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A note on the statistical power in extended twin designs

A note on the statistical power in extended twin designs
A note on the statistical power in extended twin designs

QTL’s) and sources due to background genetic vari-ance (Fulker, Cherny, & Cardon, 1995; Fulker, Cherny,Sham, et al.,1999; Nance and Neale, 1989; Boomsma and Dolan, 1998). A necessary first step in mapping complex traits to QTL’s is to establish the amount of genetic variation that underlies the phenotypic varia-tion of the trait. If phenotypic variation in a trait is found to be caused in part by genetic sources, linkage and/or association studies can be conducted in order to characterize the effects of specific genetic loci on the phenotypic variation. If phenotypic variation is not found to be heritable, the search for effects of specific genetic loci will not be initiated. However, in some cases it may be concluded that phenotypic variance in INTRODUCTION

Recent advances in molecular genetics have made it possible to partition genetic variance into sources due to particular genetic loci (quantitative trait loci’s;

A Note on the Statistical Power in Extended Twin Designs

Dani?lle Posthuma 1,2and Dorret I. Boomsma 1

Received 7 Oct. 1999—Final 20 Feb. 2000

The power to detect sources of genetic and environmental variance varies with sample size,study design, effect size and the statistical significance level chosen. We explored whether the power of the classical twin study may be increased by adding non-twin siblings to the classical twin design. Sample sizes to detect genetic and shared environmental variation were compared for kinships with only twins, kinships consisting of twins and one additional sibling, and kin-ships with twins and two additional siblings. The effect of adding siblings to the classical twin design was considered for univariate and bivariate analyses.

For the univariate case, adding one non-twin sibling resulted in a decrease in sample size needed to detect additive genetic influences in the presence of environmental influences. How-ever, adding two additional siblings did not decrease the number of subjects as compared to the classical twin design. The sample size required to detect common environmental factors was also greatly decreased by adding one non-twin sibling. Adding two non-twin siblings resulted in a small additional decrease. In models including additive genetic, dominant genetic, and unique environmental effects, adding one sibling to a twin family decreased the required sample size to detect dominant genetic influences. Adding two siblings to a twin family resulted in only a slight additional decrease in sample size.

In the bivariate case a similar pattern of results was found, in addition to the observation that the overall required sample size, as expected, was lower than in the univariate case. The decrease in sample size from bivariate testing was more pronounced in a design with one or two additional siblings, as compared to a design with twins only. It is concluded that a well con-sidered choice of family design, i.e. including families with twins and one or two additional sib-lings increases the statistical power to detect sources of variance due to additive and non-additive genetic influences, and common environment.

KEY WORDS:Sample size; heritability; methodology; sibship size; twin study.

Behavior Genetics, Vol. 30, No. 2, 2000

147

0001-8244/00/0300-0147$18.00/0 ?2000 Plenum Publishing Corporation

1

Department of Biological Psychology, Vrije Universiteit Amster-dam, Netherlands.2

Correspondence and requests for reprints should be sent to: D.Posthuma, Vrije Universiteit, Department of Biological Psychol-ogy, De Boelelaan 1111, 1081 HV, Amsterdam, The Netherlands.Telephone: +31 20 444 8814, telefax: +31 20 444 8832, email:danielle@psy.vu.nl

We gratefully acknowledge the financial support of the USF (grant number 96/22) and the HFSP (grant number rg0154/1998-B). We wish to thank Eco de Geus, Leo Beem and Conor Dolan for their comments on draft versions of this paper.

a trait can not be ascribed to genes because the statis-tical power to detect sources of genetic variation is in-sufficient (Svikis, Velz & Pickens, 1994; Pickens,Svikis, McGue, Lykken, et al.,1991). This will pre-clude further searching for effects of QTL’s on that par-ticular trait, even though such QTL’s may be present.

The statistical power of quantitative genetic stud-ies is influenced by the size of the effect (e.g. heri-tability), the sample size, the probability level (α)chosen, and the homogeneity of the sample (Neale and Cardon, 1992; Cohen, 1992; Tanaka, 1987). Increasing the sample size is the most common way to increase the statistical power of a study, but is often limited by re-sources of time and money. Another means to increase statistical power is the use of multivariate testing. In the context of structural equation modeling the statistical power to detect genetic effects rises as a (non-linear)function of multivariate testing under the condition that the measures are correlated (Schmitz, Cherny, and Fulker, 1998). In the context of partitioned twin analy-ses it has been shown that choosing a different (e.g.other than 1 to 1) MZ to DZ ratio influences statistical power such that an MZ to DZ ratio of 1 to 4 is optimal for partitioned twin analyses (Nance & Neale, 1989).

