Analyzing a randomized trial on breast self-examination with noncompliance and missing outcomes

Recently, instrumental variables methods have been used to address non-compliance in randomized experiments. Complicating such analyses is often the presence of missing data. The standard model for missing data, missing at random (MAR), has some unattractive features in this context. In this paper we compare MAR-based estimates of the complier average causal effect (CACE) with an estimator based on an alternative, nonignorable model for the missing data process, developed by Frangakis and Rubin (1999, Biometrika, 86, 365-379). We also introduce a new missing data model that, like the Frangakis-Rubin model, is specially suited for models with instrumental variables, but makes different substantive assumptions. We analyze these issues in the context of a randomized trial of breast self-examination (BSE). In the study two methods of teaching BSE, consisting of either mailed information about BSE (the standard treatment) or the attendance of a course involving theoretical and practical sessions (the new treatment), were compared with the aim of assessing whether teaching programs could increase BSE practice and improve examination skills. The study was affected by the two sources of bias mentioned above: only 55% of women assigned to receive the new treatment complied with their assignment and 35% of the women did not respond to the post-test questionnaire. Comparing the causal estimand of the new treatment using the MAR, Frangakis-Rubin, and our new approach, the results suggest that for these data the MAR assumption appears least plausible, and that the new model appears most plausible among the three choices.

Application of the principal stratification approach to the Faenza randomized experiment on breast self-examination

In this article we present an extended framework based on the principal stratification approach (Frangakis and Rubin, 2002, Biometrics 58, 21-29), for the analysis of data from randomized experiments which suffer from treatment noncompliance, missing outcomes following treatment noncompliance, and "truncation by death." We are not aware of any previous work that addresses all these complications jointly. This framework is illustrated in the context of a randomized trial of breast self-examination.

Identification and Estimation of Causal Mechanisms in Clustered Encouragement Designs: Disentangling Bed Nets using Bayesian Principal Stratification

Exploration of causal mechanisms is often important for researchers and policymakers to understand how an intervention works and how it can be improved. This task can be crucial in clustered encouragement designs (CED). Encouragement design studies arise frequently when the treatment cannot be enforced because of ethical or practical constrains and an encouragement intervention (information campaigns, incentives, etc) is conceived with the purpose of increasing the uptake of the treatment of interest. By design, encouragements always entail the complication of non-compliance. Encouragements can also give rise to a variety of mechanisms, particularly when encouragement is assigned at cluster level. Social interactions among units within the same cluster can result in spillover effects. Disentangling the effect of encouragement through spillover effects from that through the enhancement of the treatment would give better insight into the intervention and it could be compelling for planning the scaling-up phase of the program. Building on previous works on CEDs and non-compliance, we use the principal stratification framework to define stratum-specific causal effects, that is, effects for specific latent subpopulations, defined by the joint potential compliance statuses under both encouragement conditions. We show how the latter stratum-specific causal effects are related to the decomposition commonly used in the literature and provide flexible homogeneity assumptions under which an extrapolation across principal strata allows one to disentangle the effects. Estimation of causal estimands can be performed with Bayesian inferential methods using hierarchical models to account for clustering. We illustrate the proposed methodology by analyzing a cluster randomized experiment implemented in Zambia and designed to evaluate the impact on malaria prevalence of an agricultural loan program intended to increase the bed net coverage. Farmer households assigned to the program could take advantage of a deferred payment and a discount in the purchase of new bed nets. Our analysis shows a lack of evidence of an effect of the offering of the program to a cluster of households through spillover effects, that is through a greater bed net coverage in the neighborhood.

Autologous hematopoietic stem cell transplantation vs low-dose immunosuppression in secondary-progressive multiple sclerosis

Background and purpose

Effectiveness of autologous haematopoietic stem cell transplantation (AHSCT) in relapsing–remitting multiple sclerosis (MS) is well known, but in secondary–progressive (SP)‐MS it is still controversial. Therefore, AHSCT activity was evaluated in SP‐MS using low‐dose immunosuppression with cyclophosphamide (Cy) as a comparative treatment.

Methods

In this retrospective monocentric 1:2 matched study, SP‐MS patients were treated with intermediate‐intensity AHSCT (cases) or intravenous pulses of Cy (controls) at a single academic centre in Florence. Controls were selected according to baseline characteristics adopting cardinality matching after trimming on the estimated propensity score. Kaplan–Meier and Cox analyses were used to estimate survival free from relapses (R‐FS), survival free from disability progression (P‐FS), and no evidence of disease activity 2 (NEDA‐2).

