Directional penalties for optimal matching in observational studies

Multivariate matching in observational studies tends to view covariate differences symmetrically: a difference in age of 10 years is thought equally problematic whether the treated subject is older or younger than the matched control. If matching is correcting an imbalance in age, such that treated subjects are typically older than controls, then the situation in need of correction is asymmetric: a matched pair with a difference in age of 10 years is much more likely to have an older treated subject and a younger control than the opposite. Correcting the bias may be easier if matching tries to avoid the typical case that creates the bias. We describe several easily used, asymmetric, directional penalties and illustrate how they can improve covariate balance in a matched sample. The investigator starts with a matched sample built in a conventional way, then diagnoses residual covariate imbalances in need of reduction, and achieves the needed reduction by slightly altering the distance matrix with directional penalties, creating a new matched sample. Unlike penalties commonly used in matching, a directional penalty can go too far, reversing the direction of the bias rather than reducing the bias, so the magnitude of the directional penalty matters and may need adjustment. Our experience is that two or three adjustments, guided by balance diagnostics, can substantially improve covariate balance, perhaps requiring fifteen minutes effort sitting at the computer. We also explore the connection between directional penalties and a widely used technique in integer programming, namely Lagrangian relaxation of problematic linear side constraints in a minimum cost flow problem. In effect, many directional penalties are Lagrange multipliers, pushing a matched sample in the direction of satisfying a linear constraint that would not be satisfied without penalization. The method and example are in an R package DiPs at CRAN .     

Substantial gains in bias reduction from matching with a variable number of controls

In observational studies that match several controls to each treated subject, substantially greater bias reduction is possible if the number of controls is not fixed but rather is allowed to vary from one matched set to another. In certain cases, matching with a fixed number of controls may remove only 50% of the bias in a covariate, whereas matching with a variable number of controls may remove 90% of the bias, even though both control groups have the same number of controls in total. An example of matching in a study of surgical mortality is discussed in detail.     

Estimating counterfactuals for evaluation of ecological and conservation impact: an introduction to matching methods

Matching methods encompass non-parametric approaches to estimating counterfactual states through a rigorous selection of control units with similar characteristics to units submitted to an intervention. These methods enable comparisons between treated and control units in a way that facilitates understanding of causal relationships between interventions and outcomes. Matching methods have been used only recently in ecology and conservation biology, where such applications changed the way the field investigates causal questions, for example, in impact-evaluation studies. However, the strengths and limitations of matching methods are not well understood by most ecologists and environmental scientists. Herein, we review state-of-the-art matching methods aiming to help fill this gap in understanding. First, we present relevant theoretical concepts related to matching methods and related subjects such as counterfactual states and causation. Next, we propose guidelines and strategies for the application of matching methods in ecology and conservation biology. Finally, we discuss the possibilities for future applications of matching methods in the environmental sciences.     

Estimating the Counterfactual Impact of Conservation Programs on Land Cover Outcomes: The Role of Matching and Panel Regression Techniques

Deforestation and conversion of native habitats continues to be the leading driver of biodiversity and ecosystem service loss. A number of conservation policies and programs are implemented—from protected areas to payments for ecosystem services (PES)—to deter these losses. Currently, empirical evidence on whether these approaches stop or slow land cover change is lacking, but there is increasing interest in conducting rigorous, counterfactual impact evaluations, especially for many new conservation approaches, such as PES and REDD, which emphasize additionality. In addition, several new, globally available and free high-resolution remote sensing datasets have increased the ease of carrying out an impact evaluation on land cover change outcomes. While the number of conservation evaluations utilizing ‘matching’ to construct a valid control group is increasing, the majority of these studies use simple differences in means or linear cross-sectional regression to estimate the impact of the conservation program using this matched sample, with relatively few utilizing fixed effects panel methods—an alternative estimation method that relies on temporal variation in the data. In this paper we compare the advantages and limitations of (1) matching to construct the control group combined with differences in means and cross-sectional regression, which control for observable forms of bias in program evaluation, to (2) fixed effects panel methods, which control for observable and time-invariant unobservable forms of bias, with and without matching to create the control group. We then use these four approaches to estimate forest cover outcomes for two conservation programs: a PES program in Northeastern Ecuador and strict protected areas in European Russia. In the Russia case we find statistically significant differences across estimators—due to the presence of unobservable bias—that lead to differences in conclusions about effectiveness. The Ecuador case illustrates that if time-invariant unobservables are not present, matching combined with differences in means or cross-sectional regression leads to similar estimates of program effectiveness as matching combined with fixed effects panel regression. These results highlight the importance of considering observable and unobservable forms of bias and the methodological assumptions across estimators when designing an impact evaluation of conservation programs.     

