Deaths averted: An unbiased alternative to rate ratios for measuring the performance of cancer screening programs.

INTRODUCTION: Screening trials and meta-analyses emphasize the ratio of cancer death rates in screening and control arms. However, this measure is diluted by the inclusion of deaths from cancers that only became detectable after the end of active screening. METHODS: We review traditional analysis of cancer screening trials and show that ratio estimates are inevitably biased to the null, because follow-up (FU) must continue beyond the end of the screening period and thus includes cases only becoming detectable after screening ends. But because such cases are expected to occur in equal numbers in the two arms, calculation of the difference between the number of cancer deaths in the screening and control arms avoids this dilutional bias. This difference can be set against the number of invitations to screening; we illustrate by reanalyzing data from all trials of tomography screening of lung cancer (LC) using this measure. RESULTS: In nine trials of LC screening from 2000 to 2013, a total of 94,441 high-risk patients were invited to be in screening or control groups, with high participation rates (average 95%). In the older trials comparing computed tomography to chest X-ray, 88,285 invitations averted 83 deaths (1068 per death averted (DA)). In the six more recent trials with no screening in the control group, 69,976 invitations averted 121 deaths (577 invitations per DA). DISCUSSION: Screens per DA is an undiluted measure of screening's effect and it is unperturbed by the arbitrary duration of FU. This estimate can be useful for program planning and informed consent.

The (Im)precision of Life Expectancy Numbers.

Life expectancy figures for countries and population segments are increasingly being reported to more decimal places and used as indicators of the strengths or failings of countries' health and social systems. Reports seldom quantify their intrinsic statistical imprecision or the age-specific numbers of deaths that determine them. The SE formulas available to compute imprecision are all model based. This note adds a more intuitive data-based SE method and extends the jackknife to the analysis of event rates more generally. It also describes the relationships between the magnitude of the SE and the numbers of person-years and deaths on which it is based. These relationships can help quantify the statistical noise present in published year-to-year differences in life expectancies, as well as in same-year differences between or within countries. Agencies and investigators are encouraged to use one of these SEs to report the imprecision of life expectancy numbers and to tailor the number of decimal places accordingly. (Am J Public Health. 2022;112(8):1151-1160. https://doi.org/10.2105/AJPH.2022.306805).

"Translating" All-Cause Mortality Rate Ratios or Hazard Ratios to Age-, Longevity-, and Probability-Based Measures.

Epidemiologists commonly use an adjusted hazard ratio or incidence density ratio, or a standardized mortality ratio, to measure a difference in all-cause mortality rates. They seldom translate it into an age-, time-, or probability-based measure that would be easier to communicate and to relate to. Several articles have shown how to translate from a standardized mortality ratio or hazard ratio to a longevity difference, a difference in actuarial ages, or a probability of being outlived. In this paper, we describe the settings where these translations are and are not appropriate and provide some of the heuristics behind the formulae. The tools that yield differences in "effective age" and in longevity are applicable when both 1) the mortality rate ratio (hazard ratio) is constant over age and 2) the rates themselves are log-linear in age. The "probability/odds of being outlived" metric is applicable whenever the first condition holds, and thus it provides no direct information on the magnitude of the effective age/longevity difference.

LASSO type penalized spline regression for binary data.

BACKGROUND: Generalized linear mixed models (GLMMs), typically used for analyzing correlated data, can also be used for smoothing by considering the knot coefficients from a regression spline as random effects. The resulting models are called semiparametric mixed models (SPMMs). Allowing the random knot coefficients to follow a normal distribution with mean zero and a constant variance is equivalent to using a penalized spline with a ridge regression type penalty. We introduce the least absolute shrinkage and selection operator (LASSO) type penalty in the SPMM setting by considering the coefficients at the knots to follow a Laplace double exponential distribution with mean zero. METHODS: We adopt a Bayesian approach and use the Markov Chain Monte Carlo (MCMC) algorithm for model fitting. Through simulations, we compare the performance of curve fitting in a SPMM using a LASSO type penalty to that of using ridge penalty for binary data. We apply the proposed method to obtain smooth curves from data on the relationship between the amount of pack years of smoking and the risk of developing chronic obstructive pulmonary disease (COPD). RESULTS: The LASSO penalty performs as well as ridge penalty for simple shapes of association and outperforms the ridge penalty when the shape of association is complex or linear. CONCLUSION: We demonstrated that LASSO penalty captured complex dose-response association better than the Ridge penalty in a SPMM.

