1. Self-controlled Studies
Alec Walker
September 2016

2. Blocking the effect of confounders
Randomization
Self-matching
Self-matching
Instruments

3. Roadmap for self-matching
Implications of rates that vary within person
Case-crossover studies
Self-controlled case series

4. Example of heterogeneous daily risks
Rash in children before and after the 12-month-MMR (mumps, measles, rubella) vaccination
A positive vaccine-related effect, peaking Day 9
A positive office-visit effect at Day 0
A negative pre-visit (anticipatory) effect at Days -4 through -1
A negative post-screening effect at Days 1-3
A downward age-trend
A step effect up following visit
A day of-the-week effect, with peaks at 7-day cycles before and after immunization
Brookhart MA, Walker AM, Lu Y, Polakowski L, Li J, Paeglow C, Puenpatom T, Izurieta H, Daniel GW. Characterizing vaccine-associated risks using cubic smoothing splines. Am J Epidemiol 2012 Nov 15;176(10):949-57

5. A model for transient risks
Maclure M. Am J Epidemiol 1991:133:

6. A model for transient risks
Hypothesized curve of incidence rate in temporal relation to exposure
Approximating step function
Exposure
Baseline Incidence
Baseline Incidence
Risk Periods
Ref. Maclure M. Am J Epidemiol 1991:133:

10. A model for transient risks of rash
Associated with the MMR vaccine given at 12 months of age.
Day

11. A model for transient risks of rash
Associated with the MMR vaccine given at 12 months of age.
Each interval of daily risk that is modeled as being internally homogenous could create a definition of person time.
Day

12. A model for transient risks of rash
Associated with the MMR vaccine given at 12 months of age.
Not yet vaccinated
>14 days after vaccine
Each interval of daily risk that is modeled as being internally homogenous could create a definition of person time.
Day
It looks like there might be some natural reference levels within person.

13. Example Celecoxib, Naproxen and GI Bleeding in the treatment of pain
versus
Naproxen versus
No Treatment
Example Celecoxib, Naproxen and GI Bleeding in the treatment of pain
MD-perceived risk of peptic ulcer & bleeding (PUB)
High risk for peptic ulcer and bleeding makes treatment with naproxen inadvisable. Celecoxib would be better. No treatment at all is safest but on the average less effective.
True risk of PUB
PUB
Hospital
Admission

14. Example Celecoxib, Naproxen and GI Bleeding in the treatment of pain
versus
Naproxen
No Treatment
Example Celecoxib, Naproxen and GI Bleeding in the treatment of pain
MD-perceived risk of peptic ulcer & bleeding (PUB)
The physician’s belief about patient risk, not the true risk, is what affects the choice of therapy.
True risk of PUB
PUB
Hospital
Admission

15. Example Celecoxib, Naproxen and GI Bleeding in the treatment of pain
versus
Naproxen
No Treatment
Example Celecoxib, Naproxen and GI Bleeding in the treatment of pain
MD-perceived risk of peptic ulcer & bleeding (PUB)
Both the true risk and the prescriber-perceived risk are likely to be largely inaccessible to the investigator.
True risk of PUB
PUB
Hospital
Admission

16. Intractable “confounding by indication”?
Celecoxib or naproxen or no Rx
PUB
Risk factors for PUB
Both the true risk and the prescriber-perceived risk are likely to be largely inaccessible to the investigator.
Physician perception
Patient signs & symptoms

17. Matching on the individual
Celecoxib or naproxen or no Rx
PUB
Risk factors for PUB
Matching on person would mean that all comparisons are within person and therefore at a common level of physician perception.
Physician perception
Patient signs & symptoms

18. Time-varying exposures
Cohort Study
Calendar Time

19. Time-varying exposures and matching on individual
Individually Matched Cohort Study
Cohort Study
Calendar Time
Calendar Time

20. Time-varying exposures and matching on individual
Individually Matched Cohort Study
Cohort Study
Calendar Time
Calendar Time
Drop person hisotries when there the individual does not suffer an event is a consequence of extreme stratification. With the individual as the unit of stratum formation, all the individuals for whom no event is recorded (read: all strata in which no event occurs) drop out of the analysis. This will turn out to have enormous implications for data gathering and cost.

21. Compare different risk periods within individuals
Between-person confounding
Does not exist because there are no comparisons between persons
Time-dependent confounding
If risk factors can vary over time in synchrony with exposure status, there could still be time-dependent confounding. We’ll have to consider control for this when we go into the analysis.