In the present paper we focus on increasing the sta-tistical power of the classical twin study by adding non-twin siblings to MZ and DZ twin pairs. Since non-twin siblings share on average half of their segregating genes,just like DZ twins, adding non-twin siblings to the clas-sical twin design may provide an efficient way to in-crease the power to detect sources of genetic and shared environmental variance. Adding two more siblings to a twin kinship provides five additional observed covari-ances, whereas adding a whole new family consisting of two siblings provides only one additional observed co-variance. In the present paper we examine the effects of adding non-twin siblings to twin families on the esti-mated sample size needed to detect additive genetic (A)variance (V a ), dominant genetic (D) variance (V d ), and common environmental (C) variance (V c ), with a power of 80% in the context of structural equation modeling.METHOD

We calculated covariance matrices for three ex-perimental designs, which differed in family constitu-tion. Design 1 included only MZ twins and DZ twins.Design 2 included families with MZ and DZ twins and one additional sibling. Design 3 included families with MZ and DZ twins and two additional siblings. For all three designs we calculated the sample size needed to 148Posthuma and Boomsma

detect an effect of interest with a power of 80%. The MZ twins to DZ twins ratio was 1 to 1 for all three de-signs (thus, the ratio MZ to ‘non MZ sibpairs’, is not 1 to 1 for all designs). It should be noted that we re-port sample size in subjects and not in twin pairs. The same number of subjects refers to different numbers of twin pairs and a different number of families for all three designs. We will use the terms ‘highest power’and ‘fewest subjects needed’ to refer to an optimal de-sign to detect sources of phenotypic variance.

All analyses were carried out using the statistical software package Mx (Neale, 1997). Estimation of pa-rameters was obtained by normal theory maximum like-lihood. Goodness of fit testing was based on the likelihood ratio tests. First univariate models were con-sidered. In order to obtain the sample size needed to detect varying levels of additive genetic variance with a fixed power level of (1 ?β) =.80, covariance matri-ces were calculated with sources of additive genetic variance (V a ) accounting for 10% to 90% of the phe-notypic variance in the presence of sources of common environmental variance (V c ) accounting for 00%, 10%,and 20% of the variance. Remaining variance was at-tributed to unique environmental (E) sources of vari-ance (V e ). To detect sources of V c covariance matrices were calculated with V c accounting for 10% to 90% of the phenotypic variance in the context of sources of V a accounting for 00%, 10%, and 20% of the phenotypic variance. In addition, covariance matrices were calcu-lated with sources of variation due to A, D (dominant genetic variance) and E. Only the situation in which dominance was ‘complete’ (V a to V d =2 to 1; see ap-pendix I) was considered. In the ADE-models the total genetic variance, i.e. V a and V d together accounted for 30% to 90% of the total phenotypic variance. For all situations, remaining variance was attributed to V e .

Since non-twin siblings, like DZ twins, share on average half of their genes, expectations for non-twin sibling covariances were modeled similarly to expec-tations for DZ covariances.

In the ACE-models the expected phenotypic vari-ance (σ2) of twins and siblings is V a +V c +V e , the ex-pected MZ covariance V a +V c , and the expected DZ and sibling covariance .5 V a +V c . In ADE-models, the expected phenotypic variance is V a +V d +V e , the ex-pected MZ covariance V a +V d , and the expected DZ and sibling covariance .5 V a +.25 V d .

It is known that the use of a multivariate pheno-type, as opposed to a univariate phenotype, results in a gain of statistical power if the multivariate traits are correlated (Schmitz et al.1998). To find out how much

adding siblings and using a multivariate phenotype af-fects statistical power we also looked at several bi-variate designs. We calculated covariance matrices for two traits with a phenotypic correlation of .50. Both traits could be influenced by A, C, and E or by A, D,and E. Total influences of sources of A, C or D, and E were uniform for each trait. The phenotypic correlation between the two traits could be due to additive genetic correlation (rA), dominant genetic correlation (rD),common environmental correlation (rC), or to unique environmental correlation (rE), depending on the spe-cific situation that was considered. Figure 1 depicts the construction of covariance matrices for kinships con-sisting of twins and one additional sibling for a bi-variate ADE-model (Cholesky decomposition) in which rE is absent and all phenotypic correlation is due to rA and rD. All latent variables have unit variance.