Modeling perinatal mortality in twins via generalized additive mixed models: a comparison of estimation approaches.

BACKGROUND: The analysis of twin data presents a unique challenge. Second-born twins on average weigh less than first-born twins and have an elevated risk of perinatal mortality. It is not clear whether the risk difference depends on birth order or their relative birth weight. This study evaluates the association between birth order and perinatal mortality by birth order-specific weight difference in twin pregnancies. METHODS: We adopt generalized additive mixed models (GAMMs) which are a flexible version of generalized linear mixed models (GLMMs), to model the association. Estimation of such models for correlated binary data is challenging. We compare both Bayesian and likelihood-based approaches for estimating GAMMs via simulation. We apply the methods to the US matched multiple birth data to evaluate the association between twins' birth order and perinatal mortality. RESULTS: Perinatal mortality depends on both birth order and relative birthweight. Simulation results suggest that the Bayesian method with half-Cauchy priors for variance components performs well in estimating all components of the GAMM. The Bayesian results were sensitive to prior specifications. CONCLUSION: We adopted a flexible statistical model, GAMM, to precisely estimate the perinatal mortality risk differences between first- and second-born twins whereby birthweight and gestational age are nonparametrically modelled to explicitly adjust for their effects. The risk of perinatal mortality in twins was found to depend on both birth order and relative birthweight. We demonstrated that the Bayesian method estimated the GAMM model components more reliably than the frequentist approaches.

A more intuitive and modern way to compute a small-sample confidence interval for the mean of a Poisson distribution.

Small-sample confidence intervals for the mean of a Poisson distribution have been used since the 1930s. They can be computed by trial and error, or using a computation-saving link that few are aware of and that, even if they are, is neither intuitive nor easy to remember. I trace how and why this link has been used, even if the basis for it has been lost or ignored. I promote a direct and more meaningful link that can be easily used today without having to resort to tables or approximations suited to hand calculators. More importantly, this (time-based) link is instructive and intuitive, and thus more easily derived and understood.

A comparison of technique survival in Canadian peritoneal dialysis and home hemodialysis patients.

BACKGROUND: High discontinuation rates remain a challenge for home hemodialysis (HHD) and peritoneal dialysis (PD). We compared technique failure risks among Canadian patients receiving HHD and PD. METHODS: Using the Canadian Organ Replacement Register, we studied adult patients who initiated HHD or PD within 1 year of beginning dialysis between 2000 and 2012, with follow-up until 31 December 2013. Technique failure was defined as a transfer to any alternative modality for a period of ≥60 days. Technique survival between HHD and PD was compared using a Fine and Gray competing risk model. We also examined the time dependence of technique survival, the association of patient characteristics with technique failure and causes of technique failure. RESULTS: Between 2000 and 2012, 15 314 patients were treated with a home dialysis modality within 1 year of dialysis initiation: 14 461 on PD and 853 on HHD. Crude technique failure rates were highest during the first year of therapy for both home modalities. During the entire period of follow-up, technique failure was lower with HHD compared with PD (adjusted hazard ratio = 0.79; 95% confidence interval 0.69-0.90). However, the relative technique failure risk was not proportional over time and the beneficial association with HHD was only apparent after the first year of dialysis. Comparisons also varied among subgroups and the superior technique survival associated with HHD relative to PD was less pronounced in more recent years and among older patients. Predictors of technique failure also differed between modalities. While obesity, smoking and small facility size were associated with higher technique failure in both PD and HHD, the association with age and gender differed. Furthermore, the majority of discontinuation occurred for medical reasons in PD (38%), while the majority of HHD patients experienced technique failure due to social reasons or inadequate resources (50%). CONCLUSIONS: In this Canadian study of home dialysis patients, HHD was associated with better technique survival compared with PD. However, patterns of technique failure differed significantly among these modalities. Strategies to improve patient retention across all home dialysis modalities are needed.

