On estimation of vaccine efficacy using validation samples with selection bias

Design and Analysis of Vaccine Studies
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Contents:

  • Design and Analysis of Vaccine Studies | SpringerLink
  • Urn models and vaccine efficacy estimation
  • References
  • Background
  • About this book

    • These problems would be most pronounced when the duration of follow-up is relatively short, the hazard is not constant, and the extent of misclassification differs between the groups.

    While within-subject study designs such as the case-crossover [ 28 ] and self-controlled case series [ 29 , 30 ] minimize bias due to confounding by time-invariant characteristics and comorbidities, they remain susceptible to bias due to misclassification of exposure. The ability to study rare clinical outcomes in a very large, population-based sample is a potential strength of claims data, but likewise a source of concern due to potential misclassification.

    Outcomes such as death are considered reliable in some data sources while they are only observed when they occur in the hospital in other data sources [ 31 ].

    Design and Analysis of Vaccine Studies | SpringerLink

    Clinical events may be acute and result in hospitalization such as hip fracture or chronic with or without specific clinical interventions such as type II diabetes. The degree of misclassification of these outcomes can vary considerably. Medical procedures are considered reliable in billing data given the close relationship and regulated nature of billings for procedures and physician payment.

    ICD-9 procedure codes, used by hospitals to bill for the facility component of charges, are not sufficiently specific in many instances, while CPT codes, used by physicians to bill for their services, are more specific. The importance of validating clinical outcomes has been appreciated since the early days of studies conducted using health care claims data as a means by which to assure that a highly specific outcome definition was devised. Misclassification of outcomes can occur differentially by exposure status by virtue of the fact that individuals who receive a prescription may receive more intensive health screenings and monitoring than patients who are not receiving medication or are receiving a different medication.

    These might include differences in health-seeking behaviors screening or diagnostic workups for suspected health problems [ 33 ], more frequent lab testing for potential liver or kidney damage if the medication is suspected to increase risk [ 34 ], or use of follow-up colonoscopies after selected types of radiation [ 35 , 36 ].

    Urn models and vaccine efficacy estimation

    This would decrease the proportion of individuals who have the outcome who are incorrectly classified as unaffected among patients with the exposure. Misclassification in the setting of claims data is a significant concern in light of the fact that the absence of a diagnosis or related procedures in claims during a specified time period is taken to indicate the absence of the condition.

    Patients who do not have healthcare encounters will not generate evidence of their conditions, and those with significant co-morbidity may not have evidence of common, less serious conditions such as hypertension when they are under active treatment CABG [ 37 ]. Typically, studies using insurance claims data define a baseline period during which individuals must be continuously enrolled [ 38 ].

    The robustness of this finding under a variety of conditions is still being established, but it serves as a challenge to reconsider the status quo. As questions were being raised about the use of placebo-controlled trials when effective treatment alternatives were available [ 40 ], so did pharmacoepidemiologists begin to recognize the value of active comparators in the setting of non-experimental research on medication safety and effectiveness.

    The comparison of two active agents has made pharmacoepidemiologic studies less susceptible to biases due to confounding by indication, healthy user bias, confounding by frailty, and other sources of unmeasured confounding [ 41 ]. In addition, biases due to misclassification of confounders and outcomes described above are likely less pronounced with an active comparator.

    That said, there are several aspects of comparative effectiveness studies which make them particularly susceptible to bias due to misclassification including the comparison of two active treatments, modest effect sizes that are clinically meaningful, the value of absolute measures of effect such as the risk difference , and the extreme precision that comes from analyzing large datasets.

    In studies of comparative effectiveness in which two active treatments are being compared, there are at least three and possibly more levels of exposure: non-user, user of medication A, and user of medication B. Misclassification of individuals who were truly exposed to medications A and B would place individuals in the non-user category, not in the other category of exposure. Misclassification of this type could result in estimates that are toward or away from the null, even though there are only two levels of exposure being analyzed.

    References

    An original paper copy of this issue can be obtained from the Superintendent of Documents, U. Change from —11 to —12 influenza season percentage points. The impact of the misclassification parameters was comparable across designs. Fig 1. CDC is not responsible for the content of pages found at these sites. Similarly, the true positives and false positives for vaccination determine the disease risk among the subjects indicated as vaccinated or 9.

    Hypothetical example of studies in which individuals exposed to one of two drugs are each compared with non-users, or compared with each other in the presence of nondifferential exposure misclassification. Drug A vs. Drug B vs. All are non-differential with respect to disease Y status. No individuals exposed to Drug A are misclassified as exposed to Drug B or vice versa. The potential for bias to obscure a clinically relevant difference or create the appearance of a difference where there is none is heightened in this context.

    Modest effect sizes are particularly susceptible to the effects of residual confounding due to misclassified covariate data.

    In light of the potential for bias due to exposure misclassification that could be in any direction, this is a setting in which validation studies and quantifying the impact on estimates and uncertainty are particularly important. The choice of effect measures in CER also increases concern about bias due to misclassification. While relative effect measures remain dominant, there is growing recognition that absolute measures are important, particularly in terms of communicating the relevance of the findings to patients [ 45 , 46 ].

    Achieving near perfect specificity in the outcome classification may allow us to claim that the relative effect estimate is unlikely to be considerably biased, but the estimated risks and risk differences will still be under-estimated if the sensitivity is not perfect unless further analysis is used to correct for the non-perfect sensitivity of the outcome definition.