Power calculations were carried out by fitting the known model to the exact (population) covariance ma-trices as described in Neale and Cardon (1992). In mod-els which contain a parameter which is known to be zero,the zero parameter can either be fixed at zero or freed (estimated) while computing the power to detect one of the other non-zero parameters. For example, when treat-ing the ACE-model in which V c is zero as an AE-model,the power to detect sources of variation due to A is sig-nificantly higher than when the ACE-model is treated as an ACE-model, i.e. with V c estimated as a free param-eter. In the power calculations the zero-parameter was

Power and Sibship Size 149

estimated as a free parameter because we are interested in computing the power to detect V a , in ACE-models,regardless of the value of V c (and vice versa). The same reasoning applies to the bivariate calculations.

Constraining a certain set of parameters to zero and refitting the model provides the non-centrality parame-ter. From this non-centrality parameter the sample size required to reject the false model with a power of 80%and a significance level αof .05 can be calculated (Mar-tin et al.,1978; Hewitt and Heath, 1988) and is conve-niently supplied by Mx.RESULTS Univariate Models ACE-models

We fitted full univariate models with sources of variation due to additive genetic (A), common environ-mental (C) and unique environmental influences (E).Dropping either genetic or common environmental parameters and refitting the model provides the non-cen-trality parameter. With Mx (Neale, 1997) the cor-responding number of subjects required to detect the parameter that was dropped with a power of 80% and αof 5% was calculated for 1 degree of freedom. Results concerning the estimated sample size (in subjects)needed to detect V a in ACE-models for the three designs

are depicted in Figure 2 (and appendix II). Figure 2a con-

Fig. 1.Pathdiagram for the bivariate ADE-model, cholesky decomposition. Example for twins and one additional sibling, no unique environ-mental correlation (rE). The covariance between trait 1 and trait 2 is (a 11*a 21) +(d 11*d 21) and the correlation between trait 1 and trait 2 is (a 11*a 21) +(d 11*d 21)/√(σ21*σ22).

cerns low values of V a (10% ?20%), Figure 2b concerns intermediate values of V a (30%–50%), and Figure 2c concerns high values of V a (60%–90%) accounting for the total phenotypic variance. All values of V a are re-ported three times, i.e. in the context of values of V c of 0%, 10%, and 20%.

As can be seen in Figure 2a, 2b, and 2c, for vari-ous values of V a and V c , design 2 (families consisting of MZ and DZ twins and one non-twin sibling) is the most optimal design to detect sources of variation due to A, i.e. with design 2 fewer subjects are required to achieve a power of 80% (see appendix II). The number of subjects needed to detect a fixed value of V a is on average 9.3% more in the classical twin design (design 1) compared with a design with twins and one additional sibling. This can result in 2849 fewer subjects that are needed with design 2 to detect an additive genetic in-fluence of 10% compared with the classical twin design.

Including families with twins and two additional sibs, is less powerful than including families with twins and one additional sibling, and also less powerful than including families with twins only for the detection of V a ; adding two siblings at the cost of the total number of MZ twins is disadvantageous, but adding one sib-ling is ideal.

Results for detecting common environmental in-fluences are given in Figures 3a, 3b, and 3c, for low,moderate, and high values of V c respectively (see also Appendix III).

150Posthuma and Boomsma

Under various values of V c and V a , the power to detect sources of variation due to C rises substantially when one sibling is added to the classical twin design;on average 50.4% fewer subjects are needed as com-pared to the classical twin design (design 1). Adding two siblings decreases sample size even more, but not as dramatically as the decrease from no additional sib-lings to one additional sibling.

Many empirical studies suggest models in which sources of variation due to C are of less importance than sources of variation due to A (Plomin, DeFries, &McClearn, 1990). Therefore, we also calculated the sam-ple size required to detect small values of V c in the con-text of higher values of V a . Figure 4 depicts the number of subjects needed to detect values of V c of 10% and 20% in the context of values of V a of 20% , 30%, 40%or 50% (Appendix IV).

