Allowing for random errors in radiation dose estimates for the atomic bomb survivor data

The presence of random errors in the individual radiation dose estimates for the A-bomb survivors causes underestimation of radiation effects in dose-response analyses, and also distorts the shape of dose-response curves. Statistical methods are presented which will adjust for these biases, provided that a valid statistical model for the dose estimation errors is used. Emphasis is on clarifying some rather subtle statistical issues. For most of this development the distinction between radiation dose and exposure is not critical. The proposed methods involve downward adjustment of dose estimates, but this does not imply that the dosimetry system is faulty. Rather, this is a part of the dose-response analysis required to remove biases in the risk estimates. The primary focus of this report is on linear dose-response models, but methods for linear-quadratic models are also considered briefly. Some plausible models for the dose estimation errors are considered, which have typical errors in a range of 30-40% of the true values, and sensitivity analysis of the resulting bias corrections is provided. It is found that for these error models the resulting estimates of excess cancer risk based on linear models are about 6-17% greater than estimates that make no allowance for dose estimation errors. This increase in risk estimates is reduced to about 4-11% if, as has often been done recently, survivors with dose estimates above 4 Gy are eliminated from the analysis.     

Multistage models and the incidence of cancer in the cohort of atomic bomb survivors

The analyses in this paper show that a number of biologically based models describe cancer incidence among the A-bomb survivors equally well. However, these different models can predict very different temporal patterns of risk after irradiation. No evidence was found to support the previous claim of Pierce and Mendelsohn that excess cancer risks for the solid tumors depend only upon attained age and not on age at exposure or time since exposure. Although the A-bomb survivor cohort is the largest epidemiological data set for the study of radiation and cancer, it is not large enough to discriminate among various possible carcinogenic mechanisms. Unfortunately for hypothesis generation, the data appear to be consistent with a number of different mechanistic interpretations of the role of radiation in carcinogenesis.     

Experimental derivation of relative biological effectiveness of A-bomb neutrons in Hiroshima and Nagasaki and implications for risk assessment

Epidemiological data on the health effects of A-bomb radiation in Hiroshima and Nagasaki provide the framework for setting limits for radiation risk and radiological protection. However, uncertainty remains in the equivalent dose, because it is generally believed that direct derivation of the relative biological effectiveness (RBE) of neutrons from the epidemiological data on the survivors is difficult. To solve this problem, an alternative approach has been taken. The RBE of polyenergetic neutrons was determined for chromosome aberration formation in human lymphocytes irradiated in vitro, compared with published data for tumor induction in experimental animals, and validated using epidemiological data from A-bomb survivors. The RBE of fission neutrons was dependent on dose but was independent of the energy spectrum. The same RBE regimen was observed for lymphocyte chromosome aberrations and tumors in mice and rats. Used as a weighting factor for A-bomb survivors, this RBE system was superior in eliminating the city difference in chromosome aberration frequencies and cancer mortality. The revision of the equivalent dose of A-bomb radiation using DS02 weighted by this RBE system reduces the cancer risk by a factor of 0.7 compared with the current estimates using DS86, with neutrons weighted by a constant RBE of 10.     

Allowance for random dose estimation errors in atomic bomb survivor studies: a revision

Allowing for imprecision of radiation dose estimates for A-bomb survivors followed up by the Radiation Effects Research Foundation can be improved through recent statistical methodology. Since the entire RERF dosimetry system has recently been revised, it is timely to reconsider this. We have found that the dosimetry revision itself does not warrant changes in these methods but that the new methodology does. In addition to assumptions regarding the form and magnitude of dose estimation errors, previous and current methods involve the apparent distribution of true doses in the cohort. New formulas give results conveniently and explicitly in terms of these inputs. Further, it is now possible to use assumptions about two components of the dose errors, referred to in the statistical literature as "classical" and "Berkson-type". There are indirect statistical indications, involving non-cancer biological effects, that errors may be somewhat larger than assumed before, in line with recommendations made here. Inevitably, methods must rely on uncertain assumptions about the magnitude of dose errors, and it is comforting to find that, within the range of plausibility, eventual cancer risk estimates are not very sensitive to these.     

A systems-based mathematical modelling framework for investigating the effect of drugs on solid tumours

Background and Purpose

Most information on the dose-response of radiation-induced cancer is derived from data on the A-bomb survivors. Since, for radiation protection purposes, the dose span of main interest is between zero and one Gy, the analysis of the A-bomb survivors is usually focused on this range. However, estimates of cancer risk for doses larger than one Gy are becoming more important for radiotherapy patients. Therefore in this work, emphasis is placed on doses relevant for radiotherapy with respect to radiation induced solid cancer.