Results

A total of 93 SP‐MS patients were included: 31 AHSCT, 62 Cy. Mean follow‐up was 99 months in the AHSCT group and 91 months in the Cy group. R‐FS was higher in AHSCT compared to Cy patients: at Year 5, 100% versus 52%, respectively (p < 0.0001). P‐FS did not differ between the groups (at Year 5: 70% in AHSCT and 81% in Cy, p = 0.572), nor did NEDA‐2 (p = 0.379). A sensitivity analysis including only the 31 “best‐matched” controls confirmed these results. Three neoplasms (2 Cy, 1 AHSCT) and two fatalities (2 Cy) occurred.

Conclusions

This study provides Class III evidence, in SP‐MS, on the superior effectiveness of AHSCT compared to Cy on relapse activity, without differences on disability accrual. Although the suppression of relapses was observed in the AHSCT group only, AHSCT did not show advantages over Cy on disability, suggesting that in SP‐MS disability progression becomes based more on noninflammatory neurodegeneration than on inflammation.

Causal inference with interfering units for cluster and population level treatment allocation programs

Interference arises when an individual's potential outcome depends on the individual treatment level, but also on the treatment level of others. A common assumption in the causal inference literature in the presence of interference is partial interference, implying that the population can be partitioned in clusters of individuals whose potential outcomes only depend on the treatment of units within the same cluster. Previous literature has defined average potential outcomes under counterfactual scenarios where treatments are randomly allocated to units within a cluster. However, within clusters there may be units that are more or less likely to receive treatment based on covariates or neighbors' treatment. We define new estimands that describe average potential outcomes for realistic counterfactual treatment allocation programs, extending existing estimands to take into consideration the units' covariates and dependence between units' treatment assignment. We further propose entirely new estimands for population-level interventions over the collection of clusters, which correspond in the motivating setting to regulations at the federal (vs. cluster or regional) level. We discuss these estimands, propose unbiased estimators and derive asymptotic results as the number of clusters grows. For a small number of observed clusters, a bootstrap approach for confidence intervals is proposed. Finally, we estimate effects in a comparative effectiveness study of power plant emission reduction technologies on ambient ozone pollution.

PM2.5 and hospital admissions among Medicare enrollees with chronic debilitating brain disorders

BACKGROUND

Although long-term exposure to particulate matter<2.5 μm (PM2.5) has been linked to chronic debilitating brain disorders (CDBD), the role of short-term exposure in health care demand, and increased susceptibility for PM2.5-related health conditions, among Medicare enrollees with CDBD has received little attention. We used a causal modeling approach to assess the effect of short-term high PM2.5 exposure on all-cause admissions, and prevalent cause-specific admissions among Medicare enrollees with CDBD (Parkinson's disease-PD, Alzheimer's disease-AD and other dementia).

METHODS

We constructed daily zipcode counts of hospital admissions of Medicare beneficiaries older than 65 across the United-States (2000-2014). We obtained daily PM2.5 estimates from a satellite-based model. A propensity score matching approach was applied to match high-pollution (PM2.5 > 17.4 μg/m3) to low-pollution zip code-days with similar background characteristics. Then, we estimated the percent change in admissions attributable to high pollution. We repeated the models restricting the analysis to zipcode-days with PM2.5 below of 35 μg/m3.

RESULTS

We observed significant increases in all-cause hospital admissions (2.53% in PD and 2.49% in AD/dementia) attributable to high PM2.5 exposure. The largest observed effect for common causes was for pneumonia and urinary tract infection. All the effects were larger in CDBD compared to the general Medicare population, and similarly strong at levels of exposure considered safe by the EPA.

CONCLUSION

We found Medicare beneficiaries with CDBD to be at higher risk of being admitted to the hospital following acute exposure to PM2.5 levels well below the National Ambient Air Quality Standard defined as safe by the EPA.

Individual longitudinal patterns in biochemical and hematological markers for the early prediction of pre-eclampsia

OBJECTIVE

To analyze the individual longitudinal patterns of maternal biochemical and hematological tests performed throughout gestation in order to predict at the 20th week of pregnancy the later development of pre-eclampsia.