As expected, sample size required to detect V c with a power of 80% decreases as a result of higher values of V c and higher values of V a . Comparing the sample size required to detect sources of variation due to A (Figure 2b) with the sample size required to detect sources of variation due to C, shows that in the realis-tic situation where V a > V c sources of variation due to C are very difficult to detect. Even if the sample size is large enough to detect sources of variation due to A, the small value of V c may still go undetected. If for exam-ple the true model is an ACE-model with V a =50%, V c =20%, and V e =

30%, and the total sample size 328

Fig. 2 a,b,c.Required sample size to detect sources of variance due to additive genetic effects in ACE models for three different family de-signs with a power of 80%. Design 1 =MZ and DZ twins only, Design 2 =MZ and DZ twins and one additional sibling, Design 3 =MZ and DZ twins and two additional siblings.

(just enough for design 1 to detect V a of 50%, with power of 80%), V c will not be detected and the AE-model will be proposed as the most parsimonious model.This results in a biased estimate of V a (in this case V a is estimated to be 70%).

Adding siblings to the classical twin design de-creases the sample size required to detect both V a and V c and has the largest effect on the sample size required to detect V c (i.e. 50.4% fewer subjects needed for V c ,9.3% fewer subjects needed for V a ). Therefore, the bias towards overestimating values of V a as a result of not detecting V c in situations where V a > V c , is less likely

Power and Sibship Size 151

to be present in designs where siblings are added to the classical twin design.ADE-Models

We also fitted full univariate models with sources of variation due to additive genetic (A), dominance (D)and unique environmental influences (E). Since a DE-model is unrealistic we report the sample size required to detect sources of variation due to A and D (2 df test)and to detect sources of variation due to D (1 df test)with a power of 80%. Results for detecting V a and V d ,or V d

are given in Figures 5a and 5b (and appendix V).

Fig. 3 a,b,c.Required sample size to detect sources of variance due to common environmental in?uences in ACE models for three different

family designs with a power of 80%.

Fig. 4.Required sample size to detect sources of variance due to common environmental in?uences in ACE models where V a > V c , for three

different family designs with a power of 80%.

Under various values of V a and V d , with fixed ratio of V a to V d is 2 to 1, adding one sibling to a twin family decreases the sample size required to detect V d . Adding two siblings decreases sample size even more but less than the decrease due to adding one sibling. Absolute ef-fects are slightly higher with increasing values of V a and V d . Figure 5a also emphasizes the very large sample size that is required to detect dominant genetic influences.Even the largest possible value of V d under complete dominance with the most optimal design will go unde-tected if the sample is smaller than 1776 subjects.

Sample sizes required to detect both V a and V d si-multaneously are considerably smaller as compared to sample sizes required to detect V d . In contrast, how-ever, adding siblings does not decrease sample size needed to detect V a and V d simultaneously. In fact, a design with one or two siblings requires somewhat more subjects to detect V a and V d with a power of 80%,as can be seen in Figure 5b. It should be noted how-ever that the number of subjects needed to detect V a and V d at the same time is considerably less than the number of subjects needed to detect V d only. This im-plies that if the sample size is large enough to detect V d it will also be sufficient to detect V a and V d .

152Posthuma and Boomsma

In conclusion, to optimize the power to detect V d ,a design with additional siblings, as compared to a de-sign with twins only, is preferred.

Bivariate Models ACE-Models

To detect sources of variance due to additive ge-netic influence (A), we calculated both the sample size required to detect all sources of V a (df =3; paths a 11,a 21, and a 22in Figure 1) and the required sample size to detect the common genetic pathway (df =1; path a 21).We considered the test for the detection of the common pathway to be a test for the presence of a genetic cor-relation (rA). The following situations to detect sources of variance due to A were considered: a) The genetic correlation (rA) is ‘moderate’ and equal to the common environmental correlation (rC) and to the unique envi-ronmental correlation (rE). Variances due to A, C and E (uniform for both traits) are 40%, 10%, and 50% re-spectively of the phenotypic variance. b) rC is absent,rA is high (.80), and rE is small (.36), variances due

to A, C and E are 40%, 10%, and 50% respectively.