Ability to Predict New-Onset Psychological Distress Using Routinely Collected Health Data: A Population-Based Cohort Study of Women Diagnosed With Breast Cancer.

Objectives: The primary objective of this study was to identify the predictors of new-onset psychological distress available in routinely collected administrative health databases for women diagnosed with breast cancer. The secondary objective was to explore whether the predictors vary based on the period of cancer care. Methods: A population-based cohort study followed 16,495 female patients with newly diagnosed breast cancer who did not experience psychological distress during the 14 months before breast cancer surgery. The incidence of psychological distress was reported overall and by type of mental health problem. Time-varying Cox proportional hazards models were developed to identify predictors of new-onset psychological distress during 2 key periods of cancer care: (1) hospital-based treatment during which women undergo treatment with breast surgery, chemotherapy, and/or radiation, and (2) 1-year transitional survivorship when women begin follow-up care. Results: The incidence of psychological distress was 16% within each period. Anxiety was present in 85.1% and 65.5% of new cases during hospital-based treatment and transitional survivorship, respectively. Predictors during both periods were younger age, receipt of axillary lymph node dissection, rheumatologic disease, and baseline menopausal symptoms, as well as new opioid dispensations, emergency department visits, and hospital contacts that occurred during follow-up. Other predictors varied based on the period of cancer care. More advanced breast cancer and type of treatment were associated with onset of psychological distress during hospital-based treatment. Psychological distress during transitional survivorship was predicted by diagnosis of localized breast disease, shorter duration of hospital-based treatment, receipt of additional hospital-based treatment in survivorship, and newly diagnosed comorbidities or symptoms. Conclusions: This study identified the predictors of new-onset psychological distress available in routinely collected administrative health databases, and showed how predictors change between hospital-based treatment and transitional survivorship periods. The results highlight the importance of developing predictive models tailored to the period of cancer care.

Individually-matched etiologic studies: classical estimators made new again.

With greater access to regression-based methods for confounder control, the etiologic study with individual matching, analyzed by classical (calculator) methods, lost favor in recent decades. This design was costly, and the data sometimes mis-analyzed. Now, with Big Data, individual matching becomes an economical option. To many, however, conditional logistic regression, commonly used to estimate the incidence density ratio parameter, is somewhat of a black box whose output is not easily checked. An epidemiologist-statistician pair recently proposed a new estimator that is easily applied to data from individually-matched series with a 2:1 ratio (and no other confounding variables) using just a hand calculator or spreadsheet. Surprisingly-or possibly not-they overlooked classical estimators developed in earlier decades. This prompts me to re-introduce some of these, to highlight their considerable flexibility and ease of use, and to update them. Nowadays, for any matching ratio (M:1), the Maximum Likelihood result can be easily computed from data gathered under the matched design in two different ways, each using just the summary data. One is via any binomial regression program that allows offsets, applied to just M 'rows' of data. The other is by hand! The aim of this note is not to save on computation; instead, it is to make connections between classical and regression-based methods, to promote terminology that reflects the concepts and structure of the etiologic study, and to focus attention on what parameter is being estimated.

Statistical Behaviors: Personal and Computer-Aided Observations.

