Self-controlled case series studies: Just how rare does a rare non-recurrent outcome need to be?

The self-controlled case series method assumes that adverse outcomes arise according to a non-homogeneous Poisson process. This implies that it is applicable to independent recurrent outcomes. However, the self-controlled case series method may also be applied to unique, non-recurrent outcomes or first outcomes only, in the limit where these become rare. We investigate this rare outcome assumption when the self-controlled case series method is applied to non-recurrent outcomes. We study this requirement analytically and by simulation, and quantify what is meant by 'rare' in this context. In simulations we also apply the self-controlled risk interval design, a special case of the self-controlled case series design. To illustrate, we extract data on the incidence rate of some recurrent and non-recurrent outcomes within a defined study population to check whether outcomes are sufficiently rare for the rare outcome assumption to hold when applying the self-controlled case series method to first or unique outcomes. The main findings are that the relative bias should be no more than 5% when the cumulative incidence over total time observed is less than 0.1 per individual. Inclusion of age (or calendar time) effects will further reduce bias. Designs that begin observation with exposure maximise bias, whereas little or no bias will be apparent when there is no time trend in the distribution of exposures, or when exposure is central within time observed.

Investigating the assumptions of the self-controlled case series method.

We describe some simple techniques for investigating 2 key assumptions of the self-controlled case series (SCCS) method, namely, that events do not influence subsequent exposures and that events do not influence the length of observation periods. For each assumption, we propose some simple tests based on the standard SCCS model, along with associated graphical displays. The methods also enable the user to investigate the robustness of the results obtained using the standard SCCS model to failure of assumptions. The proposed methods are investigated by simulations and applied to data on measles, mumps and rubella vaccine, and antipsychotics.

Spline-based self-controlled case series method.

The self-controlled case series (SCCS) method is an alternative to study designs such as cohort and case control methods and is used to investigate potential associations between the timing of vaccine or other drug exposures and adverse events. It requires information only on cases, individuals who have experienced the adverse event at least once, and automatically controls all fixed confounding variables that could modify the true association between exposure and adverse event. Time-varying confounders such as age, on the other hand, are not automatically controlled and must be allowed for explicitly. The original SCCS method used step functions to represent risk periods (windows of exposed time) and age effects. Hence, exposure risk periods and/or age groups have to be prespecified a priori, but a poor choice of group boundaries may lead to biased estimates. In this paper, we propose a nonparametric SCCS method in which both age and exposure effects are represented by spline functions at the same time. To avoid a numerical integration of the product of these two spline functions in the likelihood function of the SCCS method, we defined the first, second, and third integrals of I-splines based on the definition of integrals of M-splines. Simulation studies showed that the new method performs well. This new method is applied to data on pediatric vaccines. Copyright © 2017 John Wiley & Sons, Ltd.

Comparison of Statistical Algorithms for the Detection of Infectious Disease Outbreaks in Large Multiple Surveillance Systems.

A large-scale multiple surveillance system for infectious disease outbreaks has been in operation in England and Wales since the early 1990s. Changes to the statistical algorithm at the heart of the system were proposed and the purpose of this paper is to compare two new algorithms with the original algorithm. Test data to evaluate performance are created from weekly counts of the number of cases of each of more than 2000 diseases over a twenty-year period. The time series of each disease is separated into one series giving the baseline (background) disease incidence and a second series giving disease outbreaks. One series is shifted forward by twelve months and the two are then recombined, giving a realistic series in which it is known where outbreaks have been added. The metrics used to evaluate performance include a scoring rule that appropriately balances sensitivity against specificity and is sensitive to variation in probabilities near 1. In the context of disease surveillance, a scoring rule can be adapted to reflect the size of outbreaks and this was done. Results indicate that the two new algorithms are comparable to each other and better than the algorithm they were designed to replace.

Flexible modelling of vaccine effect in self-controlled case series models.

