Avoid TOCTOU (time-of-check, time-of-use) race condition between stat and rename

How to avoid TOCTOU(time-of-check, time-of-use) race condition for race condition between stat and rename for LOGFILE ?

Required to move the log file after its size value exceeds the max size.

result = stat(LOGFILE, & data);
if (result != 0) {
  // stat failed
  // file probably does not exist
} else if (data.st_size > MAX_LOGSIZE) {
  unlink(PREV_LOGFILE);
  (void) rename(LOGFILE, PREV_LOGFILE);
}