is, those that have died until that time. The last column (Number remaining) is the number of subjects that remain at each moment without the final event or outcome being evaluated, and they represent the individuals that “are at risk in the next period.”

Then the excel program gives information about the total number of subjects evaluated (Number of cases), the number of censored (Censored), and the number of outcomes (Events). If marked, it will give the values ​​of the average survival time and the median survival time with their corresponding standard errors and confidence intervals to 95%, indicating that the study is limited by the maximum period of follow-up, as shown in the table above. Then it shows us the Survival Curve, a graph that can be modified by placing it on it with the left mouse button (edit). In it, the accumulated survival in terms of probability (between 0 and 1), and the survival time on the abscissa axis.

There were no differences regarding the cases under study, and the Log-rank test establishes that there is no statistical significance for that variable at a significance level of 0.05 (p = 0.09> 0.05). The 95% confidence interval for relative risk (RR) confirms this result and also brings more information than the p-value alone. This interval calculated between the groups. Survival medians indicate that 50% of the grafts survived. On the other hand, there were fewer deaths observed, and the RR confidence intervals allowed comparing the groups and verifying that there was a lower risk of death. This was corroborated using the Log-Rank test (p = 0.0005 <0.05). since the p-value is greater than the significant value, the null hypothesis should be accepted.

In the graph above is the classic survival curve (stel et al., 2011), which shows how survival decreases over time. To demonstrate whether two or more survival curves are different, the Log-Rank test was used to perform hypothesis tests, which assumes no particular distribution of the survival function. In the Kaplan-Meier Model, survival curves and confidence intervals of relative risk confirm the results of the Log-Rank test. In the Cox Model, in all cases, the Deviance test and the inclusion or not of the one within the RR confidence intervals corroborated the results of the Wald test. In this case, the multiple regression analysis and the selection of variables using the step-by-step method did not obtain information other than that obtained in the univariate analyses.

Conclusion

The Kaplan-Meier Model was feasible to be applied and interpreted their results under similar conditions because the explanatory variables considered only discrete values ​​since they come from a design of experiments. In the case of the consideration of continuous explanatory variables, the Kaplan Meier model makes it necessary to create categories that include ranges of values ​​to compare between categories. However, the use of each technique depends on the objectives pursued by the researcher.

References

Guyot, P., Ades, A. E., Ouwens, M. J., & Welton, N. J. (2012). Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC medical research methodology, 12(1), 9.

Lacny, S., Wilson, T., Clement, F., Roberts, D. J., Faris, P. D., Ghali, W. A., & Marshall, D. A. (2015). Kaplan-Meier survival analysis overestimates the risk of revision arthroplasty: a meta-analysis. Clinical Orthopaedics and Related Research®, 473(11), 3431-3442.

Miller Jr, R. G. (2011). Survival analysis (Vol. 66). John Wiley & Sons.

Stel, V. S., Dekker, F. W., Tripepi, G., Zoccali, C., & Jager, K. J. (2011). Survival analysis I: the Kaplan-Meier method. Nephron Clinical Practice, 119(1), c83-c88.

Survival distribution function

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