發表文章
Cockcroft 醫師的回憶
25 年前進行的一項簡單且小型的居民研究專案，導致了一個快速估計肌酸酐清除率的公式的發表；該公式基於年齡、體重和血清肌酸酐。這篇發表該公式的論文在 1992 年被命名為「經典引用」，表示它已被引用超過 500 次。我將回顧這項研究專案背後的歷史，在我位於薩斯卡通辦公室衣櫥深處發現原始數據收集工作手冊，大大幫助了我。
作為一名呼吸科醫生（或許更恰當地說是哮喘病學家），至少有一些哮喘研究方面的適度記錄，我覺得很諷刺且有點好笑的是，我的非呼吸科醫療同事中，我最常與肌酸酐清除率公式聯繫在一起。我的一次三個月腎臟病學次專科住院醫師實習相當偶然地發生。在蒙特婁皇家維多利亞醫院（麥吉爾大學）第一年住院期間，我已決定從事呼吸科作為我的職業選擇。
當輪到次專科時（那時候是第三年住院），皇家維多利亞醫院有大量合格申請者競爭少數幾個呼吸次專科職位。因此，我延遲了一年的呼吸訓練。由於皇家維克沒有提供第三年一般內科，所以我和兩位同事各自選擇一個次專科，並輪流進行，每個次專科花六個月時間，其他兩個則花三個月時間。因此，偶然地，我在 1974 年 1 月、2 月和 3 月有一次為期三個月的腎臟病學次專臨床工作，由 Henry Gault 博士帶領，在瑪麗女王退伍軍人醫院進行。
Gault 博士期望輪到他服務部門實習的腎臟病學住院醫師在他們三個月期間完成一個研究項目。不久之後我開始，他從他的檔案中拿出我的項目主題。這項項目是一份關於一位或多種肝酶正常化隨著腎周圍膿瘍引流而恢復的一位男士的手術報告。一份相當厚重退伍軍人醫院圖表檢查最終暗示，這種肝酶變化可能是巧合，因此放棄了報告。
還剩下至少兩個月，所以 Gault 博士和我決定試試第二項項目。我們第二項任務目標是評估並驗證 Siersback-Nielsen 等人所出版用於快速評估肌酸酐廓清率的一張圖表式方程式。此第二嘗試取得成功。我們收集用以驗證該圖表式方程式所需資料導致我們發展出自己的方程式。在設計並主要獨立執行此第一件研究所中，這也是我的首篇領銜作者出版物。我非常感謝 Gault 博士給予指導及鼓勵。
Siersback-Nielsen 法則允許對肌酸酐廓清率做快速評估。此法則不同於同時期可用的其他方程式之處，在於其預測上佔重要角色的是年齡。在臨床操作上，此法則使用起來相當順手：先將患者之年齡及體重與尺規校準，再將尺規支點置于垂直線標記"R"處，使得尺規右側與血液檢測值交會于血清肌酸酐線上，再讀取尺規左側交會左軸座標上的預測值即可。此外，有一些重要原因可以解釋需要能夠迅速準確地估算出肌酸酐廓清率，因此認爲對此圖形化方程式做進一步評價及驗證 是很有意義的。
我們蒐集到的資料包括1974 年初至1971 年中期間瑪麗女王退伍軍人醫院男性受試者所進行的24 小時肌酸酐廓清率配對檢查。我們以倒序時間順序檢查連續受試者，從 1974 年初開始回溯到 1971 年中，評估每位進行超過兩次廓清率檢查之受試者的最後兩次肌酸酐廓清率。完整數據蒐集包括 505 對男性穩定狀態（即血液中肌酸酐濃度穩定（在20%範圍內））下的肌酸酐廓清率。我們將注意力集中在236 位肌酸酐排泄量可重複（在20%範圍內）且總肌酸酐排泄量超過10 毫克/公斤/天的受試者上。
我們假設可重複的24 小時尿液肌酸酐排泄值更有可能是準確的。觀察各年齡組間之關係時，我們還納入了13 位符合條件但其尿液容積合理（>500 毫升/24 小時）的其他受試者，這些人的資料顯示其排泄量小於10 毫克/公斤/天，但似乎是準確、可重複且與合理尿容積相關。
儘管最初爲該研究之次要目標，但我們首先探討了血清中的肌酸酐與年齡之間 的關係。這種關聯性導致了公式開發。在看待此關係時，我們審視249 對經測量後得到的24 小時肌酸酐廓清率結果。我們計算每位個案每公斤體重所需之平均24小時肌酸酐廓清，並為每十年計算一平均值。結果顯示，20 多歲的人和80多歲的人相比，其24小時肌酸酐廢棄物減少近50%，分別約為：(約) 每公斤體重含有 24毫克 / 每天 (mg/kg/day) 及12 mg/kg/day. 這七個數據點 (一個點代表從二十多歲到八十多歲(包括) 的每十年的資料)，連同西爾斯巴克-尼爾森等人相似的比較資料，一併繪製成圖表。來自加拿大249名男性的數據和 Siersback-Nielsen 149名丹麥男性的數據非常吻合。
將這498項肌酸酐廓清單法(249對) 縮減至僅 7 個數據點後，我門應用傳統線性迴歸至以年齡(yrs) 為橫軸，以mg /kg/day 肌酸酐廢棄物爲縱軸畫出的圖形。此迴歸直線如下：
FORMULA I:
Creatinine excretion/kg = (28-0.2 age) mg/24 h(r=0.99)
我記得是在1974 年二月底或三月初的一個週六早晨，在蒙特婁寒冷又刮風的一天裡，我坐下來與高特博士一起審閱專案進展。那是我第一次看到如此令人印象深刻地呈現出線性迴歸及緊密符合 Siersback-Nielsen 資料的圖形。當我們在審閱數據時，我突然有了一個數學上的洞察力：如果將迴歸公式的兩側都乘以患者體重，就可以得到一個基於患者年齡和體重來預測24 小時肌酸酐廓清率的公式，如下：