Materials and methods

For various organs and tissues the analysis of cancer induction was extended by an attempted combination of the linear-no-threshold model from the A-bomb survivors in the low dose range and the cancer risk data of patients receiving radiotherapy for Hodgkin's disease in the high dose range. The data were fitted using organ equivalent dose (OED) calculated for a group of different dose-response models including a linear model, a model including fractionation, a bell-shaped model and a plateau-dose-response relationship.

Results

The quality of the applied fits shows that the linear model fits best colon, cervix and skin. All other organs are best fitted by the model including fractionation indicating that the repopulation/repair ability of tissue is neither 0 nor 100% but somewhere in between. Bone and soft tissue sarcoma were fitted well by all the models. In the low dose range beyond 1 Gy sarcoma risk is negligible. For increasing dose, sarcoma risk increases rapidly and reaches a plateau at around 30 Gy.

Conclusions

In this work OED for various organs was calculated for a linear, a bell-shaped, a plateau and a mixture between a bell-shaped and plateau dose-response relationship for typical treatment plans of Hodgkin's disease patients. The model parameters (α and R) were obtained by a fit of the dose-response relationships to these OED data and to the A-bomb survivors. For any three-dimensional inhomogenous dose distribution, cancer risk can be compared by computing OED using the coefficients obtained in this work.     

Cancer risk estimates from the combined Japanese A-bomb and Hodgkin cohorts for doses relevant to radiotherapy

Most information on the dose–response of radiation-induced cancer is derived from data on the A-bomb survivors who were exposed to γ-rays and neutrons. Since, for radiation protection purposes, the dose span of main interest is between 0 and 1 Gy, the analysis of the A-bomb survivors is usually focused on this range. However, estimates of cancer risk for doses above 1 Gy are becoming more important for radiotherapy patients and for long-term manned missions in space research. Therefore in this work, emphasis is placed on doses relevant for radiotherapy with respect to radiation-induced solid cancer. The analysis of the A-bomb survivor’s data was extended by including two extra high-dose categories (4–6 Sv and 6–13 Sv) and by an attempted combination with cancer data on patients receiving radiotherapy for Hodgkin’s disease. In addition, since there are some recent indications for a high neutron dose contribution, the data were fitted separately for three different values for the relative biological effectiveness (RBE) of the neutrons (10, 35 and 100) and a variable RBE as a function of dose. The data were fitted using a linear, a linear-exponential and a plateau-dose–response relationship. Best agreement was found for the plateau model with a dose-varying RBE. It can be concluded that for doses above 1 Gy there is a tendency for a nonlinear dose–response curve. In addition, there is evidence of a neutron RBE greater than 10 for the A-bomb survivor data. Many problems and uncertainties are involved in combing these two datasets. However, since very little is currently known about the shape of dose–response relationships for radiation-induced cancer in the radiotherapy dose range, this approach could be regarded as a first attempt to acquire more information on this area. The work presented here also provides the first direct evidence that the bending over of the solid cancer excess risk dose response curve for the A-bomb survivors, generally observed above 2 Gy, is due to cell killing effects.     

T-cell immunosenescence and inflammatory response in atomic bomb survivors

In this paper we summarize the long-term effects of A-bomb radiation on the T-cell system and discuss the possible involvement of attenuated T-cell immunity in the disease development observed in A-bomb survivors. Our previous observations on such effects include impaired mitogen-dependent proliferation and IL-2 production, decreases in naive T-cell populations, and increased proportions of anergic and functionally weak memory CD4 T-cell subsets. In addition, we recently found a radiation dose-dependent increase in the percentages of CD25(+)/CD127(-) regulatory T cells in the CD4 T-cell population of the survivors. All these effects of radiation on T-cell immunity resemble effects of aging on the immune system, suggesting that ionizing radiation might direct the T-cell system toward a compromised phenotype and thereby might contribute to an enhanced immunosenescence. Furthermore, there are inverse, significant associations between plasma levels of inflammatory cytokines and the relative number of na?ve CD4 T cells, also suggesting that the elevated levels of inflammatory markers found in A-bomb survivors can be ascribed in part to T-cell immunosenescence. We suggest that radiation-induced T-cell immunosenescence may result in activation of inflammatory responses and may be partly involved in the development of aging-associated and inflammation-related diseases frequently observed in A-bomb survivors.     

