class: center, middle, inverse, title-slide # The self-controlled case series (SCCS) ## 성균관의대 사회의학교실 강의 ### 김진섭 ### 2019-02-18 (updated: 2019-02-06) --- layout: true <div class="my-footer"><span><a href="https://www.anpanman.co.kr">ANPANMAN Co.,Ltd</a> &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; &emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp; <a href="https://github.com/jinseob2kim">김진섭</a></span></div> --- # Executive Summary .large[ * Self-controlled methods는 자기 자신을 대조군으로 비교, time-invariant confounders의 영향을 최소화할 수 있다. * **Self-controlled case series (SCCS)**, case-crossover (CCO) design, sequence symmetry analysis (SSA)가 대표적이다. * SCCS는 위험에 노출된 기간과 그렇지 않은 기간의 **상대위험도 (RR)** 를 구한다. * 한 사람에게 일어나는 각 **사건(ex: 노출, 발생, 나이)이 변화할 때 마다 데이터를 만든다** (Long format data). * Matched case-control study와 유사, **Conditional logistic regression**으로도 분석할 수 있다. ] --- # Self-controlled methods 비교 <div class="figure" style="text-align: center"> <img src="https://media.springernature.com/lw785/springer-static/image/art%3A10.1186%2Fs12874-017-0457-7/MediaObjects/12874_2017_457_Fig1_HTML.gif" alt="a: SCCS, b: CCO, c: SSA" width="50%" /> <p class="caption">a: SCCS, b: CCO, c: SSA</p> </div> Figure from <a name=cite-Takeuchi2018></a>[Takeuchi, Shinozaki, and Matsuyama [1]](https://doi.org/10.1186/s12874-017-0457-7) --- <div id="htmlwidget-4e085af0c99878d93e3d" style="width:100%;height:auto;" class="datatables html-widget"></div> <script type="application/json" data-for="htmlwidget-4e085af0c99878d93e3d">{"x":{"filter":"none","data":[["Self-controlled case series","Case-crossover design","Sequence symmetry analysis"],["Incident rate ratio","(Exposure) odds ratio","Adjusted sequence ratio"],["Case patients who experienced at least one event during each observation period","Case patients who experienced at least one event during each observation period","Case patients who experienced at least one exposure or one event during each observation period"],["Every exposure and every event for each case patient","Every exposure and the first event for each case patient","The first exposure and first event for the study population"],["Events do not alter the probability of subsequent exposure and events.","There are no time-trends in the occurrence of exposure.","Events do not alter the probability of subsequent exposure. \r\n Trends in the occurrence of exposure and events are similar to those for the study population.\n"]],"container":"<table class=\"display\">\n <thead>\n <tr>\n <th>Methods<\/th>\n <th>Effect measures<\/th>\n <th>Study populations<\/th>\n <th>Information used in analysis<\/th>\n <th>Main assumptions<\/th>\n <\/tr>\n <\/thead>\n<\/table>","options":{"dom":"<t>","order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script> Table from [Takeuchi, Shinozaki, and Matsuyama [1]](https://doi.org/10.1186/s12874-017-0457-7) --- # R example ```r library(readr);library(tidyr);library(purrr);library(dplyr);library(rmarkdown) ## Raw data dat <- read_tsv("http://statistics.open.ac.uk/sccs/R/ox.txt") paged_table(dat) ``` <div data-pagedtable="false"> <script data-pagedtable-source type="application/json"> {"columns":[{"label":["indiv"],"name":[1],"type":["dbl"],"align":["right"]},{"label":["eventday"],"name":[2],"type":["dbl"],"align":["right"]},{"label":["start"],"name":[3],"type":["dbl"],"align":["right"]},{"label":["end"],"name":[4],"type":["dbl"],"align":["right"]},{"label":["exday"],"name":[5],"type":["dbl"],"align":["right"]}],"data":[{"1":"1","2":"398","3":"365","4":"730","5":"458"},{"1":"2","2":"413","3":"365","4":"730","5":"392"},{"1":"3","2":"449","3":"365","4":"730","5":"429"},{"1":"4","2":"455","3":"365","4":"730","5":"433"},{"1":"5","2":"472","3":"365","4":"730","5":"432"},{"1":"6","2":"474","3":"365","4":"730","5":"395"},{"1":"7","2":"485","3":"365","4":"730","5":"470"},{"1":"8","2":"524","3":"365","4":"730","5":"496"},{"1":"9","2":"700","3":"365","4":"730","5":"428"},{"1":"10","2":"399","3":"365","4":"730","5":"716"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}} </script> </div> From https://rpubs.com/kaz_yos/sccs1 --- # Assumptions - 노출 위험 기간: 노출 시작부터 14-35일. - 나이 바뀌는 날: 365-730일의 중간인 547일. -- <div data-pagedtable="false"> <script data-pagedtable-source type="application/json"> {"columns":[{"label":["indiv"],"name":[1],"type":["dbl"],"align":["right"]},{"label":["eventday"],"name":[2],"type":["dbl"],"align":["right"]},{"label":["start"],"name":[3],"type":["dbl"],"align":["right"]},{"label":["end"],"name":[4],"type":["dbl"],"align":["right"]},{"label":["exday"],"name":[5],"type":["dbl"],"align":["right"]}],"data":[{"1":"1","2":"398","3":"365","4":"730","5":"458"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}} </script> </div> - 365: 관찰 시작 - 472: 노출 시작 (458 + 14) - 493: 노출 종료 (458 + 35) - 547: 나이 증가 - 730: 관찰 종료 4개 구간 각각의 **사건 발생, 노출 상태, 나이** 데이터를 만들어야 함. --- # Long format data ```r datLong <- dat %>% mutate(start1 = exday +14, end1 = exday + 35, age1 = 547) %>% split(.