    Analyses of claims data are powerful and allow us to examine rare outcomes. Very large sample sizes which may give the appearance of precision, making a very small increase or decrease e. In the presence of misclassification, these confidence intervals misrepresent the true uncertainty about the estimate. Because of the very nature of comparative effectiveness research, quantifying the extent of these errors and adjusting the effect estimates and their confidence intervals is particularly important. Various methods for doing so have been developed and are discussed in the following section.

    Sources: Rothman et al. Code: Lash et al.

    Background

    Analytic variable Exposure, outcome, covariate. Fink and Lash [ 61 ] conducted a simple bias analysis in a birth cohort in Massachusetts to explore a range of sensitivity values for maternal smoking reported on the birth certificate, based on results of prior validation studies. Jurek and Greenland [ 62 ] simultaneously considered misclassification of exposure maternal smoking and outcome clefting using the matrix adjustment method of bias analysis. Code: Fox et al.

    Background

    Data source s Internal validation sample, external validation study, prior literature or study results, expert opinion. Ahrens et al. Lash et al.

    1. Nat Turner: A Slave Rebellion in History and Memory;
    2. The Expeditions;
    3. On Estimation of Vaccine Efficacy Using Validation Samples with Selection Bias (2006).

    Code: MacLehose et al. MacLehose et al. Keil et al. Sources: Magder and Hughes [ 68 ], Neuhaus [ 69 ], Lyles et al.

    Statistical methods used to calculate sample sizes

    Code: Edwards et al. Analytic variable Exposure, outcome. Edwards et al. Shebl et al. Multiple imputation for measurement error MIME. Sources: Cole et al. Code: Cole et al. Data source s Internal validation study,. Sources: Rosner et al. Analytic variable Exposure, covariate. Data source s Internal validation study, external validation sample. Murphy et al. Toh et al. This method is the easiest to implement, but also has the most limited potential for use in the setting of pharmacoepidemiology.

    About this book

    The corrections can be applied to categorized exposure, outcome, or covariates. Corrections can be implemented based only on expert opinion or estimates from the literature — an advantage in the setting where validation data are not available. This approach would be suitable for the analysis of short-term outcomes such as in-hospital mortality where all individuals are followed for a consistent period of time, but it is not suitable for outcomes that are partially censored time-to-event.

    It does not account for error in the estimation of the sensitivity and specificity in the adjusted effect estimates, and it does not simultaneously control for other covariates. This approach is essentially an iterative version of the simple bias analysis which uses a distribution of values for sensitivity and specificity or positive and negative predictive values combined with a Monte Carlo process to produce a distribution of estimates adjusted for misclassification.

    The credible intervals from this analysis can reflect the uncertainty around the validation measures. This method is also described in detail by Lash et al. Bayesian bias analysis is similar to the probabilistic bias analysis, but with the addition of prior distributions for all parameters — not just those for misclassification. Like probabilistic bias analysis, random error is reflected in the adjusted effect estimates. In most cases, this method does not out-perform probabilistic bias analysis [ 49 ].

    The more complex implementation in terms of software and programming makes the Bayesian approach less attractive as a general method for application in analyses of claims data, although code for applying this method using BUGS has been published by MacLehose et al. This method uses the full data rather than tabled data to fit a modified maximum likelihood that forces the sensitivity and specificity to be less than perfect. This method has been demonstrated with dichotomous and polytomous exposures and outcomes, including outcomes that are Poisson distributed to estimate the rate ratio.

    This method would be suitable for analyses in which follow-up time varies between individuals for estimating rates rather than risks and the hazard is approximately constant. In this approach, the true value of the misclassified variable is treated as partially missing data. The gold standard measures from an internal validation sample are used to fit a model for the imperfect data, and multiple datasets with imputed values for the misclassified variable are created.

    The effect estimates from analyses of these datasets are then combined to account for the variability introduced through the imputation. This approach would be well suited to analyses of claims data in which the exposure or covariate are misclassified and the outcome has been ascertained during differing amounts of follow-up time. Cole et al. This method is best suited to the setting in which a continuous variable exposure or covariate is measured with error. Regression calibration can take advantage of multiple, imperfect measures of a characteristic such as blood pressure in the absence of a single gold standard measure [ 53 , 54 ].

    This approach has been used extensively in the field of nutritional epidemiology, but could be useful in pharmacoepidemiology studies in which lab results are available. A SAS macro is provided by Logan and Spiegelman for the correction of measurement error in the context of logistic regression [ 55 ]. Propensity score calibration addresses covariate misclassification and measurement error by treating the propensity score as having been estimated with error.

    Like regression calibration, propensity score calibration requires a surrogacy assumption. Surrogacy is, however, less likely to hold for the propensity score than for a mismeasured covariate [ 56 ]. Given the prominence of propensity score analyses in the pharmacoepidemiology field, this is a natural extension of the analytic methods used in many studies.

    In the context of claims data, hundreds of covariates many of which are presumably measured with error related to thousands of individuals pose difficult logistical problems for applying these methods and presenting an integrated view of the effect of misclassification.

    Edited by Peter G. Smith, Richard H. Morrow, and David A. Ross

    There has also been an assumption that prescription claims data were sufficiently reliable that there was little concern for misclassification of exposure. Compared to self-reported data on medication use, often even retrospective, these data are likely more reliable. But they are not infallible, as shown by Li et al. Lauffenberger et al. It is not yet clear what the gold-standard measure for prescription medications use should be in light of research showing that administrative claims, physician orders, medical records, pharmacy records, and self-report are all subject to some degree of error.

    In the context of pharmacoepidemiologic analyses, follow-up time is typically censored which necessitates the use of methods such as Poisson, Kaplan-Meier lifetables, or Cox proportional hazards regression to estimate the treatment effect.