Type I error rates, coverage of confidence intervals, and variance estimation in propensity-score matched analyses

Propensity-score matching is frequently used in the medical literature to reduce or eliminate the effect of treatment selection bias when estimating the effect of treatments or exposures on outcomes using observational data. In propensity-score matching, pairs of treated and untreated subjects with similar propensity scores are formed. Recent systematic reviews of the use of propensity-score matching found that the large majority of researchers ignore the matched nature of the propensity-score matched sample when estimating the statistical significance of the treatment effect. We conducted a series of Monte Carlo simulations to examine the impact of ignoring the matched nature of the propensity-score matched sample on Type I error rates, coverage of confidence intervals, and variance estimation of the treatment effect. We examined estimating differences in means, relative risks, odds ratios, rate ratios from Poisson models, and hazard ratios from Cox regression models. We demonstrated that accounting for the matched nature of the propensity-score matched sample tended to result in type I error rates that were closer to the advertised level compared to when matching was not incorporated into the analyses. Similarly, accounting for the matched nature of the sample tended to result in confidence intervals with coverage rates that were closer to the nominal level, compared to when matching was not taken into account. Finally, accounting for the matched nature of the sample resulted in estimates of standard error that more closely reflected the sampling variability of the treatment effect compared to when matching was not taken into account.     

Optimal matching with minimal deviation from fine balance in a study of obesity and surgical outcomes

In multivariate matching, fine balance constrains the marginal distributions of a nominal variable in treated and matched control groups to be identical without constraining who is matched to whom. In this way, a fine balance constraint can balance a nominal variable with many levels while focusing efforts on other more important variables when pairing individuals to minimize the total covariate distance within pairs. Fine balance is not always possible; that is, it is a constraint on an optimization problem, but the constraint is not always feasible. We propose a new algorithm that returns a minimum distance finely balanced match when one is feasible, and otherwise minimizes the total distance among all matched samples that minimize the deviation from fine balance. Perhaps we can come very close to fine balance when fine balance is not attainable; moreover, in any event, because our algorithm is guaranteed to come as close as possible to fine balance, the investigator may perform one match, and on that basis judge whether the best attainable balance is adequate or not. We also show how to incorporate an additional constraint. The algorithm is implemented in two similar ways, first as an optimal assignment problem with an augmented distance matrix, second as a minimum cost flow problem in a network. The case of knee surgery in the Obesity and Surgical Outcomes Study motivated the development of this algorithm and is used as an illustration. In that example, 2 of 47 hospitals had too few nonobese patients to permit fine balance for the nominal variable with 47 levels representing the hospital, but our new algorithm came very close to fine balance. Moreover, in that example, there was a shortage of nonobese diabetic patients, and incorporation of an additional constraint forced the match to include all of these nonobese diabetic patients, thereby coming as close as possible to balance for this important but recalcitrant covariate.     

How well can fine balance work for covariate balancing

Fine balance is a matching technique to improve covariate balance in observational studies. It constrains a match to have identical distributions for some covariates without restricting who is matched to whom. However, despite its wide application and excellent performance in practice, there is very little theory indicating when the method is likely to succeed or fail and to what extent it can remove covariate imbalance. In order to answer these questions, this paper studies the limits of what is possible for covariate balancing using fine balance and near-fine balance. The investigations suggest that given the distributions of the treated and control groups, in large samples, the maximum achievable balance by using fine balance only depends on the matching ratio (ie, the ratio of the sample size of the control group to that of the treated group). In addition, the results indicate how to estimate this matching ratio threshold without knowledge of the true distributions in finite samples. The findings are also illustrated by numerical studies in this paper.     

Omega-3 Polyunsaturated Fatty Acid Supplementation Reduced Atrial Fibrillation Recurrence after Pulmonary Vein Antrum Isolation

Objective

To assess if patients treated with omega-3(n-3) polyunsaturated fatty acids (PUFAS) had lower procedural failure rates compared to an untreated population.

