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Design of Statistical Investigations

Design of Statistical Investigations. 13 Cohort Studies. Stephen Senn. Two Major Types of Epidemiological Observational Study. This section partly based on Rothman Cohort study Sometimes referred to as prospective study But this terms is best avoided

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Design of Statistical Investigations

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  1. Design of Statistical Investigations 13 Cohort Studies Stephen Senn SJS SDI_13

  2. Two Major Types of Epidemiological Observational Study This section partly based on Rothman • Cohort study • Sometimes referred to as prospective study • But this terms is best avoided • Some cohort studies are not prospective • Case-control study • Sometimes referred to as retrospective study • But this term is also best avoided • Since some cohort studies are retrospective SJS SDI_13

  3. Cohorts • A cohort was the tenth part of a legion of Roman soldiers • It is used by epidemiologists to mean a group of individuals followed over time • Analogy of a body of marching men • In demography it is sometimes used to distinguish generational as opposed to cross-sectional approaches SJS SDI_13

  4. Cohort Study • The epidemiological equivalent of clinical trial • Subjects are compared according to exposure • Followed up for outcome • However unlike a clinical trial, the exposure is not assigned SJS SDI_13

  5. Example Obs_2 • John Snow & Cholera London 1854 • Two different companies supplied water to London • Lambeth • 26,107 houses • 14 houses with fatal attacks • Southwark and Vauxhall • 40,046 houses • 286 houses with fatal attacks SJS SDI_13

  6. Obs_2Notes • Sampling is by exposure • Lambeth company versus Southwark & Vauxhall company • The study is retrospective however. • Snow obtained data once the outbreak was known SJS SDI_13

  7. Population at Risk • Population chosen should be capable (in principle) of suffering event of interest • Standard requirement that population at risk must be free of disease of interest at outset • Argument is that you cannot develop a disease if you already have it • WARNING. Consider how this agrees with our notions of causality? SJS SDI_13

  8. Closed and Open Cohorts • Closed cohort • Membership is defined at outset • Numbers can only get smaller as study progresses • Open Cohort (dynamic cohort) • Can take on new members as study progresses • Usually defined geographically SJS SDI_13

  9. Confounding • Confounding is the major problem of observational studies • We fear that the presence of hidden variables (confounders) rather than the variable under study may explain results • In the extreme case we have a complete reversal known as “Simpson’s Paradox” SJS SDI_13

  10. Simpson’s ParadoxObs_3Berkeley Example • Case of graduate admissions to University of Berkeley in California in early 1970s • Data by sex show that a lower proportion of females are admitted • status |sex • |Female |Male |RowTotl| • -------+-------+-------+-------+ • accept | 628 |1198 |1826 | • |0.34 |0.45 | | • -------+-------+-------+-------+ • reject |1207 |1493 |2700 | • |0.66 |0.55 | | • -------+-------+-------+-------+ • ColTotl|1835 |2691 |4526 | • -------+-------+-------+-------+ SJS SDI_13

  11. Logistic Regression • Call: glm(formula = p.accepted ~ sex, family = binomial, weights = n.applied) • Coefficients: • Value Std. Error t value • (Intercept) -0.4367435 0.03132617 -13.941811 • sex 0.2166095 0.03132617 6.914651 • Males have significantly higher admission rate SJS SDI_13

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  13. Logistic Regression 2 • Call: glm(formula = p.accepted ~ sex + faculty, family = binomial, weights = n.applied) • Coefficients: • Value Std. Error t value • (Intercept) -0.55965018 0.03934316 -14.2248409 • sex -0.16941771 0.04053734 -4.1792997 • faculty1 -0.01350673 0.05494827 -0.2458081 • faculty2 -0.46041466 0.03363771 -13.6874569 • faculty3 -0.13233587 0.02145413 -6.1683158 • faculty4 -0.25473989 0.02143709 -11.8831374 • faculty5 -0.42417774 0.02617420 -16.2059518 Males have significantly lower admission rate SJS SDI_13

  14. A Paradox? • If we do not take faculty into account admission is more difficult for females • If we allow for the faculty the reverse is the case • In the extreme case (no quite here) when the trend in each and every stratum is the opposite of the overall trend we have “Simpson’s paradox”. SJS SDI_13

  15. Simpson’s Paradox? • Given some information we come to one conclusion • Given further information we come to the opposite conclusion • This is worrying because, given yet further information we might restore the original conclusion. • But is this a paradox?…consider the following story SJS SDI_13