The self-controlled case series (SCCS) method, commonly used to investigate the safety of vaccines, requires information on cases only and automatically controls all age-independent multiplicative confounders, while allowing for an age-dependent baseline incidence. Currently, the SCCS method represents the time-varying exposures using step functions with pre-determined cut points. A less prescriptive approach may be beneficial when the shape of the relative risk function associated with exposure is not known a priori, especially when exposure effects can be long-lasting. We therefore propose to model exposure effects using flexible smooth functions. Specifically, we used a linear combination of cubic M-splines which, in addition to giving plausible shapes, avoids the integral in the log-likelihood function of the SCCS model. The methods, though developed specifically for vaccines, are applicable more widely. Simulations showed that the new approach generally performs better than the step function method. We applied the new method to two data sets, on febrile convulsion and exposure to MMR vaccine, and on fractures and thiazolidinedione use.

Antipsychotic drugs and risks of myocardial infarction: a self-controlled case series study.

AIM: Antipsychotics increase the risk of stroke. Their effect on myocardial infarction remains uncertain because people prescribed and not prescribed antipsychotic drugs differ in their underlying vascular risk making between-person comparisons difficult to interpret. The aim of our study was to investigate this association using the self-controlled case series design that eliminates between-person confounding effects. METHODS AND RESULTS: All the patients with a first recorded myocardial infarction and prescription for an antipsychotic identified in the Clinical Practice Research Datalink linked to the Myocardial Ischaemia National Audit Project were selected for the self-controlled case series. The incidence ratio of myocardial infarction during risk periods following the initiation of antipsychotic use relative to unexposed periods was estimated within individuals. A classical case-control study was undertaken for comparative purposes comparing antipsychotic exposure among cases and matched controls. We identified 1546 exposed cases for the self-controlled case series and found evidence of an association during the first 30 days after the first prescription of an antipsychotic, for first-generation agents [incidence rate ratio (IRR) 2.82, 95% confidence interval (CI) 2.0-3.99] and second-generation agents (IRR: 2.5, 95% CI: 1.18-5.32). Similar results were found for the case-control study for new users of first- (OR: 3.19, 95% CI: 1.9-5.37) and second-generation agents (OR: 2.55, 95% CI: 0.93-7.01) within 30 days of their myocardial infarction. CONCLUSION: We found an increased risk of myocardial infarction in the period following the initiation of antipsychotics that was not attributable to differences between people prescribed and not prescribed antipsychotics.

Self-controlled case series method with smooth age effect.

The self-controlled case series method, commonly used to investigate potential associations between vaccines and adverse events, requires information on cases only and automatically controls all age-independent multiplicative confounders while allowing for an age-dependent baseline incidence. In the parametric version of the method, we modelled the age-specific relative incidence by using a piecewise constant function, whereas in the semiparametric version, we left it unspecified. However, mis-specification of age groups in the parametric version can lead to biassed estimates of exposure effect, and the semiparametric approach runs into computational problems when the number of cases in the study is moderately large. We, thus, propose to use a penalized likelihood approach where the age effect is modelled using splines. We use a linear combination of cubic M-splines to approximate the age-specific relative incidence and integrated splines for the cumulative relative incidence. We conducted a simulation study to evaluate the performance of the new approach and its efficiency relative to the parametric and semiparametric approaches. Results show that the new approach performs equivalently to the existing methods when the sample size is small and works well for large data sets. We applied the new spline-based approach to data on febrile convulsions and paediatric vaccines. Co

Self-controlled case series and misclassification bias induced by case selection from administrative hospital databases: application to febrile convulsions in pediatric vaccine pharmacoepidemiology.