Methods and Results

From January 2004 to 2007, 1500 PVAI patients underwent catheter ablation. Two hundred and eighty five (19%) patients were treated with PUFAs. These patients were matched in a nested case controlled analysis. After matching, there were 129 patients in the PUFA group and 129 in the control group. Thirty-five (27.1%) patients in the study group had early recurrence vs. 57 (44.1%) in the control group p-value< 0.0001. Twenty-nine (23.2%) patients in the PUFA group vs. 41 (31.7%) in the non-PUFA group had procedural failure (p-value < 0.003). There were no significant differences in complications in the PUFA and non-PUFA groups.

Conclusion

Patients treated with PUFAs had lower incidences of early recurrence and procedural failure compared to an untreated population.     

ADAPTIVE DIVERGENCE IN DARWIN'S RACE: HOW COEVOLUTION CAN GENERATE TRAIT DIVERSITY IN A POLLINATION SYSTEM

Understanding how reciprocal selection shapes interacting species in Darwin's coevolutionary race is a captivating pursuit in evolutionary ecology. Coevolving traits can potentially display following three patterns: (1) geographical variation in matched traits, (2) bias in trait matching, and (3) bimodal distribution of a trait in certain populations. Based on the framework of adaptive dynamics, we present an evolutionary model for a coevolving pollination system involving the long‐proboscid fly (Moegistorhynchus longirostris) and the long‐tubed iris (Lapeirousia anceps). The model successfully demonstrates that Darwin's hypothesis can lead to all three patterns if costs are involved. Geographical variation in matched traits could be driven by geographical variation in environmental factors that affect the cost rate of trait escalation. Unequal benefits derived from the interaction by the fly and the flower could potentially cause the bias in trait matching of the system. Different cost rates to trait elongation incurred by the two species and weak assortative interactions in the coevolutionary race can drive divergent selection (i.e., an evolutionary branching) that leads to the bimodal distribution of traits. Overall, the model highlights the importance of assortative interactions and the balance of costs incurred by coevolving species as factors determining the eventual phenotypic outcome of coevolutionary interactions.     

Predictive glycoengineering of biosimilars using a Markov chain glycosylation model

Biosimilar drugs must closely resemble the pharmacological attributes of innovator products to ensure safety and efficacy to obtain regulatory approval. Glycosylation is one critical quality attribute that must be matched, but it is inherently difficult to control due to the complexity of its biogenesis. This usually implies that costly and time‐consuming experimentation is required for clone identification and optimization of biosimilar glycosylation. Here, a computational method that utilizes a Markov model of glycosylation to predict optimal glycoengineering strategies to obtain a specific glycosylation profile with desired properties is described. The approach uses a genetic algorithm to find the required quantities to perturb glycosylation reaction rates that lead to the best possible match with a given glycosylation profile. Furthermore, the approach can be used to identify cell lines and clones that will require minimal intervention while achieving a glycoprofile that is most similar to the desired profile. Thus, this approach can facilitate biosimilar design by providing computational glycoengineering guidelines that can be generated with a minimal time and cost.     

Covariate measurement error adjustment for matched case-control studies

We propose a conditional scores procedure for obtaining bias-corrected estimates of log odds ratios from matched case-control data in which one or more covariates are subject to measurement error. The approach involves conditioning on sufficient statistics for the unobservable true covariates that are treated as fixed unknown parameters. For the case of Gaussian nondifferential measurement error, we derive a set of unbiased score equations that can then be solved to estimate the log odds ratio parameters of interest. The procedure successfully removes the bias in naive estimates, and standard error estimates are obtained by resampling methods. We present an example of the procedure applied to data from a matched case-control study of prostate cancer and serum hormone levels, and we compare its performance to that of regression calibration procedures.     

The relation between treatment benefit and underlying risk in meta-analysis.

