LIFE TABLE

LIFE TABLE implements the actuarial life-table method for calculating cumulative survival and mortality probabilities across user-defined time intervals. The program accepts inputs for the number of intervals and enrolled subjects, then iterates through each interval collecting counts of “lost” (withdrawn or censored) and “dead” (event) subjects. For each interval it computes the effective exposure (number entered minus half the lost, a standard actuarial adjustment: EX = EN − L×0.5), the proportion dead, proportion surviving, and the cumulative chance of survival using the product-limit approach (multiplying successive interval survival proportions). Results are displayed in a formatted multi-section screen layout using AT-addressed PRINT statements, with values rounded to three decimal places via the INT((x + 0.0005)×1000)/1000 idiom.

---

Program Structure

The program divides into four logical phases:

1. Introduction (lines 10–160): Sets display attributes, prints multi-screen explanatory text about the life-table method, and uses a GO SUB 540 pause-and-clear routine between screens.
2. Data entry preamble (lines 170–210): Collects the total number of intervals (IN) and the initial number of subjects entered (EN).
3. Screen layout (lines 220–300): Prints three labeled column-header blocks at fixed screen positions using AT to create a persistent dashboard for interval-by-interval results.
4. Interval loop (lines 310–530): A FOR N=1 TO IN loop processes each interval, collecting lost (L) and dead (D) counts, computing statistics, and updating the screen in-place.

Key Variables

Variable	Role
IN	Total number of time intervals
EN	Number of subjects entering current interval
L	Number lost/withdrawn in current interval
D	Number of events (deaths) in current interval
EX	Effective exposure: EN − L×0.5
PD	Proportion dead (interval mortality rate)
PSN	Proportion surviving this interval
PSO	Cumulative survival probability (carried forward)
CCS	Updated cumulative survival: PSO × PSN

Actuarial Method

The program faithfully implements the standard life-table (Kaplan–Meier-adjacent) technique. The effective exposure calculation at line 390 — EX = EN − L × 0.5 — applies the actuarial assumption that censored subjects (lost or withdrawn) contribute, on average, half an interval of observation. The interval mortality proportion is PD = D / EX, and cumulative survival is the running product of interval survival fractions (PSN = 1 − PD), accumulated in PSO/CCS. Cumulative mortality is derived as 1 − CCS and expressed as a percentage at line 490.

Rounding Idiom

Results are rounded to three decimal places using the classic BASIC idiom at lines 410 and 470:

INT((x + 0.0005) × 1000) / 1000

This is a standard technique to work around the absence of a built-in rounding function, adding half a unit in the last place before truncating with INT.

Screen Layout Technique

Rather than scrolling output, the program establishes three fixed display regions (rows 3–4, 11–12, 19–20) for interval header, per-interval statistics, and cumulative statistics respectively. All dynamic values are written with PRINT AT row, col;, allowing results to update in-place for each interval without redrawing the column headers. Trailing spaces (e.g., ;" " or ;" ") are used to overwrite stale digits from previous iterations — a common technique where a CLEAR or CLS would destroy the persistent header layout.

Note that PI (approximately 3.14159) is used as a row argument in several PRINT AT PI, col calls (lines 320–380, 400–440, 510). The interpreter truncates it to integer 3, so these statements all address row 3. Similarly, line 110 uses PRINT AT 5, PI, addressing column 3. This is an unconventional but functional shorthand for the integer 3.

Subroutine

Line 540 is a utility subroutine called three times (lines 50, 100, 210) that prints a prompt on the lower channel (PRINT #0), waits for a keypress with PAUSE 0, clears the screen, and returns. This is an efficient use of a single routine for all inter-screen transitions.

Notable Anomalies

• Line 510 contains PRINT AT PI,21;" "; AT PI,30, — the trailing comma after 30 is unusual syntax; it may set a print position without printing anything, effectively just repositioning the cursor, which is harmless but redundant given the next iteration immediately overwrites that area.
• IN is used as a variable name. While legal, it closely resembles the keyword INPUT (though the interpreter disambiguates by tokenization), and could cause confusion when reading the listing.
• The STOP at line 530 halts execution after the loop rather than returning to a menu or offering a restart, leaving the user at a break prompt.
• Line 560 saves the program with LINE 10, causing it to auto-run from line 10 on load.