Fig. 5 a,b.Required sample size to detect sources of variance due to dominant genetic in?uences (a) and total genetic (dominant & additive

in?uences)(b) in?uences in ADE models, for three different family designs with a power of 80%.

c) Variances due to C are absent. rA is .60, rE is .27,variances due to A and E are 70% and 30% respec-tively. As mentioned before, all parameters were es-timated, as opposed to constraining these parameters,which were zero in the full model. It should also be noted that considering the tests for total V a , total V c , and total V d to be 3 df-tests is a conservative approach, as it could be argued these are actually 2 df-tests, or tests with df’s somewhere between 2 and 3. Testing, for ex-ample, whether either or both univariate genetic vari-ances equal zero, implies that the genetic covariance is zero. If variances due to additive genetic influences for both traits equal zero, a correlation between these sources of variance is not possible. In other words, if the sample size required to detect each of the univa-riate variances due to additive genetic influences is insufficient, a correlation due to additive genetic in-fluences can also not be detected. Therefore, consider-ing the test for the power to detect ‘total V a ’ (i.e. both univariate variances due to additive genetic influences and the correlation due to additive genetic influences in the bivariate case) a 3 df test will provide an overesti-mation of the sample size needed for a power of 80%.Results of situation a, b, and c for the three different kinships, are given in Table I.

As can be seen in Table I the same pattern of re-sults is found in the bivariate case as in the univariate case; a design with one additional sibling is optimal for the detection of V a in ACE-models. In addition, sig-nificantly fewer subjects are needed in the bivariate case as compared to the univariate case. Depending on whether the phenotypic correlation is due to rA, rC, or rE, the sample size required to detect V a may decrease and is lowest in cases where there is no influence of common environmental sources (i.e. statistical power Power and Sibship Size 153

is highest in these cases). However, when there are uni-variate common environmental influences but no com-mon environmental correlation, the sample size required to detect variance due to additive genetic influences in-creases. Comparing situations a, b, and c leads to the conclusion that the power to detect sources of variance and covariance due to A (df 3) is highest (and the re-quired sample size is smallest) when there is no uni-variate common environmental source of variation.However, if there are common environmental sources of variation, sources of variance due to A are easier to detect when there is also a correlation between these two univariate common environmental sources of vari-ation, and again a design with one additional sibling is optimal.

To detect sources of common environmental sources of variation, we calculated both the power to detect all sources of variation due to C (df =3) and the power to detect the common pathway (df =1), which is a test to detect the environmental correlation (rC).We considered situations analogous to the situations in which power was calculated to detect sources of vari-ation due to A; a) The common environmental corre-lation is ‘moderate’ and equal to the genetic correlation and to the unique environmental correlation, i.e. rC =rA =rE =.50. Uniform univariate variances due to A,C and E are 10%, 40%, and 50% respectively. b) rA is absent. rC is high (.80), and rE is small (.36), variances due to A, C and E are 10%, 40%, and 50% respectively,c) Variances due to A and rA are absent. rC is .60, rE is .27, variances due to C and E are 70% and 30% re-spectively. Again, for all situations the phenotypic cor-relation was .50. Results are given in Table II.

Although the results in the bivariate case resem-ble those in the univariate case (i.e. a design with two

Table I.Total samplesize (in number of subjects) needed to detect additive genetic in?uences in full bivariate ACE models under three dif-ferent sibship sizes with power (1 ?β) =.80 and α=.05

V a =40% rA =.50V a =40% rA =.80V a =70% r A =.60V c =10% rC =.50V c =10% rC =.00V c =00% r C =.00V e =50% rE =.50

V e =50% rE =.36

V c =30% r E =.27

all V a (df =3)

rA (df =1)all V a (df =3)

rA (df =1)

all V a (df =3)

rA (df =1)

design 16602392782884156270design 25641917678735147237design 3

680

2260

820

876

180

284

Note : MZ/DZ ratio =1/1; design 1 =twins only, design 2 =twins and one additional sibling, design 3 =twins and two additional siblings.‘All V a ’ refers to both univariate variances and the genetic correlation.

In order to calculate the total number of families needed, all cells concerning design 1 need to be divided by 2, all cells concerning design 2need to be divided by 3, and all cells concerning design 3 need to be divided by 4.

additional siblings is optimal for the detection of V c ),the difference between design 2 and design 3 (i.e.adding one or two siblings) in the bivariate case is more substantial. Whereas in the univariate case only a small additional effect was found, in the bivariate case 4 to 5 times less subjects are needed with two additional siblings as compared to one additional sibling.ADE-Models

We calculated covariance matrices for two traits that were influenced by A, D, and E in the context of complete dominance. Sources of variance due to A and D accounted for 40% and 20% respectively of the total phenotypic variance. We assumed that the ratio V a to V d remained equal over the two traits. This implies that rA =rD (see appendix I). Three situations were con-sidered: a) rA =rD =.80,; b) rA =rD =.50; c) rA =rD =.30. For all three situations the phenotypic correla-tion was fixed at .50 by attributing all remaining co-variance to rE. We report the total number of individual subjects needed to detect sources of total V a and V d due to A and D (df =6), rA & rD (df =2), total D (df =3),and rD (df =1) for a power of 80%. Results are given in Table III.