Effective dose of A-bomb radiation in Hiroshima and Nagasaki as assessed by chromosomal effectiveness of spectrum energy photons and neutrons

The effective dose of combined spectrum energy neutrons and high energy spectrum γ-rays in A-bomb survivors in Hiroshima and Nagasaki has long been a matter of discussion. The reason is largely due to the paucity of biological data for high energy photons, particularly for those with an energy of tens of MeV. To circumvent this problem, a mathematical formalism was developed for the photon energy dependency of chromosomal effectiveness by reviewing a large number of data sets published in the literature on dicentric chromosome formation in human lymphocytes. The chromosomal effectiveness was expressed by a simple multiparametric function of photon energy, which made it possible to estimate the effective dose of spectrum energy photons and differential evaluation in the field of mixed neutron and γ-ray exposure with an internal reference radiation. The effective dose of reactor-produced spectrum energy neutrons was insensitive to the fine structure of the energy distribution and was accessible by a generalized formula applicable to the A-bomb neutrons. Energy spectra of all sources of A-bomb γ-rays at different tissue depths were simulated by a Monte Carlo calculation applied on an ICRU sphere. Using kerma-weighted chromosomal effectiveness of A-bomb spectrum energy photons, the effective dose of A-bomb neutrons was determined, where the relative biological effectiveness (RBE) of neutrons was expressed by a dose-dependent variable RBE, RBE(γ, D _n), against A-bomb γ-rays as an internal reference radiation. When the newly estimated variable RBE(γ, D _n) was applied to the chromosome data of A-bomb survivors in Hiroshima and Nagasaki, the city difference was completely eliminated. The revised effective dose was about 35% larger in Hiroshima, 19% larger in Nagasaki and 26% larger for the combined cohort compared with that based on a constant RBE of 10. Since the differences are significantly large, the proposed effective dose might have an impact on the magnitude of the risk estimates deduced from the A-bomb survivor cohort.     

Fitting distributions to microbial contamination data collected with an unequal probability sampling design

Aims

The fitting of statistical distributions to microbial sampling data is a common application in quantitative microbiology and risk assessment applications. An underlying assumption of most fitting techniques is that data are collected with simple random sampling, which is often times not the case. This study develops a weighted maximum likelihood estimation framework that is appropriate for microbiological samples that are collected with unequal probabilities of selection.

Methods and Results

A weighted maximum likelihood estimation framework is proposed for microbiological samples that are collected with unequal probabilities of selection. Two examples, based on the collection of food samples during processing, are provided to demonstrate the method and highlight the magnitude of biases in the maximum likelihood estimator when data are inappropriately treated as a simple random sample.

Conclusions

Failure to properly weight samples to account for how data are collected can introduce substantial biases into inferences drawn from the data.

Significance and Impact of the Study

The proposed methodology will reduce or eliminate an important source of bias in inferences drawn from the analysis of microbial data. This will also make comparisons between studies and the combination of results from different studies more reliable, which is important for risk assessment applications.     

Possible selection effects for radiation risk estimates in Japanese A-bomb survivors: reanalysis of acute radiation symptoms data

An earlier analysis examined the possibility of bias in the Life Span Study (LSS) cohort by studying Japanese A-bomb survivors with bomb-related acute injuries and those without such injuries (Stewart and Kneale in Int J Epidemiol 29:708–714, 2000). The authors reported significantly higher radiation risks, both for cancers and non-cancers, among those survivors with acute injuries compared with those without. The risks were reported to be particularly large among survivors aged <10 or ≥55 years of age at the time of bombings. The aim of this paper is to examine these findings more closely using the LSS acute effects data. All the analyses were carried out using Poisson regression. Relative risk models were fitted with adjustment for sex and other factors. Significant differences in relative risk between survivors with epilation and burns and those without epilation and burns are found for leukaemia. There is also some evidence for heterogeneity in the leukaemia risk between survivors with two or more acute injuries and those with no injuries, but the evidence is disappeared when survivors with one or more injuries are compared with those without injuries. For solid cancers, cardiovascular disease and all deaths combined, the risks do not differ to a statistically significant extent between survivors with and without injuries. There is no statistically significant heterogeneity in risk across age-at-exposure categories for survivors with injuries. For all deaths combined, relative risk estimates and their uncertainties are significantly higher for survivors exposed at ages <10 years when compared with other exposure ages, but risks are not significantly raised for survivors exposed at ≥55 years of age. With the exception of leukaemia, the findings from the present work are inconsistent with those of Stewart and Kneale.     