In meta-analyses of clinical trials comparing a treated group with a control group it has been common to ask whether the treatment benefit varies according to the underlying risk of the patients in the different trials, with the hope of defining which patients would benefit most and which least from medical interventions. The usual analysis used to investigate this issue, however, which uses the observed proportions of events in the control groups of the trials as a measure of the underlying risk, is flawed and produces seriously misleading results. This arises through a bias due to regression to the mean and will be particularly acute in meta-analyses which include some small trials or in which the variability in the true underlying risks across trials is small. Approaches which previously have been thought to be more appropriate are to substitute the average proportion of events in the control and treated groups as the measure of underlying risk or to plot the proportion of events in the treated group against that in the control group (L''Abbé plot). However, these are still subject to bias in most circumstances. Because of the potentially seriously flawed conclusions that can result from such analyses, they should be replaced either by statistically appropriate (but more complex) approaches or, preferably, by analyses which investigate the dependence of the treatment effect on measured baseline characteristics of the patients in each trial.     

Extremely complex pattern of microsatellite mutation in the germline of wheat exposed to the post-Chernobyl radioactive contamination

The molecular structure of rare variants at 13 microsatellite loci found in a population of wheat plants grown for one generation in the heavily contaminated 30 km exclusion zone around the Chernobyl Nuclear Power Plant and in a control population was compared. Evidence for rare alterations (variants) was obtained for all 13 loci, including gain and loss of repeats, as well as the complete loss of microsatellite bands. The ratio between gains and losses among variants in the control group was similar to that in the exposed group. Sequencing of variants at six microsatellite loci found in the exposed population revealed extremely complex pattern of germline mutations, including complete deletions of loci, a bias towards mutations with gains and losses of multiple repeat units, and relatively frequent insertions of DNA of unknown origin. The occurrence of large deletions at two loci may be attributed to direct and inverted repeats sequences located just upstream and downstream of the array. The results of our study also suggest that the majority of mutations within the studied wheat microsatellite loci are represented by gains and losses of multiple repeat units, implying that a simple model of replication slippage cannot account for mutation events at these loci. Our data also support the conclusion that the spectra of spontaneous and radiation-induced mutation in wheat may be similar.     

Self-perception of self-regulatory skills in children with attention-deficit/hyperactivity disorder aged 8–10 years

Several studies have reported a characteristic "positive illusory bias" in the self-evaluation of children with ADHD. However, results are controversial. The aim of the present study was to investigate whether children with ADHD aged 8 to 10 years can rate their self-regulatory skills accurately when assessed with an age appropriate instrument. Twenty-seven children with ADHD and 27 matched normal control children completed the Self-rating Scale of Self-regulatory Function (SelfReg), a new rating scale that has been specifically designed for this age group. As expected, children with ADHD rated themselves significantly more dysfunctional than control children. In most domains, self-ratings of children with ADHD did not diverge from parent and teacher ratings to a greater extent than self-ratings of control children, although overall results indicated a moderate tendency toward a positive bias. When a cluster analysis based on discrepancies between children's and adults' evaluations was carried out, three groups with different self-rating patterns emerged: A "positive bias" group containing exclusively children with ADHD, a "negative bias" group containing both children with ADHD and control children, and the largest group of accurate self-raters which also included children from both diagnostic groups. It is concluded that overly positive self-judgments are not a ubiquitous finding in ADHD, but may be confined to a specific subgroup of children whose specific characteristics remain to be determined.     

Strategies to Improve Child Immunization via Antenatal Care Visits in India: A Propensity Score Matching Analysis

Numerous studies have examined the empirical evidence concerning the influence of demographic and socio-economic factors influencing child immunization, but no documentation is available which shows the actual impact of antenatal care (ANC) visits on subsequent child immunization. Therefore, this paper aims to examine the net impact of ANC visits on subsequent utilization of child immunization after removing the presence of selection bias. Nationwide data from India’s latest National Family Health Survey conducted during 2005–06 is used for the present study. The analysis has been carried out in the two separate models, in the first model 1–2 ANC visit and in the second model three or more ANC visits has been compared with no visit. We have used propensity score matching method with a counterfactual model that assesses the actual ANC visits effect on treated (ANC visits) and untreated groups (no ANC visit), and have employed Mantel-Haenszel bounds to examine whether result would be free from hidden bias or not. Using matched sample analysis result shows that child immunization among the groups of women who have completed 1–2 ANC visits and those who had more than two visits was about 13 percent and 19 percent respectively, higher than the group of women who have not made any ANC visit. Findings of nearest neighbor matching with replacement method, which completely eliminated the bias, indicate that selection bias present in data set leads to overestimates the positive effects of ANC visits on child immunization. Result based on Mantel-Haenszel bounds method suggest that if around 19 percent bias would be involved in the result then also we could observe the true positive effect of 1–2 ANC visits on child immunization. This also indicates that antenatal clinics are the conventional platforms for educating pregnant women on the benefits of child immunization.     