FORMULA 2:
Creatinine excretion = (28-0.2 age) x wt (kg)
mg/24 h
從那裡開始，透過除以1440 分鐘/24 小時，推斷出每分鐘尿液中肌酸酐廓清率（UV），就相對簡單了，如下所示：
FORMULA 3:
Creatinine excretion (UV) = (28-0.2 age) x wt
(kg)/(1440 min/24 hr)
mg/min
=(140-age) x wt (kg)/(7200 min/24 hr)
=(140-age) x wt (kg)/7200 mg/min
如果可以預測尿液中的肌酸酐廓清率（UV）並測量血清中的肌酸酐（Scr=P），那麼將其轉換為可預測肌酸酐廓清率（UV/P）的公式就很簡單了，如下所示：
FORMULA 4:
Ccr= UV/P= [(140-age)xwt(kg)]/[7200xScr(mg/dL)]
ml/minx100 ml
=[(140-age)xwt(kg)]/[72xScr(mg/dL)]
ml/min
我記得 Gault 博士在我面前進行這些計算時，流露出一種驚訝和喜悅的心情。就在1974 年冬季的一個寒冷早晨，我們的肌酸酐廓清率公式誕生了。
該論文其餘部分——我懷疑很少被引用——由統計比較組成，用於比較我們的方程式、圖表式方程式以及其他方程式與經過測量後得到之創造素廓 清結果，並與彼此進行比較；使用未轉換之原始數據、對數及平方根變換。我們發現，我們的方程式與圖表化 方程 式非常吻合，而且它們比那些幾乎不考慮年齡因素之其他方程式更好地反映出實際狀況。此外，預估值與實際值之間差異，或是兩次經過測量後得到創造素 廓 清結果間差異，其程度大致相同。
該公式基於男性受試者的資料，因此僅適用於男性受試者。受試者應處於穩定狀態。此外，由於預測是基於肌肉質量，因此在預測時應該使用患者的理想體重；這對肥胖者以及可能有明顯液體過多的受試者來說很重要。該公式可能不適用於原發性肌肉疾病或嚴重肌肉消耗之受試者。在1976 年，我們建議女性應降低15%；目前仍建議採用此方法。
該公式已轉換為國際單位制，如下：
FORMULA 5:
Ccr= [(140-age)xwt(kg)]/[72xScr(mg/dL)]
ml/min=
[(140-age)xwt(kg)]/[72xScr(umol/L)/88.4]
ml/min=
1.23(140-age)xwt(kg)/Scr(umol/L) ml/min
=[(140-age)xwt(kg)]/[56.8xScr (umol/L)]
ml/sec
我們的方程式經得起"時間考驗"。我猜想，它偶爾會因其科學依據得到引用，即確認隨著年齡增長，肌酸酐廓清率大幅減少。大多數引用似乎出現在藥物劑量和其他藥理算法中。它在加拿大常見醫學手冊（CPS）前言中佔有重要地位，並在加拿大常見醫學手冊（CPS）和美國醫師桌上參考書（PDR）中的個別藥品條目中被引用好幾次。不正式審查了十幾本最新的一般內科教科書，發現其中一半以上都直接引述了我們的方程式，有時甚至沒有提到原始出處，就像《哈里森內科學原理》一書那樣。
審查《科學引文索引》（SCI，由賓夕法尼亞州費城資訊研究所出版），至1999 年中期，該論文已被引用近1850 次。每年的引用率一直在上升，這些年來接近每年200 次引用。SCI 審查證實，大多數引用的地方是在藥理或腎臟病相關期刊上。
總結
1974 年，一項簡單居民研究專案產生了一個用於預測肌酸酐廓清率之公式。此公式基於20 歲至90 歲人群尿液中肌酸酐廢棄物呈線性遞減關係，在1976 年出版。在穩定狀態、性別、肥胖者的理想體重（特別是）、以及肌肉疾病/消耗等相關警告下，該公式至今仍被廣泛有效地使用。
A SIMPLE AND SMALL resident research project performed 25 years ago resulted in the publication of a formula for rapid estimation of creatinine clearance; theformula was based on age, weight and serum creatinine. The paper in which this formula was published was named a "citation classic" in 1992 indicating that it has been cited more than 500 times. I will review the history behind this research project, aided greatly by the discovery of the original data collection workbook stored deep in a closet in my office in Saskatoon.