22. Comparative vs. Crossover designs
Treatments are compared between individuals. Baseline comparability of groups is sought through random allocation (RCT) or through careful subject selection and covariate control.
Randomized trial
Cohort Study
“Self-controlled” analyses, in which treatments are compared within individuals, are common in intervention trials, but are also possible in purely observational studies. The design greatly enhances the baseline similarity of comparison groups.
Today we need to consider another type of trial as the counterpart for our observational studies, the cross-over design.
Randomized trial Cross-over design
Cohort Study with Changing Exposure

23. In sum
When risk varies within individual, it may be possible to construct an analysis that restricts all the comparisons between risk levels to within- person comparisons.
With restriction to within-person comparisons,
Between-person differences in time-invariant risk factors cannot cause confounding
Data collection is restricted to those individuals who experience an event
Time-dependent confounding is still a threat.

24. Roadmap More implications of rates that vary within person
Case-crossover studies
Self-controlled case series

25. Case-Crossover mechanics
Use only for events that may be triggered by a discrete exposure.
For each case, identify the presence or absence of the exposure during the postulated trigger period.
Identify the “expected” exposure in the trigger period from
Usual frequency of exposure over a long time
Documented occurrence of exposure during one or more comparable times in the past
Summarize Observed vs. Expected across all cases using an appropriate matched analysis.

26. Match analyses on person
Recall that individual histories drop out of a matched analysis when there is no event.
Case-crossover studies are matched cohort studies that take personal matching to its limit:
The individual forms the unit of stratification, and the comparison is between different exposure windows within individuals.
Time  26

27. If it’s difficult to ascertain exposure at all times in the past, Sample
This becomes a case-control study nested within a matched cohort.
Time  27

28. Person-days not sampled drop out of consideration
Case-crossover studies are matched cohort studies that take personal matching to its limit:
The individual forms the unit of stratification, and the comparison is between different exposure windows within individuals.
Time  28

29. Final product: Matched sets of person-days
Case-crossover studies are matched cohort studies that take personal matching to its limit:
The individual forms the unit of stratification, and the comparison is between different exposure windows within individuals.
Time  29

30. Case and control windows
Case window: period preceding the event during which the exposure may have altered the risk
Control window(s): periods of the same length as, and not overlapping with, the case window that provide an estimate of the expected frequency of exposure for each case.
The core study technique is to identify cases, then ascertain exposure status in the case window and at earlier points in time – the control windows. 30

31. Case and control windows: Matched sets of person-days
Case window
Case-crossover studies are matched cohort studies that take personal matching to its limit:
The individual forms the unit of stratification, and the comparison is between different exposure windows within individuals.
Time  31

32. Estimating the relative risk
Case Window
Control Window Exposed
Exposed
Yes No
f10
f01
For dichotomous exposures
Form the matched 2x2 table
Place each case according to exposures in the case and control windows
Mantel-Haenszel odds ratio for matched sets reduces to ratio of counts in discordant exposure windows: ( f10 / f01 ) when there is one control
Concordant case-control windows are uninformative
Dichotomous exposures and two risk periods can be handled as described in the preceding paragraph.
Polytomous, or continuous exposure measures and multiple risk periods require a conditional logistic regression analysis.
Risk periods of varying length can be analyzed using the techniques of stratified analysis of person-time data.
The matched analysis may also be stratified by fixed personal characteristics to look for factors that modify the effect of the exposure on the risk of outcome.

33. Estimating the relative risk
Case Window
Control Window Exposed
Exposed
Yes No
f10
f01
For dichotomous exposures
Form the matched 2x2 table
Place each case according to exposures in the case and control windows
Mantel-Haenszel odds ratio for matched sets reduces to ratio of counts in discordant exposure windows: ( f10 / f01 ) when there is one control
Concordant case-control windows are uninformative
For polytomous and multiple exposures (covariates)
Conditional logistic regression is used when
There are several different exposures or exposure levels
There are concurrent time-varying confounders
Dichotomous exposures and two risk periods can be handled as described in the preceding paragraph.
Polytomous, or continuous exposure measures and multiple risk periods require a conditional logistic regression analysis.
Risk periods of varying length can be analyzed using the techniques of stratified analysis of person-time data.
The matched analysis may also be stratified by fixed personal characteristics to look for factors that modify the effect of the exposure on the risk of outcome.

34. Celecoxib or naproxen or no Rx
Example
Celecoxib or naproxen or no Rx
PUB
Risk factors for PUB
Matching on person would mean that all comparisons are within person and therefore at a common level of physician perception.
Physician perception
Patient signs & symptoms