Analogous to the univariate case a design with two additional siblings is optimal for the detection of V d and a design with twins only is optimal for the detec-tion of V a and V d simultaneously. Comparison with the univariate results shows that in a design with twins only, fewer subjects are needed to detect sources of variance due to D as a result from bivariate testing. This effect, however, is stronger when a design consisting of twins and two additional siblings is used, suggest-ing that in addition to the decrease in sample size as a result from bivariate testing, adding siblings will de-crease the sample size required to detect sources of variance due to D even further.

154Posthuma and Boomsma

Designs Where Only Sibs of mz Twins are Included In the previous analyses all families were of the same structure; consisting of MZ and DZ twins only,or with one or two additional siblings. For several rea-sons this may not always be realistic. For illustrative purposes, we included two other designs in which one (design 4) or two siblings (design 5) were added to MZ twin families, but not to DZ families. Analyses were run for a few ‘standard’ situations of the ACE-models and ADE-models for univariate testing only. Results for ACE and ADE models are given in Table IV.

Comparison of the results of designs 4 and 5 and the results of designs 2 and 3 shows that in ACE-mod-els a design consisting of MZ twins and one additional sibling and DZ twins only (design 4) is optimal for the detection of V a , and performs even better than design 2.For the detection of V c in ACE-models design 3 and 5are both optimal.

In the context of ADE-models, design 3 (MZ/DZ twins with two additional siblings), requires the smallest sample size and is more optimal than design 4 or 5 for the detection of sources of variation due to dominance.CONCLUSION

We demonstrated that with a fixed power of 80%,a probablity level of 5% and under varying levels of heritability and common environmental influences,adding one sibling to the classical twin design signifi-cantly decreases the number of subjects that are needed to detect each of these sources of variation. Adding two siblings to a twin pair yields an additional decrease of sample size to detect sources of variation due to the common environment but is not optimal for the detec-tion of additive genetic influences. If the trait is influ-enced by additive and non-additive genetic factors,adding one sibling to the classical twin design decreases the sample size needed to detect sources of variation

Table II.Total samplesize (in number of subjects) needed to detect common environmental in?uences in full bivariate ACE models under

three different sibship sizes with power (1 ?β) =.80 and α=.05

V a =10% r A =.50V a =10% rA =.00V a =0% rA =.00V c =40% r C =.50V c =40% r C =.80V c =70% r C =.60V e =50% r E =.50

V e =50% rE =.36

V e =30% rE =.27

all V c (df =3)

r C (df =1)all V c (df =3)

r C (df =1)

all V c (df =3)

rC (df =1)

design 14441498518560100156design 22137742492794896design 3

48

760

44

268

16

108

Note : see table 1 for definitions.

Power and Sibship Size 155

due to dominance. Adding two siblings decreases the number of required subjects somewhat more but the de-crease is relatively small (compared to the decrease due to adding one sibling). These effects are more pro-nounced in the bivariate case than in the univariate case. An additional benefit of adding siblings is that these designs, as compared to the classical twin design,are less likely to result in an overestimation of additive genetic influences as a result of not detecting small sources of common environmental influences.

We modeled the sibling covariances under the as-sumption that age differences in heritability are not im-portant. A more complex model would take into account age differences between non-twin siblings. It is known that for some measures heritability increases with age as a result of amplification of genetic effects across ages (e.g. intelligence; Boomsma, 1993),whereas for other measures heritability estimates may decrease with age (e.g. problem behaviour; Van der Valk et al.,1998). Assuming that the same genes op-erate across the age span, adding siblings who are older than the twins will increase power when heritability in-crease with age, and will decrease power when heri-tability estimates decrease with age. Similarly, adding parents will increase power to detect genetic factors if heritability increases with age.

