Go to SWOG Web site   Expected Deaths on a Study

Introduction

This program calculates the expected number of deaths for a planned study. The program assumes uniform accrual and exponential survival. It allows the user to specify a follow-up period after the close of study accrual. The program default presents a table of results. Alternatively, user can calculate the expected proportion of deaths at a given time, or the time at which a given proportion of deaths have occurred. The program will allow the user to specify a percentage of patients that have no risk ('Cures').

Program Code

The program is written in JavaScript.

Input

Follow-up Time: Enter the number of years between the last patient accrual to the time of the final analysis.

Accrual Time: Enter the number of years of patient accrual.

Sample Size: Enter n, the planned sample size.

Hazard rate: Enter l, the exponential death rate.

Survival probability and time(default): Enter a time, t (in years), and the probability of patients alive at that time, S(t). The program will calculate l as follows.

l=-1n(S(t))/t

Percentage of patients cured: A number between 0 and 1.

Calculation of the Expected Number of Deaths

Probability of death at analysis time is

P(death|Analysis time t)=1 - e(-l*follow)*(1-e(-l*accrual))/l*accrual).

At times before accrual has completed

P(death|t) =(l-1e(-l t) + t - l-1)/accrual.

At other times

P(death|t) = 1 - e(-l (t-accrual))*(1-e(-l*accrual))/(l*accrual).

The survival density f(t) is assumed to be exponential with rate l and cure rate p, i.e.,

f(t)=(1-p)(l)e(-lt)

Output

There are three options for calculations. The default option is a table of results in new page. The second and third options provide expected deaths for a given time, or time at which the expected proportion of deaths have occurred.


Back to Expected Death program.