$indiv) %>% map_dfr(MakeLongformat) %>% filter(start < 730) paged_table(datLong) ``` <div data-pagedtable="false"> <script data-pagedtable-source type="application/json"> 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</script> </div> --- ```r MakeLongformat <- function(df) { ## Cut points cuts <- with(df, sort(c(start, end, start1, end1, age1))) ## Split observation times out <- tibble(indiv = df$indiv, exday = df$exday, eventday = df$eventday, start = head(cuts, -1), end = cuts[-1]) ## Event, exposure, and age group status for each interval out %>% mutate(event = as.integer(start <= eventday & eventday <= end), exgr = as.integer(df$start1 <= start & end <= df$end1), agegr = as.integer(start >= df$age1), interval = end - start, loginterval = log(interval)) } ``` --- # Poisson regression with matched sample A Poisson distribution during the period `\(k\)` of patient `\(i\)` with expected events: `\(\lambda_{ik}\)` `$$\lambda_{ik} = t_{ik}\exp(\phi_i + \beta X_i(k))$$` - `\(t_{ik}\)`: Length of period `\(k\)` (as an **offset term**) - `\(\exp(\phi_i)\)`: The baseline (i.e., unexposed) incidence rate - `\(X_i(k)\)`: The exposure status of period `\(k\)` (0 for the control period and 1 for the exposure period) of patient `\(i\)` -- **[gnm](https://cran.r-project.org/package=gnm)** package 이용<a name=cite-dnmRpackage></a>[[2](https://cran.r-project.org/package=gnm)]. --- ```r library(gnm) gnm(event ~ exgr + agegr + offset(loginterval), eliminate = factor(indiv), family = poisson, data = datLong) %>% summary ``` ``` ## ## Call: ## ## gnm(formula = event ~ exgr + agegr + offset(loginterval), eliminate = factor(indiv), ## family = poisson, data = datLong) ## ## Deviance Residuals: ## Min 1Q Median 3Q Max ## -1.05409 -0.60311 -0.42566 0.08177 1.72741 ## ## Coefficients of interest: ## Estimate Std. Error z value Pr(>|z|) ## exgr 2.4880 0.7085 3.512 0.000445 *** ## agegr -1.4906 1.1182 -1.333 0.182543 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## (Dispersion parameter for poisson family taken to be 1) ## ## Residual deviance: 20.177 on 26 degrees of freedom ## AIC: 64.177 ## ## Number of iterations: 5 ``` --- # Conditional logistic regression Event는 포아송 분포를 따른다는 가정, 그러나 **0 아니면 1** 두 가지 뿐. - Conditional logistic regression을 이용해도 같은 결과를 얻음. - `offset(loginterval)` 옵션 추가로 끝. - **[survival](https://CRAN.R-project.org/package=survival)** 패키지의 `clogit` 함수<a name=cite-survival-package></a>[[3](https://CRAN.R-project.org/package=survival)]. --- ```r library(survival) clogit(event ~ exgr + agegr + offset(loginterval) + strata(indiv), data = datLong) %>% summary ``` ``` ## Call: ## coxph(formula = Surv(rep(1, 38L), event) ~ exgr + agegr + offset(loginterval) + ## strata(indiv), data = datLong, method = "exact") ## ## n= 38, number of events= 10 ## ## coef exp(coef) se(coef) z Pr(>|z|) ## exgr 2.4880 12.0369 0.7085 3.512 0.000445 *** ## agegr -1.4906 0.2252 1.1182 -1.333 0.182543 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## exp(coef) exp(-coef) lower .95 upper .95 ## exgr 12.0369 0.08308 3.00226 48.259 ## agegr 0.2252 4.43965 0.02517 2.016 ## ## Concordance= 0.75 (se = 0.138 ) ## Rsquare= 0.392 (max possible= 0.643 ) ## Likelihood ratio test= 18.92 on 2 df, p=8e-05 ## Wald test = 19.1 on 2 df, p=7e-05 ## Score (logrank) test = 42.29 on 2 df, p=7e-10 ``` --- # 조심 .large[ - Time-varying confounder - Time trends in both exposures and events - Erroneously long risk periods - Patient restriction based on event history ] --- <div id="htmlwidget-0aec2abe34c7a45687a9" style="width:100%;height:auto;" class="datatables html-widget"></div> <script type="application/json" data-for="htmlwidget-0aec2abe34c7a45687a9">{"x":{"filter":"none","caption":"<caption>Violation