Use this Aalen estimator tool to calculate non-parametric cumulative hazard estimates for survival data.

## Aalen-Johansen Estimator Calculator

This calculator estimates the cumulative hazard function using the Aalen-Johansen estimator.

### How to Use

1. Enter the time points as a comma-separated list in the “Time Points” field.

2. Enter the number of events at each time point as a comma-separated list in the “Number of Events” field.

3. Enter the number of subjects at risk at each time point as a comma-separated list in the “Number at Risk” field.

4. Click the “Calculate” button to compute the cumulative hazard.

### How it Calculates

The Aalen-Johansen estimator computes the cumulative hazard by summing the hazard increments over time. Each hazard increment is calculated as the ratio of the number of events to the number of subjects at risk at each time point.

### Limitations

This calculator assumes that the input data is properly aligned and that the number of elements in each input field is equal. It does not handle missing values or data points with zero subjects at risk.

## Use Cases for This Calculator

### Calculating Aalen Estimator for Survival Analysis

To calculate the Aalen estimator for survival analysis, you gather data on the duration of time until an event of interest occurs, such as death or failure.

### Accounting for Time-Varying Covariates

When using the Aalen estimator, you can account for time-varying covariates by updating the estimates at each event time using the available data.

### Handling Censored Observations

Censored observations can occur when the event of interest has not yet happened by the end of the study. The Aalen estimator handles censored data appropriately to provide accurate estimates.

### Interpreting Hazard Ratios

The Aalen estimator allows you to interpret hazard ratios, which indicate the relative risk of experiencing the event of interest based on different covariate values.

### Comparing Survival Curves

With the Aalen estimator, you can compare survival curves for different groups or covariate values to understand how these factors influence the time to the event of interest.

### Modeling Time-to-Event Data

The Aalen estimator is useful for modeling time-to-event data, such as the time until a medical treatment fails or the duration until a machine breaks down.

### Assessing Survival Probabilities

Using the Aalen estimator, you can assess survival probabilities at various time points to understand the likelihood of not experiencing the event of interest up to a certain time.

### Handling Multiple Events

When dealing with multiple events of interest, the Aalen estimator can be adapted to handle competing risks to provide accurate estimates for each event type.

### Adjusting for Confounding Variables

The Aalen estimator allows you to adjust for confounding variables that may influence both the covariates and the event of interest, improving the accuracy of the estimates.

### Validating the Model

After calculating the Aalen estimator, you can validate the model by assessing its goodness of fit and checking assumptions to ensure that the estimates are reliable and meaningful.