Vaccine safety studies are increasingly conducted by using administrative health databases and self-controlled case series designs that are based on cases only. Often, several criteria are available to define the cases, which may yield different positive predictive values, as well as different sensitivities, and therefore different numbers of selected cases. The question then arises as to which is the best case definition. This article proposes new methodology to guide this choice based on the bias of the relative incidence and the power of the test. We apply this methodology in a validation study of 4 nested algorithms for identifying febrile convulsions from the administrative databases of 10 French hospitals. We used a sample of 695 children aged 1 month to 3 years who were hospitalized in 2008-2009 with at least 1 diagnosis code of febrile convulsions. The positive predictive values of the algorithms ranged from 81% to 98%, and their sensitivities were estimated to be 47%-99% in data from 1 large hospital. When applying our proposed methods, the algorithm we selected used a restricted diagnosis code and position on the discharge abstract. These criteria, which resulted in the selection of 502 cases with a positive predictive value of 95%, provided the best compromise between high power and low relative bias.

Correlated infections: quantifying individual heterogeneity in the spread of infectious diseases.

In this paper, we propose new methods for investigating the extent of heterogeneity in effective contact rates relevant to the transmission of infections. These methods exploit the correlations between ages at infection for different infections within individuals. The methods are developed for serological surveys, which provide accessible individual data on several infections, and are applied to a wide range of infections. We find that childhood infections are often highly correlated within individuals in early childhood, with the correlations persisting into adulthood only for infections sharing a transmission route. We discuss 2 applications of the methods: 1) to making inferences about routes of transmission when these are unknown or uncertain and 2) to estimating epidemiologic parameters such as the basic reproduction number and the critical immunization threshold. Two examples of such applications are presented: elucidating the transmission route of polyomaviruses BK and JC and estimating the basic reproduction number and critical immunization coverage of varicella-zoster infection in Belgium, Italy, Poland, and England and Wales. We speculate that childhood correlations stem from confounding of different transmission routes and represent heterogeneity in childhood circumstances, notably nursery-school attendance. In contrast, it is suggested that correlations in adulthood are route-specific.

Estimation of basic reproduction numbers: individual heterogeneity and robustness to perturbation of the contact function.

The basic reproduction number of an infection in a given population, R0, is inflated by individual heterogeneity in contact rates. Recently, new methods for estimating R0 using social contact data and serological survey data have been proposed. These methods, like most of their predecessors, ignore individual heterogeneity, and are sensitive to perturbation of the contact function. Using a frailty framework, we derive expressions for R0 in the presence of age-varying heterogeneity. In this case, R0 is the spectral radius of a population version of the next generation operator, which involves the variance function of the age-dependent frailty. This variance can be estimated within a shared frailty framework from paired data on two infections transmitted by the same route. We propose two estimators of R0 for infections in endemic equilibrium. We investigate their performance by simulation, and find that one is generally less efficient but more robust than the other to perturbation of the effective contact function. These methods are applied to data on varicella zoster virus infection from two European countries.

Automated biosurveillance data from England and Wales, 1991-2011.

Outbreak detection systems for use with very large multiple surveillance databases must be suited both to the data available and to the requirements of full automation. To inform the development of more effective outbreak detection algorithms, we analyzed 20 years of data (1991-2011) from a large laboratory surveillance database used for outbreak detection in England and Wales. The data relate to 3,303 distinct types of infectious pathogens, with a frequency range spanning 6 orders of magnitude. Several hundred organism types were reported each week. We describe the diversity of seasonal patterns, trends, artifacts, and extra-Poisson variability to which an effective multiple laboratory-based outbreak detection system must adjust. We provide empirical information to guide the selection of simple statistical models for automated surveillance of multiple organisms, in the light of the key requirements of such outbreak detection systems, namely, robustness, flexibility, and sensitivity.

A new measure of time-varying association for shared frailty models with bivariate current status data.

In this paper, a new measure for assessing the temporal variation in the strength of association in bivariate current status data is proposed. This novel measure is relevant for shared frailty models. We show that this measure is particularly convenient, owing to its connection with the relative frailty variance and its interpretability in suggesting appropriate frailty models. We introduce a method of estimation and standard errors for this measure. We discuss its properties and compare it to an existing measure of association applicable to current status data. Small sample performance of the measure in realistic scenarios is investigated using simulations. The methods are illustrated with bivariate serological survey data on a pair of infections, where the time-varying association is likely to represent heterogeneities in activity levels and/or susceptibility to infection.