  16. Reversal of OpinionAn Illustrative Story “In the Welsh legend, the returning Llewelyn is met by his hound Gelert at the castle door. Its muzzle is flecked with blood. In the nursery the scene is one of savage disorder and the infant son is missing. Only once the hound has been put to the sword is the child heard to cry and discovered safe and sound by the body of a dead wolf. The additional evidence reverses everything: Llewelyn and not his hound is revealed as a faithless killer.” (From chapter 1 of Senn, SJ, Dicing with Death ) So reversal of opinion is not a purely statistical phenomenon. It is a human one, we accept. So why do we regard this as being a “paradox”? SJS SDI_13

  17. Obs_4Poole Diabetic Cohort(Julious and Mulee) SJS SDI_13

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  19. “Suppose that the numbers in the table remain the same but refer now to a clinical trial in some life-threatening condition and we replace “Type of Diabetes” by “Treatment “ and “non-insulin dependent” by “A” and “insulin-dependent by B” and “Subjects” by “Patients”. An incautious interpretation of the table would then lead us to a truly paradoxical conclusion. Treating young patients with A rather than B is beneficial (or at least not harmful – the numbers of deaths 0 in the one case and 1 in the other are very small). Treating older patients with A rather than B is beneficial. However, the overall effect of switching patients from B to A would be to increase deaths overall.” From Dicing with Death SJS SDI_13

  20. “In his brilliant book, Causality(1), Judea Pearl gives Simpson’s paradox pride of place. Many statisticians have taken Simpson’s paradox to mean that judgements of causality based on observational studies are ultimately doomed. We could never guarantee that further refined observation would not lead to a change in opinion. Pearl points out, however, that we are capable of distinguishing causality from association because there is a difference between seeing and doing. In the case of the trial above we may have seen that the trial is badly imbalanced but we know that the treatment given cannot affect the age of the patient at baseline, that is to say before the trial starts. However, age very plausibly will affect outcome and so it is a factor that should be taken account of when judging the effect of treatment. If in future we change a patient’s treatment we will not (at the moment we change it) change their age. So there is no paradox. We can improve the survival of both young and the old and will not, in acting in this way, adversely affect the survival of the population as a whole.” Dicing with Death • (1) Pearl, J. (2000) Causality. Cambridge University Press, New York. SJS SDI_13

  21. Lessons • Confounders can be a problem for cohort studies • We may need to measure many potential confounders • We will almost certainly need to include them in our models • Interpretation may have to be cautious. SJS SDI_13

  22. Questions A survey of women in Wickham, England in 1972-1974, with 20 year follow-up gave results recorded in the following slide. • Do the results show smoking to be dangerous? • What explanation can you think of for the result? • What further data would you like to see? SJS SDI_13

  23. Obs_5Wickham Wonders • status |smoker? • |no |yes |RowTotl| • -------+-------+-------+-------+ • alive |502 |443 |945 | • |0.69 |0.76 | | • -------+-------+-------+-------+ • dead |230 |139 |369 | • |0.31 |0.24 | | • -------+-------+-------+-------+ • ColTotl|732 |582 |1314 | • -------+-------+-------+-------+ SJS SDI_13

  24. More Questions Look at the study by Best et al, described on the next slide • What sort of interaction is described? • What explanations can you think of? • What further information would you like to have? SJS SDI_13

  25. Obs_6Best, et al 1. The relationship between blood cyclosporin concentration (CyACb) and a patient's risk of organ rejection following heart-lung (HL) transplantation was investigated. 2. Longitudinal data were collected for 90 days post-operation for 31 HL transplant recipients. Following exploratory analysis, a multiple logistic regression model with a binary outcome variable representing presence or absence of lung rejection (as defined on biopsy findings and/or intention to treat) in the next 5 days was fitted to the data. 3. A significant interaction between time post-transplant and CyACb was found. During weeks 1-3, the relative risk (RR) of rejection per unit increase in log(e) (5-day mean CyACb) was reduced: RR = 0.29, 95% confidence interval (CI) = (0.12, 0.72). After 3 post-operative weeks, this trend was reversed: RR = 1.61, 95% CI = (0.96, 2.70). Best, Trull, Tan, Hue, Spiegelhalter, Gore, Wallwork, Brit J Clin Pharm, 1992 SJS SDI_13

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