Effect of radiation exposure on survival after first solid cancer diagnosis in A-bomb survivors

BackgroundComparison of the estimated effect of atomic bomb radiation exposure on solid cancer incidence and solid cancer mortality in the RERF Life Span Study (LSS) reveals a difference in the magnitude and shape of the excess relative risk dose response. A possible contributing factor to this difference is pre-diagnosis radiation effect on post-diagnosis survival. Pre-diagnosis radiation exposure theoretically could influence post-diagnosis survival by affecting the genetic makeup and possibly aggressiveness of cancer, or by compromising tolerance for aggressive treatment for cancer.MethodsWe analyze the radiation effect on post-diagnosis survival in 20,463 LSS subjects diagnosed with first-primary solid cancer between 1958 and 2009 with particular attention to whether death was caused by the first-primary cancer, other cancer, or non-cancer diseases.ResultsFrom multivariable Cox regression analysis of cause-specific survival, the excess hazard at 1 Gy (EH_1Gy) for death from the first primary cancer was not significantly different from zero – p = 0.23, EH_1Gy = 0.038 (95 % CI: −0.023, 0.104). Death from other cancer and death from non-cancer diseases both were significantly associated with radiation dose: other cancer EH_1Gy = 0.38 (95 % CI: 0.24, 0.53); non-cancer EH_1Gy = 0.24 (95 % CI: 0.13, 0.36), both p < 0.001.ConclusionThere is no detectable large effect of pre-diagnosis radiation exposure on post-diagnosis death from the first primary cancer in A-bomb survivors.ImpactA direct effect of pre-diagnosis radiation exposure on cancer prognosis is ruled out as an explanation for the difference in incidence and mortality dose response in A-bomb survivors.     

Testing for environmentally induced bias in phenotypic estimates of natural selection: theory and practice

Measuring natural selection has been a fundamental goal of evolutionary biology for more than a century, and techniques developed in the last 20 yr have provided relatively simple means for biologists to do so. Many of these techniques, however, share a common limitation: when applied to phenotypic data, environmentally induced covariances between traits and fitness can lead to biased estimates of selection and misleading predictions about evolutionary change. Utilizing estimates of breeding values instead of phenotypic data with these methods can eliminate environmentally induced bias, although this approach is more difficult to implement. Despite this potential limitation to phenotypic methods and the availability of a potential solution, little empirical evidence exists on the extent of environmentally induced bias in phenotypic estimates of selection. In this article, we present a method for detecting bias in phenotypic estimates of selection and demonstrate its use with three independent data sets. Nearly 25% of the phenotypic selection gradients estimated from our data are biased by environmental covariances. We find that bias caused by environmental covariances appears mainly to affect quantitative estimates of the strength of selection based on phenotypic data and that the magnitude of these biases is large. As our estimates of selection are based on data from spatially replicated field experiments, we suggest that our findings on the prevalence of bias caused by environmental covariances are likely to be conservative.     

Estimation of the upper limit of the mutation rate and mean heterozygous effect of deleterious mutations

Deng et al. have recently proposed that estimates of an upper limit to the rate of spontaneous mutations and their average heterozygous effect can be obtained from the mean and variance of a given fitness trait in naturally segregating populations, provided that allele frequencies are maintained at the balance between mutation and selection. Using simulations they show that this estimation method generally has little bias and is very robust to violations of the mutation-selection balance assumption. Here I show that the particular parameters and models used in these simulations generally reduce the amount of bias that can occur with this estimation method. In particular, the assumption of a large mutation rate in the simulations always implies a low bias of estimates. In addition, the specific model of overdominance used to check the violation of the mutation-selection balance assumption is such that there is not a dramatic decline in mean fitness from overdominant mutations, again implying a low bias of estimates. The assumption of lower mutation rates and/or other models of balancing selection may imply considerably larger biases of the estimates, making the reliability of the proposed method highly questionable.     

T cells of atomic bomb survivors respond poorly to stimulation by Staphylococcus aureus toxins in vitro: does this stem from their peripheral lymphocyte populations having a diminished naïve CD4 T-cell content?

