Clinical-Pathologic Conference: Use and choice of statistical methods for the clinical study, “Superficial adenocarcinoma of the esophagus”  Eugene H.

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Clinical-Pathologic Conference: Use and choice of statistical methods for the clinical study, “Superficial adenocarcinoma of the esophagus”  Eugene H. Blackstone, MDa,b, Thomas W. Rice, MDa  The Journal of Thoracic and Cardiovascular Surgery  Volume 122, Issue 6, Pages 1063-1076 (December 2001) DOI: 10.1067/mtc.2001.119858 Copyright © 2001 American Association for Thoracic Surgery Terms and Conditions

Drs Rice and Blackstone The Journal of Thoracic and Cardiovascular Surgery 2001 122, 1063-1076DOI: (10.1067/mtc.2001.119858) Copyright © 2001 American Association for Thoracic Surgery Terms and Conditions

Fig. 1 Relation of an unlimited scale of risk, here expressed in logit units, to the probability of occurrence of an event. The logistic equation mapping logit units to probability is shown. ln, Natural logarithm. The Journal of Thoracic and Cardiovascular Surgery 2001 122, 1063-1076DOI: (10.1067/mtc.2001.119858) Copyright © 2001 American Association for Thoracic Surgery Terms and Conditions

Fig. 2 Cumulative distribution of age at operation for superficial adenocarcinoma of the esophagus. Each patient's age is represented on the curve from youngest to oldest. Each unique age value increments to the curve by 1/n, where n is the total number of patients. Notice that 50% of the patients were younger than 64.5 years and 50% were older. This is the median age, expressed by horizontal and vertical solid straight lines. The coarse dashed lines enclose the 25th and 75th percentiles (or quartiles ), meaning that 25% of patients were younger than the 25th percentile and 75% were younger than the 75th percentile. For consistency with the standard deviation, which encloses about 70% of the ages, the 15th and 85th percentiles (15% of ages above and 15% below) are shown by fine dashed lines. The Journal of Thoracic and Cardiovascular Surgery 2001 122, 1063-1076DOI: (10.1067/mtc.2001.119858) Copyright © 2001 American Association for Thoracic Surgery Terms and Conditions

Fig. 3 Histogram of age and superimposed Gaussian distribution curve. Ages of patients have been categorized and counted in 5-year intervals. The smooth curve is a parametric summary of the distribution of age, expressed as the mean (the vertical line at the peak of the curve) and standard deviation (enclosed by the finely dashed vertical lines ). It is questionable whether the mean and standard deviation represent the distribution of these ages well; yet the Gaussian distribution is often used in this setting because of tradition or ease of calculation. On the other hand, notice that the mean on this figure and median on Figure 2 are similar; the ages enclosed within ±1 standard deviation of this figure are similar to those within the 15th and 85th percentiles of Figure 2. The Journal of Thoracic and Cardiovascular Surgery 2001 122, 1063-1076DOI: (10.1067/mtc.2001.119858) Copyright © 2001 American Association for Thoracic Surgery Terms and Conditions

Fig. 4 Calibration of 1-second forced expiratory volume (FEV1) to risk. A scale of risk is given on the vertical axis (akin to the logit units of Figure 1), and 8 groups of equal numbers of patients according to the value for FEV1 along the horizontal axis. Their mortality, converted to the risk scale, is shown at each closed circle. (The 8th closed circle cannot be shown because there were no deaths in the 8th group with the highest FEV1s.) A, Linear scale of FEV1. Clearly, there is a decreasing (more negative) value of risk at higher FEV1 (simple regression line shown, with explained scatter for these points of 80%). B, Inverse scale of FEV1. Because of the inverse transformation, the lower FEV1s are to the right of the scale and the higher FEV1s to the left. Risk falls from left to right , unlike in Figure 4, A. There is now tighter correspondence of risk to this rescaling of FEV1 (85% of scatter explained) than the conventional scale of Figure 4, A. The Journal of Thoracic and Cardiovascular Surgery 2001 122, 1063-1076DOI: (10.1067/mtc.2001.119858) Copyright © 2001 American Association for Thoracic Surgery Terms and Conditions