AS AN ACADEMIC RESPIROLOGIST (or perhaps more appropriately asthmatologist) with at least a modest track record in asthma research, I find it ironic and somewhat amusing that amongst my non-respiratory medical colleagues, my
name is most associated with a creatinine clearance formula. My single, three-month stint as a subspecialty nephrology resident occurred somewhat by chance. By the middle of my first-year residency at the Royal Victoria Hospital (McGill) in Montreal, I had decided on respirology as my chosen career.
When it came time to subspecialize (third year residency at that time), there were a large number of highly qualified applicants for the small number of respiratory subspecialty positions at the Royal Victoria Hospital. Consequently, I deferred my respiratory training for a year. Since there was no third year
general medicine offered at the Royal Vic, two of my colleagues and myself each chose a subspecialty and rotated through them, spending six months in our chosen specialty and three months in the other two. Therefore, by chance,
I had a single three-month rotation as a subspecialty nephrology resident working with Dr. Henry Gault at the Queen Mary's Veteran Hospital in January, February and March of 1974.
Dr. Gault expected the nephrology residents rotating through his service to perform a research project during their three months. Therefore, shortly after I started, Dr. Gault reached in his files and pulled out the subject of my project. This project was to be a case report of a gentleman in whom one or more liver enzymes normalized following the drainage of a perinephric abscess. A review of a rather thick Veterans' Hospital chart eventually suggested that the change in liver enzymes, which had been fluctuating for years, was likely a coincidence and the report was abandoned.
There was still at least two months left, so Dr. Gault and I decided that we would try a second project. The goal of this project was to evaluate and validate a nomogram for rapid evaluation of creatinine clearance published by Siersbaek-Nielsen et al. This second attempt proved a success. The data we gathered in order to validate the nomogram led to the development of our formula. This was the first research project in which I had designed and carried out the project largely on my own; this also led to my first lead-authored publication. I remain extremely grateful to Dr. Gault for his direction and his encouragement.
THE NOMOGRAM OF SIERSBACK-NIELSEN allowed for rapid estimation of creatinine clearance. The nomogram differed from other formulae available at that time in that age played a major role in the prediction. The nomogram is used by initially lining up the patient's age and weight with a ruler. The ruler is then pivoted on the vertical line marked "R" so that the right-hand side of the ruler intersects the serum creatinine line at the point of the measured serum
creatinine. The left-hand side of the ruler thus intersects the left-sided axis at the predicted or estimated value for creatinine clearance. In clinical practice, we had the impression that this nomogram was performing quite well. Since there are some important reasons for being able to accurately estimate creatinine clearance rapidly, evaluation and validation of this nomogram was felt to be worthwhile. The data collection involved examining pairs of 24-hour creatinine clearances performed at the Queen Mary's Veterans' Hospital in male subjects.
We examined consecutive subjects in reverse chronological order from early 1974 back to mid-1971, evaluating the last two-creatinine clearances in subjects who had more than two collections performed. The complete data
collection included 505 pairs of creatinine clearances in male subjects in steady state, i.e. in whom two measurements of serum creatinine were stable (within 20 percent). The majority of these were hospitalized patients. However, we did rely on healthy male volunteers (medical residents, etc.) to help increase the data available in the younger age ranges (20's and 30's). We focused much of our attention on the 236 subjects who had reproducible creatinine excretion (within 20 percent) and total creatinine excretion in excess of 10 mg/kg/day.
We made the assumption that reproducible values for 24-hour creatinine excretion were more likely to be accurate. When looking at creatinine excretion over the age range, we also included an additional 13 subjects with creatinine excretion less than 10 mg/kg/24 hours but in whom this appeared to be accurate, reproducible and associated with a reasonable (> 500 mL/24
hour) urine volume.