of assumptions, impact, and solutions with examples of good practice<\/caption>","data":[["Event temporarily decreases probability of exposure","Event temporarily increases probability of exposure","No exposure can occur (or is observed) after event",null,"Event increases probability of death",null,"Recurrences of an event are not independent"],["Include a pre-exposure period","Include a pre-exposure period","For single exposures that cannot be repeated, begin observation period at exposure, so only exposed cases are included. End observation at planned end","For single or multiple exposures, use method outlined in Farrington et al","Undertake suitable tests or sensitivity analyses excluding cases who died as a result of event","If necessary, use methods outlined in Farrington et al to adjust for bias","Study first event only"],["Stowe et al studied the risk of infections after mumps, measles, and rubella vaccination. Vaccination is delayed when a child has an infection; a 14 day pre-exposure period was included to allow for this","Gibson et al studied the association between prescription drugs and motor vehicle crashes. A four week pre-exposure period was included as some drugs may be used to treat anxiety or pain caused by the crash","Hubbard et al studied the association between first bupropion prescription and sudden death. The observation period began with date of first prescription and ended (beyond death) with date of last data collection for the cohort. At the time, bupropion could only be prescribed as a single course of treatment","Dodd et al studied the association between influenza vaccination and Guillain Barré syndrome (GBS). Some practitioners will not vaccinate patients with previous GBS.10 Various analyses were performed: standard SCCS, vaccinated cases only, and the method outlined in Farrington et al","Langan et al studied the risk of stroke after herpes zoster infection. A sensitivity analysis was performed excluding cases who died within 90 days of stroke. Findings were not modified","Brauer et al studied the association between antipsychotic drugs and myocardial infarction using both methods outlined in Farrington et al12 and a standard SCCS analysis. There was little difference in results","Recurrence of stroke is not independent of the first occurrence, so only a first stroke event can be studied. In a study on the risk of stroke, Langan et al began the observation period 12 months into follow-up time to ensure first stroke events had been correctly identified11"]],"container":"<table class=\"display\">\n <thead>\n <tr>\n <th>Problems<\/th>\n <th>Solutions<\/th>\n <th>Examples<\/th>\n <\/tr>\n <\/thead>\n<\/table>","options":{"dom":"<<t>ip>","pageLength":3,"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[3,10,25,50,100]}},"evals":[],"jsHooks":[]}</script> Table from <a name=cite-Petersen2016></a>[Petersen, Douglas, and Whitaker [4]](https://doi.org/10.1136/bmj.i4515) --- class: center, middle # END --- # References <a name=bib-Takeuchi2018></a>[[1]](#cite-Takeuchi2018) Y. Takeuchi, T. Shinozaki and Y. Matsuyama. "A comparison of estimators from self-controlled case series, case-crossover design, and sequence symmetry analysis for pharmacoepidemiological studies". In: _BMC Medical Research Methodology_ 18.1 (Jan. 2018). DOI: [10.1186/s12874-017-0457-7](https://doi.org/10.1186/s12874-017-0457-7). URL: [https://doi.org/10.1186/s12874-017-0457-7](https://doi.org/10.1186/s12874-017-0457-7). <a name=bib-dnmRpackage></a>[[2]](#cite-dnmRpackage) H. Turner and D. Firth. _Generalized nonlinear models in R: An overview of the gnm package_. R package version 1.1-0. 2018. URL: [https://cran.r-project.org/package=gnm](https://cran.r-project.org/package=gnm). <a name=bib-survival-package></a>[[3]](#cite-survival-package) T. M. Therneau. _A Package for Survival Analysis in S_. version 2.38. 2015. URL: [https://CRAN.R-project.org/package=survival](https://CRAN.R-project.org/package=survival). <a name=bib-Petersen2016></a>[[4]](#cite-Petersen2016) I. Petersen, I. Douglas and H. Whitaker. "Self controlled case series methods: an alternative to standard epidemiological study designs". In: _BMJ_ (Sep. 2016), p. i4515. DOI: [10.1136/bmj.i4515](https://doi.org/10.1136/bmj.i4515). URL: [https://doi.org/10.1136/bmj.i4515](https://doi.org/10.1136/bmj.i4515).