Censored on right and left Hazard plotting also applies to data censored on the left. Just multiply all data values by - 1 to get reversed data censored on the right, and plot that data. Data below from Sampford and Taylor (1959) are multiply censored on the right and the left. Mice were paired, and one of each pair got injection A and the other got injection B. For each pair, the difference of their log days of survival appears below. However, observation terminated after 16 days. When one mouse of a pair survives, one knows only that the difference is greater (less) than that observed. There are three such differences in the data: -0.25- and -0.18- censored on the left and 0.30t censored on the right. The differences for the 17 pairs are -0.83, -0.57, -0.49, -0.25-, -0.18-, -0.12, -0.11, -0.05, -0.04, -0.03, 0.11, 0.14. 0.30, 0.30+, 0.33, 0.43, 0.45.
(a) Calculate hazard plotting positions for all observed differences above -0.18 - . Note that the sample size is 17, not 12. Convert these cumulative hazard values to cumulative probabilities by means of the basic relationship (3.3)
(b) Reverse the data and calculate hazard plotting positions for all reversed observed differences above - 0.30 -
(c) Reversing the data reverses the probability scale. Convert the two sets of hazard plotting positions to consistent probability plotting positions.
(d) Plot all observed differences on normal probability paper. Normal paper is used because the distribution of log differences is symmetric about zero if injections A and B have the same effect
(e) Does the mean difference differ significantly from zero, corresponding to no difference between the injections? Assess this subjectively
(f) Graphically estimate the mean and standard deviation of the distribution of differences.