Although originally a secondary objective of the study, we initially examined the relationship between creatinine excretion and age. It was this
relationship which led to the development of the formula. In order to look at this relationship, we examined the 249 pairs of measured 24-hour creatinine clearances. We calculated the mean 24-hour creatinine excretion/kg for each subject and then calculated a mean value for each decade. The results showed almost 50 percent decline in 24-hr creatinine excretion between subjects in their 20's (approximately 24 mg/kg/24 hours) and subjects in their 80's (12 mg/kg/24 hours). These seven data points (one point for each decade from 20's to 80's inclusive) were plotted graphically along with the comparable data of Siersbaek-Nielsen et al. The data from the 249 Canadian subjects and the 149 Danish subjects of Siersbaek-Nielsen are remarkably similar.
Having thus reduced 498 creatinine clearances (249 pairs) to only seven data points, we applied traditional linear regression to the graph of 24-hr creatinine excretion (mg/kg/24 hours) vs. age (years). The regression line was as follows in
FORMULA I: Creatinine excretion/kg = (28-0.2 age) mg/24 h (r-0.99)
As I recall, it was about this point in late February or early March of 1974, on a cold blustery Saturday morning in Montreal, that I sat down with Dr. Gault to review the progress of our project. We initially looked at the graph with its impressive linear regression and close similarity to the Siersbaek-Nielsen data. While reviewing the data, I had a flash of mathematical insight:
if one multiplied both sides of the regression formula by the patient's weight, one then had a formula which would predict the 24-hour creatinine excretion based on patient's age and weight as follows in
FORMULA 2:
creatinine excretion = (28-0.2 age) x wt (kg)
mg/24 h
From there, it is a relatively easy step to predict the creatinine excretion (uv) per minute by dividing by 1440 min/24 h as shown in
FORMULA 3: creatinine excretion (UV) = (28-0.2 age) x wt (kg)/(1440 min/24 hr) mg/24 hr
=(140-age) x wt (kg)/(mg/min) 7200
If one can predict the creatinine excretion (uv) and measure the serum creatinine (Scr=P), then it becomes a simple job to transform this into a formula that will predict creatinine clearance (UV/P), as shown in
FORMULA 4:
Ccr= UV/P= (140-age) x wt (kg)/(7200 x Scr (mg/100mL)) mg/min x 100 ml
= (140-age) x wt (kg)/(72 x Scr (mg/100mL))
ml/min
I remember fondly Dr. Gault's mild astonishment and great joy as I performed these calculations in front of him. On that cold winter morning in late
winter of 1974, our creatinine clearance formula was born.
The remainder of the paper, which I suspect is rarely quoted, consisted of statistical comparisons of our formula, the nomogram, and other formulae with the measured creatinine clearances and with each other using untrans-
formed data as well as logarithmic and square root transformations. The nomogram and our formula agreed very well with one another and both performed better than other formulae, which took little or no account of age.
The difference between predicted and measured was similar or actually less than the difference between two measured creatinine clearances.¹ te
The formula is based on creatinine excretion in males and thus appropriate for use only in males. Subjects should be in steady state. Since the
prediction is based on muscle mass, the patient's ideal weight should probably be used in the prediction; this is important in obese individuals and perhaps in subjects who have marked fluid overload. Also, the formula is probably not appropriate for subjects with primary muscle disease or with significant muscle wasting. In 1976, we recommended a 15 percent reduction for females; this continues to be suggested.4 The formula has been converted
to SI units as per
FORMULA 5:
Ccr= (140-age) x wt (kg)/(72 x Scr (mg/100 mL))
ml/min=
(140-age) x wt (kg)/(72 x Scr (umole/L)/ 88)
ml/min=
1.2 (140-age) x wt (kg)/Scr (umole/L) ml/min=
(140-age) x wt (kg)/(56 Scr (umole/L))
ml/sec
OUR FORMULA HAS STOOD "the test of time." It is, I suspect, only occasionally cited for its science, i.e. confirmation of the large reduction in creatinine excretion with age. The majority of citations, however appear to be in drug dosing and other pharmacologic algorithms. It has a prominent role in the preamble to the Canadian CPS5 and is cited in several places under individual pharmaceutical entries in both the CPS5 and the American PDR. An informal perusal of a dozen recent general medical texts showed that it was quoted in more than half of these, occasionally without reference to its original source, as in Harrison's Principles of Internal Medicine.
A review of the Science Citation Index (SCI published by ISI - Institute for Scientific Information, Philadelphia, PA) reveals that to the middle of 1999, the paper has been cited almost 1,850 times. The annual citation rate has been
escalating and, for the last several years, has been approaching 200 citations per year. The SCI review confirms that most citations occur in pharmacologic or nephrology journals.
SUMMARY
IN 1974, A SIMPLE resident research project yielded a formula for prediction of creatinine clearance. The formula, published in 1976, was based on the near linear decline in creatinine excretion with age (from 20-90 years). With certain caveats related to steady state, gender, ideal weight (in the obese particularly) and muscle disease/wasting, the formula continues to be widely and effectively used today.