My early years as a statistician were with the Eastern Co-operative Oncology Group and the Radiation Oncology Therapy Group; three of these years were spent at the Sidney Farber Cancer Institute. Later, I collaborated widely with investigators in many clinical research areas. I reflect on the "statistical interrogations of nature" I saw (and helped some of these) investigators plan and carry out. I look back on their (and my own) statistical behaviors when interpreting the information these interrogations produced and-using a few vignettes and some computer-generated observations-draw some lessons from them. These mainly have to do with making too much of one's data.

Mortality reductions due to mammography screening: Contemporary population-based data.

Our objective was to compare breast cancer mortality in two regions of the Republic of Ireland that introduced a screening programme eight years apart, and to estimate the steady-state mortality deficits the programme will produce. We carried out age- and year-matched between-region comparison of breast cancer mortality rates, and of incidence rates of stage 2-4 breast cancer, in the eligible cohorts. The regions comprised counties that, beginning in early 2000 (region 1) and late 2007 (region 2), invited women aged 50-64 to biennial mammography screening. The data were supplied by the National Cancer Registry, Central Statistics Office. As impact measures, we used age-and-year-matched mortality (from breast cancers diagnosed from 2000 onwards), rate ratios and incidence rate ratios in the compared regions from 2000 to 2013. Ratios were adjusted for between-region differences in background rates. In cohorts too old to be invited, death rates in regions 1 and 2 were 702 per 0.91 and 727 per 0.90 million women-years respectively (Ratio 0.96). In the eligible cohorts, they were 1027 per 2.9 and 1095 per 2.67 (Ratio 0.88). Thus, rates in cohorts that could have benefitted were 9% lower in region 1 than region 2: (95%CI: -20%, +4%). The incidence rates of stage 2-4 breast cancer were 7% lower in region 2 than region 1 over the entire 14 year period, and 20% lower in 2007, i.e., before the screening in region 2 began to narrow the difference. Since mortality reductions due to screening only manifest after several years, the full impact of screening has not yet been realized in region 1. The lower rate observed in that region is a conservative estimate of the steady state benefit. Additional deaths would have been averted had screening continued beyond age 64.

Sample Size Estimation for Random-effects Models: Balancing Precision and Feasibility in Panel Studies.

Panel study designs are common in environmental epidemiology, whereby repeated measurements are collected from a panel of subjects to evaluate short-term within-subject changes in response variables over time. In planning such studies, questions of how many subjects to include and how many different exposure conditions to measure are commonly asked at the design stage. In practice, these choices are constrained by budget, logistics, and participant burden and must be carefully balanced against statistical considerations of precision and power. In this article, we provide intuitive sample size formulae for the precision of regression coefficients derived from panel studies and show how they can be applied in planning such studies. We show that there are five determinants of the precision with which regression coefficients can be estimated: (1) the residual variance of the responses; (2) the variance of the slopes; (3) the number of subjects; (4) the number of measurements/subject; and (5) the within-subject range of the exposure values "X" at which the responses are measured. The planning of such studies would be greatly improved if investigators regularly reported all of the variance components in fitted random-effects models: currently, literature values for the relevant variance parameters are often not readily available and must be estimated through pilot studies or subjective estimates of "reasonable values."

Predictors of distress in female breast cancer survivors: a systematic review.

PURPOSE: Unmanaged distress has been shown to adversely affect survival and quality of life in breast cancer survivors. Fortunately, distress can be managed and even prevented with appropriate evidence-based interventions. Therefore, the objective of this systematic review was to synthesize the published literature around predictors of distress in female breast cancer survivors to help guide targeted intervention to prevent distress. METHODS: Relevant studies were located by searching MEDLINE, Embase, PsycINFO, and CINAHL databases. Significance and directionality of associations for commonly assessed candidate predictors (n ≥ 5) and predictors shown to be significant (p ≤ 0.05) by at least two studies were summarized descriptively. Predictors were evaluated based on the proportion of studies that showed a significant and positive association with the presence of distress. RESULTS: Forty-two studies met the target criteria and were included in the review. Breast cancer and treatment-related predictors were more advanced cancer at diagnosis, treatment with chemotherapy, longer primary treatment duration, more recent transition into survivorship, and breast cancer recurrence. Manageable treatment-related symptoms associated with distress included menopausal/vasomotor symptoms, pain, fatigue, and sleep disturbance. Sociodemographic characteristics that increased the risk of distress were younger age, non-Caucasian ethnicity, being unmarried, and lower socioeconomic status. Comorbidities, history of mental health problems, and perceived functioning limitations were also associated. Modifiable predictors of distress were lower physical activity, lower social support, and cigarette smoking. CONCLUSIONS: This review established a set of evidence-based predictors that can be used to help identify women at higher risk of experiencing distress following completion of primary breast cancer treatment.