STUDY DESIGN

A longitudinal study was conducted on 187 white normotensive pregnant women all with a history of pre-eclampsia. Blood samples were performed at the 8th week of gestation and then every 4 weeks until the 36th week. The longitudinal patterns of urea, creatinine, uric acid, total proteins, hematocrit, red blood cells, hemoglobin, mean red cell volume, ferritin and iron were derived. By means of regression analysis, for each woman and each significant marker, a 'theoretical physiological pattern', from the 8th to the 20th week, was constructed. By comparing the observed values of each marker for each woman with her 'theoretical physiological pattern', variables indicating the match or mismatch to it were derived. Such variables were used, together with other maternal characteristics, in a logit regression for the probability of developing pre-eclampsia later in pregnancy.

RESULTS

In 140 cases, pregnancies followed a physiological course, while 47 women developed pre-eclampsia during the third trimester. In the physiological gestations, the weekly mean values of creatinine, hematocrit, total proteins, uric acid and urea showed patterns that were significantly different from those of the pathological group. The logit model was able to classify correctly 96% of the physiological and 87% of the pathological pregnancies, with a negative predictive value of 96% and a positive predictive value of 89% (area under the receiver operator characteristics (ROC) curve 0.98). The ability of the model to predict later complications at the 20th week was confirmed by a validation procedure.

CONCLUSION

The simultaneous use of individual longitudinal patterns of parameters, achieved non-invasively as part of the standard methods of antenatal care that provide a global evaluation of plasma volume expansion, showed a high ability to predict, early in pregnancy, the later development of pre-eclampsia.

A refreshing account of principal stratification

Pearl (2011) invites researchers to contribute to a discussion on the logic and utility of principal stratification in causal inference, raising some thought-provoking questions. In our commentary, we discuss the role of principal stratification in causal inference, describing why we view the principal stratification framework as useful for addressing causal inference problems where causal estimands are defined in terms of intermediate outcomes. We focus on mediation analysis and principal stratification analysis, showing that they generally involve different causal estimands and answer different questions. We argue that even when principal stratification may not answer the causal questions of primary interest, it can be a preliminary analysis of the data to assess the plausibility of identifying assumptions. We also discuss the use of principal stratification to address issues of surrogate outcomes. Our discussion stresses that a principal stratification analysis should account for all the principal strata and evaluate the distributions of potential outcomes in each of the principal strata. To this end, we view a Bayesian analysis particularly suited for drawing inference on principal strata membership and principal strata effects.

Assessing the short term impact of air pollution on mortality: a matching approach

BACKGROUND

The opportunity to assess short term impact of air pollution relies on the causal interpretation of the exposure-response association. However, up to now few studies explicitly faced this issue within a causal inference framework. In this paper, we reformulated the problem of assessing the short term impact of air pollution on health using the potential outcome approach to causal inference. We considered the impact of high daily levels of particulate matter ≤10 μm in diameter (PM₁₀) on mortality within two days from the exposure in the metropolitan area of Milan (Italy), during the period 2003-2006. Our research focus was the causal impact of a hypothetical intervention setting daily air pollution levels under a pre-fixed threshold.

METHODS

We applied a matching procedure based on propensity score to estimate the total number of attributable deaths (AD) during the study period. After defining the number of attributable deaths in terms of difference between potential outcomes, we used the estimated propensity score to match each high exposure day, namely each day with a level of exposure higher than 40 μg/m³, with a day with similar background characteristics but a level of exposure lower than 40 μg/m³. Then, we estimated the impact by comparing mortality between matched days.

RESULTS

During the study period daily exposures larger than 40 μg/m³ were responsible for 1079 deaths (90% CI: 116; 2042). The impact was more evident among the elderly than in the younger age classes. Exposures ≥ 40 μg/m³ were responsible, among the elderly, for 1102 deaths (90% CI: 388, 1816), of which 797 from cardiovascular causes and 243 from respiratory causes. Clear evidence of an impact on respiratory mortality was found also in the age class 65-74, with 87 AD (90% CI: 11, 163).

CONCLUSIONS

The propensity score matching turned out to be an appealing method to assess historical impacts in this field, which guarantees that the estimated total number of AD can be derived directly as sum of either age-specific or cause-specific AD, unlike the standard model-based procedure. For this reason, it is a promising approach to perform surveillance focusing on very specific causes of death or diseases, or on susceptible subpopulations. Finally, the propensity score matching is free from issues concerning the exposure-confounders-mortality modeling and does not involve extrapolation. On the one hand this enhances the internal validity of our results; on the other, it makes the approach scarcely appropriate for estimating future impacts.

