Nelson-Aalen Analysis

Nelson-Aalen Analysis is part of:

  • Life Survival analysis software

  • System configuration

    • Windows:
      • Versions: 9x/Me/NT/2000/XP/Vista/Win 7
      • Excel: 97 and later
      • Processor: 32 or 64 bits
      • Hard disk: 150 Mb
    • Mac OS X:
      • OS: OS X
      • Excel: X, 2004 and 2011
      • Hard disk: 150Mb.

Benefits

  • Easy and user-friendly
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  • Data and results shared seamlessly
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    Modular XLSTAT is a modular product. XLSTAT-Pro is a core statistical module of XLSTAT which includes all the mainstream functionalities in statistics and multivariate analysis. More advanced features contained in add-on modules can be added for specific applications. This way you can adapt the software to your needs making the software more cost-efficient.
  • Didactic
    Didactic The results of XLSTAT are organized by analysis and are easy to navigate. Moreover useful information is provided along with the results to assist you in your interpretation.
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  • Accessible - Available in many languages
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What is the Nelson-Aalen analysis

The Nelson-Aalen analysis method belongs to the descriptive methods for survival analysis such as life table analysis and Kaplan-Meier analysis. The Nelson-Aalen approach can quickly give you a curve of cumulative hazard and estimate the hazard functions based on irregular time intervals.

Nelson-Aalen analysis is used to analyze how a given population evolves with time. This technique is mostly applied to survival data and product quality data. There are three main reasons why a population of individuals or products may evolve: some individuals die (products fail), some other go out of the surveyed population because they get healed (repaired) or because their trace is lost (individuals move from location, the study is terminated, among other causes) The first type of data is usually called "failure data" or "event data", while the second is called "censored data".

Censoring of survival data for the Nelson-Aalen analysis

Censoring types for the Nelson-Aalen analysis

There are several types of censoring of survival data:

Independent censoring for the Nelson-Aalen method

The Nelson-Aalen method requires that the observations are independent. Second, the censoring must be independent – if you consider two random individuals in the study at time t-1, and one of the individuals is censored at time t, while the other survives, then both must have equal chances to survive at time t.

There are four different types of independent censoring:

Nelson-Aalen method and the cumulative hazard function

The Nelson-Aalen analysis allows comparing populations, through their hazards curves. Nelson-Aalen estimator should be preferred to Kaplan-Meier estimator when analyzing cumulative hazard functions. When analyzing cumulative survival functions, Kaplan-Meier estimator should be preferred.

The cumulative hazard function is:

H(T) = ΣTi≤T di/ri

with di being the number of observation falling at time Ti and ri, the number of observation at risk (still in the study) at time Ti.

Variances for the cumulative hazard function

Several different variance estimators are available:

Confidence interval for the cumulative hazard function

Confidence intervals can also be obtained:

The second one will be preferred with small samples.

XLSTAT results for the Nelson-Aalen analysis

Nelson-Aalen table

This table displays the various results obtained from the analysis, including:

Charts for the Nelson-Aalen analysis

Depending on the selected options, up to three charts are displayed:

Test of equality of the survival functions

This table displays the statistics for three different tests:

These tests are based on a Chi-square test. The lower the corresponding p-value, the more significant the differences between the groups is.

Tutorials

Screenshots