We found previously that the peripheral CD4 T-cell populations of heavily exposed A-bomb survivors contained fewer na?ve T cells than we detected in the corresponding unexposed controls. To determine whether this demonstrable impairment of the CD4 T-cell immunity of A-bomb survivors was likely to affect the responsiveness of their immune systems to infection by common pathogens, we tested the T cells of 723 survivors for their ability to proliferate in vitro after a challenge by each of the Staphylococcus aureus toxins SEB, SEC-2, SEC-3, SEE and TSST-1. The results presented here reveal that the proliferative responses of T cells of A-bomb survivors became progressively weaker as the radiation dose increased and did so in a manner that correlated well with the decreasing CD45RA-positive (na?ve) [but not CD45RA-negative (memory)] CD4 T-cell percentages that we found in their peripheral blood lymphocyte (PBL) populations. We also noted that the T cells of survivors with a history of myocardial infarction tended to respond poorly to several (or even all) of the S. aureus toxins, and that these same individuals had proportionally fewer CD45RA-positive (na?ve) CD4 T cells in their PBL populations than we detected in survivors with no myocardial infarction in their history. Taken together, these results clearly indicate that A-bomb irradiation led to an impairment of the ability of exposed individuals to maintain their na?ve T-cell pools. This may explain why A-bomb survivors tend to respond poorly to toxins encoded by the common pathogenic bacterium S. aureus.     

Biased estimators of quantitative trait locus heritability and location in interval mapping

In many empirical studies, it has been observed that genome scans yield biased estimates of heritability, as well as genetic effects. It is widely accepted that quantitative trait locus (QTL) mapping is a model selection procedure, and that the overestimation of genetic effects is the result of using the same data for model selection as estimation of parameters. There are two key steps in QTL modeling, each of which biases the estimation of genetic effects. First, test procedures are employed to select the regions of the genome for which there is significant evidence for the presence of QTL. Second, and most important for this demonstration, estimates of the genetic effects are reported only at the locations for which the evidence is maximal. We demonstrate that even when we know there is just one QTL present (ignoring the testing bias), and we use interval mapping to estimate its location and effect, the estimator of the effect will be biased. As evidence, we present results of simulations investigating the relative importance of the two sources of bias and the dependence of bias of heritability estimators on the true QTL heritability, sample size, and the length of the investigated part of the genome. Moreover, we present results of simulations demonstrating the skewness of the distribution of estimators of QTL locations and the resulting bias in estimation of location. We use computer simulations to investigate the dependence of this bias on the true QTL location, heritability, and the sample size.     

Improved estimates of cancer site-specific risks for A-bomb survivors

Pawel, D. J., Preston, D. L., Pierce, D. A. and Cologne, J. B. Improved Estimates of Cancer Site-Specific Risks for A-Bomb Survivors. Radiat. Res. 169, 87-98 (2008). Simple methods are investigated for improving summary site-specific radiogenic risk estimates. Estimates in this report are derived from cancer incidence data from the Life Span Study (LSS) cohort of A-bomb survivors that are followed up by the Radiation Effects Research Foundation (RERF). Estimates from the LSS of excess relative risk (ERR) for solid cancer sites have typically been derived separately for each site. Even though the data for this are extensive, the statistical imprecision in site-specific (organ-specific) risk estimates is substantial, and it is clear that a large portion of the site-specific variation in estimates is due to this imprecision. Empirical Bayes (EB) estimates offer a reasonable approach for moderating this variation. The simple version of EB estimates that we applied to the LSS data are weighted averages of a pooled overall estimate of ERR and separately derived site-specific estimates, with weights determined by the data. Results indicate that the EB estimates are most useful for sites such as esophageal or bladder cancer, for which the separately derived ERR estimates are less precise than for other sites.     

The evolution of biased codon and amino acid usage in nematode genomes

Despite the degeneracy of the genetic code, whereby different codons encode the same amino acid, alternative codons and amino acids are utilized nonrandomly within and between genomes. Such biases in codon and amino acid usage have been demonstrated extensively in prokaryote genomes and likely reflect a balance between the action of mutation, selection, and genetic drift. Here, we quantify the effects of selection and mutation drift as causes of codon and amino acid-usage bias in a large collection of nematode partial genomes from 37 species spanning approximately 700 Myr of evolution, as inferred from expressed sequence tag (EST) measures of gene expression and from base composition variation. Average G + C content at silent sites among these taxa ranges from 10% to 63%, and EST counts range more than 100-fold, underlying marked differences between the identities of major codons and optimal codons for a given species as well as influencing patterns of amino acid abundance among taxa. Few species in our sample demonstrate a dominant role of selection in shaping intragenomic codon-usage biases, and these are principally free living rather than parasitic nematodes. This suggests that deviations in effective population size among species, with small effective sizes among parasites, are partly responsible for species differences in the extent to which selection shapes patterns of codon usage. Nevertheless, a consensus set of optimal codons emerges that is common to most taxa, indicating that, with some notable exceptions, selection for translational efficiency and accuracy favors similar sets of codons regardless of the major codon-usage trends defined by base compositional properties of individual nematode genomes.     