36. Pharmacoepidemiology and Drug Safety 2011; 20: 763–771
Risk of hospitalization for upper gastrointestinal adverse events
associated with nonsteroidal anti‐inflammatory drugs: a nationwide
case‐crossover study in Taiwan
Chia‐Hsuin Chang1,2†, Hsi‐Chieh Chen1†, Jou‐Wei Lin3, Chuei‐Wen Kuo4, Wen‐Yi Shau5 and Mei‐Shu Lai1*
1Institute of Preventive Medicine, College of Public Health, National Taiwan University, Taipei, Taiwan
2Department of Internal Medicine, National Taiwan University Hospital, Taipei, Taiwan
3Cardiovascular Center, National Taiwan University Hospital Yun‐Lin Branch, Dou‐Liou City, Yun‐Lin, Taiwan
4National Health Insurance Mediation Committee, Department of Health, Executive Yuan, Taipei, Taiwan
5Division of Health Technology Assessment, Center for Drug Evaluation, Taipei, Taiwan
ABSTRACT
Purpose This study aimed to evaluate the risks of upper gastrointestinal (GI) adverse events across a variety of oral and parenteral coxibs
and nonselective nonsteroidal anti‐inflammatory drugs (nsNSAIDs) in the general population of Taiwan.
Methods In a case‐crossover study, all patients aged ≥20 years who were hospitalized for upper GI adverse events (peptic ulcer and
bleeding; gastritis and duodenitis) in 2006 were identified using the International Classification of Diseases, 9th Revision, Clinical
Modification diagnosis codes from inpatient claims from the Taiwan National Health Insurance Database. For each patient, the case period
was defined as 1–30 days and the control period as 31–60 days before the date of hospitalization. Outpatient pharmacy prescription database
was searched for individual NSAID use during the case and control periods. A conditional logistic regression model was applied, and
adjusted self‐matched odds ratios (OR) and their 95% confidence intervals (95%CI) were reported.
Results A total of patients hospitalized for upper GI adverse events were included. The adjusted OR was 1.52 (95%CI: 1.27–1.82)
for celecoxib and 2.56 (95%CI: 2.44–2.69) for oral nsNSAIDs. The ORs were above 2 for oral piroxicam, diclofenac, ketorolac, ketoprofen,
acemetacin, and naproxen and were around 1.5 for tiaprofenic acid, indomethacin, mefenamic acid, and ibuprofen. Higher risks were
evident for parenteral NSAIDs, in particular ketorolac with an OR of 5.76 (95%CI: 5.14–6.44).
Conclusion Use of celecoxib and all nsNSAIDs studied was associated with a greater risk of upper GI toxicity as compared with nonuse.
Parenteral NSAIDs posed a higher risk, but celecoxib, ibuprofen, and mefenamic acid posed a lower risk than other NSAIDs.
Risk of hospitalization for upper GI adverse events associated with nonsteroidal anti‐inflammatory drugs…
Chia‐Hsuin Chang, Hsi‐Chieh Chen, Jou‐Wei Lin, Chuei‐Wen Kuo, Wen‐Yi Shau and Mei‐Shu Lai
Purpose This study aimed to evaluate the risks of upper gastrointestinal (GI) adverse events across a variety of oral and parenteral coxibs and nonselective nonsteroidal anti‐inflammatory drugs (nsNSAIDs) in the general population of Taiwan.
Methods In a case‐crossover study, all patients aged ≥20 years who were hospitalized for upper GI adverse events (peptic ulcer and bleeding; gastritis and duodenitis) in 2006 were identified ... For each patient, the case period was defined as 1–30 days and the control period as 31–60 days before the date of hospitalization. Outpatient pharmacy prescription database was searched for individual NSAID use during the case and control periods. A conditional logistic regression model was applied ...
Results A total of patients hospitalized for upper GI adverse events were included. The adjusted OR was 1.52 (95%CI: 1.27–1.82) for celecoxib and 2.56 (95%CI: 2.44–2.69) for oral nsNSAIDs…
Conclusion Use of celecoxib and all nsNSAIDs studied was associated with a greater risk of upper GI toxicity as compared with nonuse…
Pharmacoepidemiology and Drug Safety 2011; 20: 763–771

37. Control and case windows in Chang et al
When an individual experiences no event, his/her record does not enter into the anlaysis X
Control Case
Windows X
Control Case
Windows
Key
Celecoxib
Naproxen
No Therapy
Event X

38. Pharmacoepidemiology and Drug Safety 2011; 20: 763–771
Case Window
Control Window Exposed
Exposed
Yes No
f10
f01
Pharmacoepidemiology and Drug Safety 2011; 20: 763–771

39. Control Window Exposed
Case Window
Control Window Exposed
Exposed
Yes No
413
f01
Pharmacoepidemiology and Drug Safety 2011; 20: 763–771

40. Pharmacoepidemiology and Drug Safety 2011; 20: 763–771
Case Window
Control Window Exposed
Exposed
Yes No
413
232
Pharmacoepidemiology and Drug Safety 2011; 20: 763–771

41. Pharmacoepidemiology and Drug Safety 2011; 20: 763–771
Case Window
Control Window Exposed
Exposed
Yes No
413
232
RRmatched = 413/232
= 1.78
Pharmacoepidemiology and Drug Safety 2011; 20: 763–771