Standardization of the antibody to hepatitis B surface antigen concentration

We examine sources of potential bias in the estimation of antibody to hepatitis B surface antigen concentrations by a calibration curve for conversion of RIA units to international units. We show by calculation and example that very large biases may exist, whereas accurate estimation is needed in screening programmes and in clinical trials for the evaluation of the immunogenicity of various types and schedules of hepatitis B vaccine. It is recommended that the danger of large biases be avoided by using the laboratory's own calibration curve, calibrated against dilutions of the WHO standard, using a standard as positive control in the radioimmunoassay. Furthermore, serum samples should be diluted to a concentration close to that of the positive control.     

Matching inbred lines of Brussels sprouts for flowering characteristics, as an aid to improving F1 hybrid seed production

Previous work at the National Vegetable Research Station indicated that cross-pollination of Brussels sprouts by honeybees could be improved when parent lines with similar flowering characteristics were used. During 1973-5 inbred lines were tested at three sites for matching ability based on flowering times, plant height and flower colour. One pair of inbreds satisfied all criteria at all sites, and a further twelve gave satisfactory results. Two pairs visually matched in 1973 were grown in larger plots in 1973-4 to assess the effect of matching on honeybee behaviour. Results showed that matching improved cross-pollination by honeybees between the parent lines.     

Comparison of cohort and nested case-control designs for estimating the effect of time-varying drug exposure on the risk of adverse event in the presence of ties

Cohort and nested case-control (NCC) designs are frequently used in pharmacoepidemiology to assess the associations of drug exposure that can vary over time with the risk of an adverse event. Although it is typically expected that estimates from NCC analyses are similar to those from the full cohort analysis, with moderate loss of precision, only few studies have actually compared their respective performance for estimating the effects of time-varying exposures (TVE). We used simulations to compare the properties of the resulting estimators of these designs for both time-invariant exposure and TVE. We varied exposure prevalence, proportion of subjects experiencing the event, hazard ratio, and control-to-case ratio and considered matching on confounders. Using both designs, we also estimated the real-world associations of time-invariant ever use of menopausal hormone therapy (MHT) at baseline and updated, time-varying MHT use with breast cancer incidence. In all simulated scenarios, the cohort-based estimates had small relative bias and greater precision than the NCC design. NCC estimates displayed bias to the null that decreased with a greater number of controls per case. This bias markedly increased with higher proportion of events. Bias was seen with Breslow's and Efron's approximations for handling tied event times but was greatly reduced with the exact method or when NCC analyses were matched on confounders. When analyzing the MHT-breast cancer association, differences between the two designs were consistent with simulated data. Once ties were taken correctly into account, NCC estimates were very similar to those of the full cohort analysis.     

Optimal multivariate matching before randomization

Although blocking or pairing before randomization is a basic principle of experimental design, the principle is almost invariably applied to at most one or two blocking variables. Here, we discuss the use of optimal multivariate matching prior to randomization to improve covariate balance for many variables at the same time, presenting an algorithm and a case-study of its performance. The method is useful when all subjects, or large groups of subjects, are randomized at the same time. Optimal matching divides a single group of 2n subjects into n pairs to minimize covariate differences within pairs-the so-called nonbipartite matching problem-then one subject in each pair is picked at random for treatment, the other being assigned to control. Using the baseline covariate data for 132 patients from an actual, unmatched, randomized experiment, we construct 66 pairs matching for 14 covariates. We then create 10000 unmatched and 10000 matched randomized experiments by repeatedly randomizing the 132 patients, and compare the covariate balance with and without matching. By every measure, every one of the 14 covariates was substantially better balanced when randomization was performed within matched pairs. Even after covariance adjustment for chance imbalances in the 14 covariates, matched randomizations provided more accurate estimates than unmatched randomizations, the increase in accuracy being equivalent to, on average, a 7% increase in sample size. In randomization tests of no treatment effect, matched randomizations using the signed rank test had substantially higher power than unmatched randomizations using the rank sum test, even when only 2 of 14 covariates were relevant to a simulated response. Unmatched randomizations experienced rare disasters which were consistently avoided by matched randomizations.