Matching on Generalized Propensity Scores with Continuous Exposures

In the context of a binary treatment, matching is a well-established approach in causal inference. However, in the context of a continuous treatment or exposure, matching is still underdeveloped. We propose an innovative matching approach to estimate an average causal exposure-response function under the setting of continuous exposures that relies on the generalized propensity score (GPS). Our approach maintains the following attractive features of matching: a) clear separation between the design and the analysis; b) robustness to model misspecification or to the presence of extreme values of the estimated GPS; c) straightforward assessments of covariate balance. We first introduce an assumption of identifiability, called local weak unconfoundedness. Under this assumption and mild smoothness conditions, we provide theoretical guarantees that our proposed matching estimator attains point-wise consistency and asymptotic normality. In simulations, our proposed matching approach outperforms existing methods under settings with model misspecification or in the presence of extreme values of the estimated GPS. We apply our proposed method to estimate the average causal exposure-response function between long-term PM2.5 exposure and all-cause mortality among 68.5 million Medicare enrollees, 2000-2016. We found strong evidence of a harmful effect of long-term PM2.5 exposure on mortality. Code for the proposed matching approach is provided in the CausalGPS R package, which is available on CRAN and provides a computationally efficient implementation.

Cross-sectional and longitudinal evaluation of uterine artery Doppler velocimetry for the prediction of pre-eclampsia in normotensive women with specific risk factors

OBJECTIVE

To evaluate the performance, in the prediction of pre-eclampsia, of (1) an abnormal mean uterine artery resistance index (RI; cross-sectional index) at 24 weeks of gestation, (2) the individual longitudinal flow pattern of results observed at 16, 20 and 24 weeks of gestation and (3) a multiple logistic regression model including the individual longitudinal flow pattern and the mean RI at 24 weeks.

METHODS

A total of 144 normotensive pregnant women with risk factors for pre-eclampsia were evaluated with uterine artery color Doppler at 16, 20 and 24 weeks' gestation. The following indices were obtained: (1) cross-sectional index: the mean RI of both uterine arteries at 24 weeks' gestation was calculated for each patient and considered abnormal when >/= 0.58; (2) longitudinal indices: the individual longitudinal flow pattern of mean RI of both the main uterine arteries at 16, 20 and 24 weeks' gestation was derived for each subject and defined as (a) the typical physiological flow pattern, with a trend of decrease in values or (b) the non-physiological flow pattern. The probability of having a pregnancy complicated by pre-eclampsia was also calculated by means of a multivariate logit model. The log-odds was modeled as a function of variables related to maternal characteristics, the individual longitudinal flow pattern indicator, and of the mean RI at 24 weeks' gestation as a continuous variable.

RESULTS

Pregnancies had a physiological course in 108 (75%) women, while 36 (25%) women developed pre-eclampsia during the third trimester. For the prediction of pre-eclampsia, the use of an abnormal uterine artery RI index (> or = 0.58) at 24 weeks showed a sensitivity of 77.8%, a specificity of 67.6%, a positive predictive value (PPV) of 44.4% and a negative predictive value (NPV) of 90.1%, with a likelihood ratio (LR) for an abnormal test of 2.4; with the longitudinal flow pattern indicator, sensitivity was 88.9%, specificity 82.4%, PPV 62.7% and NPV 95.7%, with a LR for an abnormal test of 4.9; the use of a logit model yielded a sensitivity of 72.2%, a specificity of 90.7%, a PPV of 72.2% and a NPV of 90.7%, with a LR for an abnormal test of 8.0.

CONCLUSIONS

In this study the use of an individual longitudinal flow pattern indicator resulted in improving accuracy in the prediction of pre-eclampsia as compared with the traditional cross-sectional mean RI at 24 weeks. A further increase in specificity and PPV was obtained using a logit model that includes the longitudinal flow pattern indicator and the cross-sectional RI at 24 weeks. Since both the longitudinal flow pattern indicator and the logit model showed a high performance in predicting pre-eclampsia in women with risk factors for impaired placentation, they might be used to identify a high-risk population in which preventive measures and/or therapeutic options might be tested.

Bayesian inference for causal mechanisms with application to a randomized study for postoperative pain control

We conduct principal stratification and mediation analysis to investigate to what extent the positive overall effect of treatment on postoperative pain control is mediated by postoperative self administration of intra-venous analgesia by patients in a prospective, randomized, double-blind study. Using the Bayesian approach for inference, we estimate both associative and dissociative principal strata effects arising in principal stratification, as well as natural effects from mediation analysis. We highlight that principal stratification and mediation analysis focus on different causal estimands, answer different causal questions, and involve different sets of structural assumptions.