Correction of Selection Bias in Survey Data: Is the Statistical Cure Worse Than the Bias?

In previous articles in the American Journal of Epidemiology (Am J Epidemiol. 2013;177(5):431-442) and American Journal of Public Health (Am J Public Health. 2013;103(10):1895-1901), Masters et al. reported age-specific hazard ratios for the contrasts in mortality rates between obesity categories. They corrected the observed hazard ratios for selection bias caused by what they postulated was the nonrepresentativeness of the participants in the National Health Interview Study that increased with age, obesity, and ill health. However, it is possible that their regression approach to remove the alleged bias has not produced, and in general cannot produce, sensible hazard ratio estimates. First, one must consider how many nonparticipants there might have been in each category of obesity and of age at entry and how much higher the mortality rates would have to be in nonparticipants than in participants in these same categories. What plausible set of numerical values would convert the ("biased") decreasing-with-age hazard ratios seen in the data into the ("unbiased") increasing-with-age ratios that they computed? Can these values be encapsulated in (and can sensible values be recovered from) 1 additional internal variable in a regression model? Second, one must examine the age pattern of the hazard ratios that have been adjusted for selection. Without the correction, the hazard ratios are attenuated with increasing age. With it, the hazard ratios at older ages are considerably higher, but those at younger ages are well below 1. Third, one must test whether the regression approach suggested by Masters et al. would correct the nonrepresentativeness that increased with age and ill health that I introduced into real and hypothetical data sets. I found that the approach did not recover the hazard ratio patterns present in the unselected data sets: The corrections overshot the target at older ages and undershot it at lower ages.

Correction of Selection Bias in Survey Data: Is the Statistical Cure Worse Than the Bias?

In previous articles in the American Journal of Epidemiology (Am J Epidemiol. 2013;177(5):431-442) and American Journal of Public Health (Am J Public Health. 2013;103(10):1895-1901), Masters et al. reported age-specific hazard ratios for the contrasts in mortality rates between obesity categories. They corrected the observed hazard ratios for selection bias caused by what they postulated was the nonrepresentativeness of the participants in the National Health Interview Study that increased with age, obesity, and ill health. However, it is possible that their regression approach to remove the alleged bias has not produced, and in general cannot produce, sensible hazard ratio estimates. First, we must consider how many nonparticipants there might have been in each category of obesity and of age at entry and how much higher the mortality rates would have to be in nonparticipants than in participants in these same categories. What plausible set of numerical values would convert the ("biased") decreasing-with-age hazard ratios seen in the data into the ("unbiased") increasing-with-age ratios that they computed? Can these values be encapsulated in (and can sensible values be recovered from) one additional internal variable in a regression model? Second, one must examine the age pattern of the hazard ratios that have been adjusted for selection. Without the correction, the hazard ratios are attenuated with increasing age. With it, the hazard ratios at older ages are considerably higher, but those at younger ages are well below one. Third, one must test whether the regression approach suggested by Masters et al. would correct the nonrepresentativeness that increased with age and ill health that I introduced into real and hypothetical data sets. I found that the approach did not recover the hazard ratio patterns present in the unselected data sets: the corrections overshot the target at older ages and undershot it at lower ages.