Minding Your P’s and Q’s and R’s DURATIONS, TRUNCATIONS, AND KAPLAN-MEIER

giving 25-year follow-up ~ on 2700 subjects with surgical repair of congenital cardiovascular defect of one of eight different types. Estimated combined exposure was 31,000 person-years with 270 observed deaths. Mean duration of FU was 11.5 years, and overall FU was 94% complete. The second is a combined morbidity/mortality abstract giving 8-year follow-up on 176 subjects with abdominal aortic aneurysm (AAA). Estimated exposure was 825 person-years with nine ruptures and 98 deaths. Mean duration of FU was 4.8 years, with FU 100% complete. The data upon which each abstract was based thus satisfied the minimum data requirements of Checklist A ("Finding Suitable Articles’’1) and had Grade A or B informational value ("Guidelines for Evaluation of FU Articles"2). The first abstract lacked an age/sex distribution, but the authors of the original article had employed ageand sex-adjusted Oregon population data in order to fashion their standardized mortality ratios (SMR’s). Hence, Singer could use the reported d and SMR values to derive d’ values, analogous to the derivation strategies given in Table I of last month’s commentary.3 The authors also did not provide interval exposure data. But Singer estimated exposure using a more approximate form of his "Life Table Reconstruction method. Then armed with his estimated exposure, E, he was able to derive q and q’, and arrive at overall EDR’s for each type of surgically-corrected defect. When these estimated q values (based on reported d and estimated E), are compared to q values corresponding to the independently provided P values, there is reasonably close agreement. (Technically speaking, this is comparing aggregate [exposure-weighted] q values [i.e., ~ d/El wi..tb geometric [compound rate] q values [i.e.,’~ ." 1 p1/~.] This approach presupposes a fairly regular distribution of losses (d+w) without unusual skewing, and such assumptions may not be justified in some studies.) Singer’s abstract records 159 early deaths ( less than 30 days) due to perioperative mortality, and 111 late deaths (up to 25 years). Of the 159 persons "lost to follow-up" Hoe President & Chief Mea~cal Director, UNUM Life Insurance Company, Portland, ME. 57 such withdrawals occur early (in the first 30 days after surgery), with half of them occurring in the PDA group. This observation is unexplained and is somewhat unusual, given the extensive tracing that was pursued. Singer notes that the mortality ratios found in the study are somewhat lower than they would be if the reference group were insured lives rather than the general population used by the authors. That is to say, the q’ in the denominator of the MR would be smaller for a select or ultimate group than it is for the U~S. or Oregon population. The impairment-specific death rates (EDRs) derived for each defect can, however, be transposed to an insured lives reference group to yield an approximate insured-life MR, in a manner described in Brackenridge.5"6 For the AAA study, age and sex compositional data were not provided directly but were available from a prior citation which detailed ’the demographic characteristics of the study group. Exposure data were not furnished, but from cumulative incidence (event-rate) curves and in/ormation supplied in the article, interval event rates could be determined. As is becoming more commonly the case, the cumulative R curve also gave some l information (~0 and ~5) permitting some inferences about w. In Singer’s mortality abstract, w represented those lost to follow-up (withdrawn alive during study) plus those alive at end of FU (withdrawn alive at end of study). But, as is typical of morbidity abstracts,7 the target event was one of several potential morbid events (in this case n ~ rupture). Hence, w consisted of deaths, plus those lost to follow-up, plus those withdrawn alive at end of study, plus those terminated from follow-up for risk-of-rupture because of some other censoring event (e.g., undergoing graft for elective repair). At the fifth year of FU, of 176 original entrants, 76 were still at risk. Of the 100 no longer in follow-up, 9 had experienced rupture. The "mortality cohort" (a closely similar though apparently not identical group) had experienced 42 deaths by the fifth year of follow-up. So the rema/nder -perhaps half -of those lost to follow-up would have been untraced (alive at last contact, but fate unknown) or alive-at-end-ofstudy. While the distribution of w over the five-year