42. Case-Crossover design options
Mueller JE. Am J Cardiol 2000;86(suppl):14F–18

43. In sum
Case crossover studies compare exposure at the time of an event to the historical frequency of exposure in the same person
Very efficient, not always feasible
Gives mathematical meaning to: “Were you doing anything unusual just before you got sick?”
Works for easily ascertained, intermittent exposures whose associated risks rise and fall quickly
Requires that the onset time of the outcome event can be pinned down with a precision that is substantially tighter than the width of the exposure window

44. Roadmap More implications of rates that vary within person
Case-crossover studies
Self-controlled case series

45. Cohorts with changing exposure and continuing follow-up
 End of f/u
 Event
Time 

46. Match analyses on person
Just as in the rationale for case-crossover studies, individual histories drop out of a matched analysis when there is no event.
 End of f/u
 Event
Time  46

47. Self-controlled case series
Look at the affected individuals’ entire exposure record
Exposures quantified by person time
Events modeled using a rate model
Could be accomplished with Mantel-Haenszel techniques for stratified cohort analyses in the case of two exposure levels
More generally accomplished by a regression that is
Conditional (i.e. stratified on person)
Log-linear, estimating ratio measures
Poisson (events in the numerator)
With “offsets” for the volume of person-time

48. Self-controlled case series
Should events terminate follow-up?
In the original formulations, they did not
Developed for vaccine studies
Air pollution
Post-event follow-up is OK when
The event itself cannot affect exposure status
Post-vaccine time windows in someone already vaccinate
Environmental exposures
Events terminating follow-up now increasingly accepted
Assumptions violated, but practical effect appears to be small

49. Whitaker HJ, Farrington CP, Spiessens B, Musonda P
Whitaker HJ, Farrington CP, Spiessens B, Musonda P. Tutorial in biostatistics: the self-controlled case series method. Statistics in Medicine. 2006; 25(10):
Age in days 

50. “Based on evidence from previous studies, and on knowledge of the time taken by the mumps virus to replicate, we choose the risk period to contain days 15–35 inclusive after receipt of MMR.”
Whitaker HJ, Farrington CP, Spiessens B, Musonda P. Tutorial in biostatistics: the self-controlled case series method. Statistics in Medicine. 2006; 25(10):
Age in days 

51. Age group 1 366-547 days Age group 2 548-705 days Age in days 
Whitaker HJ, Farrington CP, Spiessens B, Musonda P. Tutorial in biostatistics: the self-controlled case series method. Statistics in Medicine. 2006; 25(10):
Age in days 

52. Age group 1 366-547 days Age group 2 548-705 days
Whitaker HJ, Farrington CP, Spiessens B, Musonda P. Tutorial in biostatistics: the self-controlled case series method. Statistics in Medicine. 2006; 25(10):

53. Age group 1 366-547 days Age group 2 548-705 days
Whitaker HJ, Farrington CP, Spiessens B, Musonda P. Tutorial in biostatistics: the self-controlled case series method. Statistics in Medicine. 2006; 25(10):

54. Age group 1 366-547 days Age group 2 548-705 days
Whitaker HJ, Farrington CP, Spiessens B, Musonda P. Tutorial in biostatistics: the self-controlled case series method. Statistics in Medicine. 2006; 25(10):

55. Age group 1 366-547 days Age group 2 548-705 days
Whitaker HJ, Farrington CP, Spiessens B, Musonda P. Tutorial in biostatistics: the self-controlled case series method. Statistics in Medicine. 2006; 25(10):

56. Age group 1 366-547 days Age group 2 548-705 days
Whitaker HJ, Farrington CP, Spiessens B, Musonda P. Tutorial in biostatistics: the self-controlled case series method. Statistics in Medicine. 2006; 25(10):

57. Homogeneous exposure periods are distinct records
Whitaker HJ, Farrington CP, Spiessens B, Musonda P. Tutorial in biostatistics: the self-controlled case series method. Statistics in Medicine. 2006; 25(10):

58. Conditional Poisson regression
Whitaker HJ, Farrington CP, Spiessens B, Musonda P. Tutorial in biostatistics: the self-controlled case series method. Statistics in Medicine. 2006; 25(10):

59. Murphy et al. N Engl J Med 2001;344:564-72

60. Murphy et al. N Engl J Med 2001;344:564-72

61. In sum: Self-controlled case series
Self-controlled case series compare exposure at the time of an outcome event to the distributions of exposure in the same person.
Unmeasured covariates that do not vary over time within person do not confound the estimate of relative risk.
Self-matched studies work well for intermittent exposures whose associated risks rise and fall quickly.
The case-crossover study is a special example of self-controlled case series in which
Event terminates follow-up
Exposure history may be sample rather than exhaustively tabulated

62. Thank You!