Possible role of natural killer cells in negative selection of mutant lymphocytes that fail to express the human leukocyte antigen-A2 allele

Increased frequencies of cells carrying mutations at several loci have been found in the blood cells of atomic-bomb (A-bomb) survivors upon testing four or five decades after the bombing. Interestingly, though, we have been unable to demonstrate any radiation-associated increases in the frequencies of mutant blood cells in which human leukocyte antigen (HLA)-A expression has been disrupted; this is true both of preliminary tests on the T cells of a small subset of A-bomb survivors and of the much more extensive study reported here in which we screened a much larger group of survivors for HLA-A2 loss mutations in B cells and granulocytes as well as in T cells. In attempting to explain our inability to detect any increases in HLA-A2-negative cell numbers in HLA-A2 heterozygous individuals exposed to A-bomb irradiation, we decided to test the hypothesis that HLA-A mutant lymphocytes might well have been induced by radiation exposure in much the same way as every other type of mutant we encountered, but may subsequently have been eliminated by the strong negative selection associated with their almost inevitable exposure to autologous natural killer (NK) cells in the bloodstream of each of the individuals concerned. We now report that mutant B lymphocyte cell lines that have lost the ability to express the HLA-A2 antigen do indeed appear to be much more readily eliminated than their parental heterozygous counterparts during co-culture in vitro with autologous NK cells. We make this claim first because we have observed that adding autologous NK cells to in vitro cultures of HLA-A2 heterozygous B or T cell lines appeared to cause a dose-dependent decrease in the numbers of HLA-A2-negative mutants that could be detected over a period of 3 days, and second because when we used peripheral blood HLA-A2 heterozygous lymphocyte cultures from which most of the autologous NK cells had been removed we found that we were able to detect newly-arising HLA-A2 mutant T cells in substantial numbers. Taken together, these results strongly support the hypothesis that autologous NK cells are responsible for eliminating mutant lymphocytes that have lost the ability to express self-HLA class I molecules in vivo, and may well therefore explain why we have been unable to detect increased frequencies of HLA-A2 mutants in samples from any of the 164 A-bomb survivors whose HLA-A2 heterozygote status made their lymphocytes suitable for our tests.     

Impact of nonrandom selection mechanisms on the causal effect estimation for two-sample Mendelian randomization methods

Nonrandom selection in one-sample Mendelian Randomization (MR) results in biased estimates and inflated type I error rates only when the selection effects are sufficiently large. In two-sample MR, the different selection mechanisms in two samples may more seriously affect the causal effect estimation. Firstly, we propose sufficient conditions for causal effect invariance under different selection mechanisms using two-sample MR methods. In the simulation study, we consider 49 possible selection mechanisms in two-sample MR, which depend on genetic variants (G), exposures (X), outcomes (Y) and their combination. We further compare eight pleiotropy-robust methods under different selection mechanisms. Results of simulation reveal that nonrandom selection in sample II has a larger influence on biases and type I error rates than those in sample I. Furthermore, selections depending on X+Y, G+Y, or G+X+Y in sample II lead to larger biases than other selection mechanisms. Notably, when selection depends on Y, bias of causal estimation for non-zero causal effect is larger than that for null causal effect. Especially, the mode based estimate has the largest standard errors among the eight methods. In the absence of pleiotropy, selections depending on Y or G in sample II show nearly unbiased causal effect estimations when the casual effect is null. In the scenarios of balanced pleiotropy, all eight MR methods, especially MR-Egger, demonstrate large biases because the nonrandom selections result in the violation of the Instrument Strength Independent of Direct Effect (InSIDE) assumption. When directional pleiotropy exists, nonrandom selections have a severe impact on the eight MR methods. Application demonstrates that the nonrandom selection in sample II (coronary heart disease patients) can magnify the causal effect estimation of obesity on HbA1c levels. In conclusion, nonrandom selection in two-sample MR exacerbates the bias of causal effect estimation for pleiotropy-robust MR methods.