A modified self-controlled case series method to examine association between multidose vaccinations and death.

The self-controlled case series method (SCCS) was developed to analyze the association between a time-varying exposure and an outcome event. We consider penta- or hexavalent vaccination as the exposure and unexplained sudden unexpected death (uSUD) as the event. The special situation of multiple exposures and a terminal event requires adaptation of the standard SCCS method. This paper proposes a new adaptation, in which observation periods are truncated according to the vaccination schedule. The new method exploits known minimum spacings between successive vaccine doses. Its advantage is that it is very much simpler to apply than the method for censored, perturbed or curtailed post-event exposures recently introduced. This paper presents a comparison of these two SCCS methods by simulation studies and an application to a real data set. In the simulation studies, the age distribution and the assumed vaccination schedule were based on real data. Only small differences between the two SCCS methods were observed, although 50 per cent of cases could not be included in the analysis with the SCCS method with truncated observation periods. By means of a study including 300 uSUD, a 16-fold risk increase after the 4th dose could be detected with a power of at least 90 per cent. A general 2-fold risk increase after vaccination could be detected with a power of 80 per cent. Reanalysis of data from cases of the German case-control study on sudden infant death (GeSID) resulted in slightly higher point estimates using the SCCS methods than the odds ratio obtained by the case-control analysis.

Case series analysis for censored, perturbed, or curtailed post-event exposures.

A new method is developed for analyzing case series data in situations where occurrence of the event censors, curtails, or otherwise affects post-event exposures. Unbiased estimating equations derived from the self-controlled case series model are adapted to allow for exposures whose occurrence or observation is influenced by the event. The method applies to transient point exposures and rare nonrecurrent events. Asymptotic efficiency is studied in some special cases. A computational scheme based on a pseudo-likelihood is proposed to make the computations feasible in complex models. Simulations, a validation study, and 2 applications are described.

The methodology of self-controlled case series studies.

The self-controlled case series method is increasingly being used in pharmacoepidemiology, particularly in vaccine safety studies. This method is typically used to evaluate the association between a transient exposure and an acute event, using only cases. We present both parametric and semiparametric models using a motivating example on MMR vaccine and bleeding disorders. We briefly describe approaches for interferent events and a sequential version of the method for prospective surveillance of drug safety. The efficiency of the self-controlled case series method is compared to the that of cohort and case control studies. Some further extensions, to long or indefinite exposures and to bivariate counts, are described.

Monitoring vaccine safety using case series cumulative sum charts.

We adapt the self-controlled case series method for routine surveillance of vaccine safety using cumulative sum (CUSUM) charts. The CUSUM surveillance method we propose is applicable for detecting associations that arise in a short pre-determined risk period following vaccination. The performance of the case series CUSUM is investigated through simulations. We illustrate the method using retrospective analyses of influenza vaccine and Bell's palsy, and MMR vaccine and febrile convulsions.

Tutorial in biostatistics: the self-controlled case series method.

The self-controlled case series method was developed to investigate associations between acute outcomes and transient exposures, using only data on cases, that is, on individuals who have experienced the outcome of interest. Inference is within individuals, and hence fixed covariates effects are implicitly controlled for within a proportional incidence framework. We describe the origins, assumptions, limitations, and uses of the method. The rationale for the model and the derivation of the likelihood are explained in detail using a worked example on vaccine safety. Code for fitting the model in the statistical package STATA is described. Two further vaccine safety data sets are used to illustrate a range of modelling issues and extensions of the basic model. Some brief pointers on the design of case series studies are provided. The data sets, STATA code, and further implementation details in SAS, GENSTAT and GLIM are available from an associated website.

Sample sizes for self-controlled case series studies.

We derive several formulae for the sample size required for a study designed using the self-controlled case series method without age effects. We investigate these formulae by simulation, and identify one based on the signed root likelihood ratio statistic which performs well. We extend this method to allow for age effects, which can have a big impact on the sample size needed. This more general sample size formula is also found to perform well in a broad range of situations.