Schork (1993) noted the dramatic improvement in statistical power resulting from the use of larger sibships for the detection of QTL effects. In addition, Dolan,Boomsma and Neale (1999) demonstrated the value of adding non-twin siblings to two-sibling- (or DZ twin-)families for the detection of codominant QTL effects.Our aim was to determine whether the use of an ex-tended twin design, as needed for the detection of QTL-effects, would also be useful for the detection of overall

T a b l e I I I . T o t a l s a m p l e s i z e (i n s u b j e c t s ) n e e d e d t o d e t e c t a d d i t i v e g e n e t i c i n ?u e n c e s a n d d o m i n a n c e i n b i v a r i a t e A D E m o d e l s u n d e r u n d e r t h r e e d i f f e r e n t s i b s h i p s i z e s w i t h p o w e r (1 ?β) =.80 a n d α=.05

V a =40% r A =.80V a =40% r A =.50V a =40% r A =.30V d =20% r D =.80V d =20% r D =.50V d =20% r D =.30V e =40% r E =.05

V e =40% r E =.50V e =40% r E =.80

a l l V a +a l l V d

r A &r D a l l V d

r D a l l V a +a l l V d

r A &r D a l l V d

r D a l l V a +a l l V d

r A &r D a l l V d

r D (d f =6)(d f =2)(d f =3)(d f =1)(d f =6)(d f =2)(d f =3)(d f =1)(d f =6)(d f =2)(d f =3)(d f =1)d e s i g n 162648672100425418476622805432548470282356d e s i g n 26978446451216022839091407339681249041544d e s i g n 3

72

88

4076466060264363612872

40

7842272

38436

N o t e : s e e t a b l e 1 f o r d e f i n i t i o n s .

Table IV.Total sample size (in number of subjects) needed to de-tect additive genetic, dominance and common environmental in?u-ences in univariate ACE-models and ADE-models for designs with including MZ and DZ twins and siblings added to MZ families only, a power of (1 ?β) =.80, and signi?cance level α=.05

V a =40%Vc =40%V a =40%V a =40%Vc =10%

V a =10%

V d =20%

V d =20%

effect detected →V a V c V a +V d

V d design 4705338836313design 5

744285845313

Note : MZ/DZ ratio =1/1: design 4 =Mz twins and one additional sibling, DZ twins only, design 5 =MZ twins and two additional sib-lings and DZ twins onl.

sources of variance (i.e. A, C, and D). Our calculations showed that without the need to increase total sample size, adding one sibling to the classical twin design im-proves the statistical power by a large extent to detect sources of variation due to common environmental in-fluences, additive genetic influences and dominance.Adding siblings and using a bivariate phenotype results in gain of statistical power which can not only be as-cribed to bivariate testing but also to the use of an ex-tended twin design.

In conclusion, adding at least one sibling to the classical twin design, as opposed to a design with twins only, will provide a significant gain in statistical power to detects sources of variation due to A, C, and D. An attractive side-effect of a design with additional sib-lings is that it is also beneficial for the detection of QTL-effects.APPENDIX I

Consider a biallelic trait with alleles B and b. Let a be the effect of genotype BB on the phenotypic mean,?a the effect of bb, and d the effect of Bb on the phe-notypic mean. Assuming equal allele frequencies of B and b, the mean genotypic effect on the phenotypic mean is 1/2 d.The total genetic variance (σ2g) equals 1/2 a 2+1/4 d 2, =V a +V d

For complete dominance d =a. Substituting d for a in the formulae for the genetic variances, gives: V a =1/2 a 2and V d 1/4 a 2, thus V a =2 V d

156Posthuma and Boomsma

>

>

>

>>

>

a

-a

BB Bb

d

bb

A P P E N D I X I I

S a m p l e s i z e (i n s u b j e c t s ) n e e d e d t o d e t e c t a d d i t i v e g e n e t i c i n f l u e n c e s i n f u l l u n i v a r i a t e A C E m o d e l s u n d e r v a r y i n g l e v e l s o f v a r i a t i o n d u e t o c o m m o n e n v i r o n m e n t a l s o u r c e s f o r t h r e e d i f f e r e n t s i b s h i p s i z e s .M Z /D Z r a t i o =1/1, s i g n i f i c a n c e l e v e l α=.05, p o w e r (1 ?β) =.80, d e s i g n 1 =t w i n s o n l y , d e s i g n 2 =t w i n s a n d o n e a d d i t i o n a l s i b l i n g , d e s i g n 3 =t w i n s a n d t w o a d d i t i o n a l s i b l i n g s .I n o r d e r t o c a l c u l a t e t h e t o t a l n u m b e r o f f a m i l i e s n e e d e d , a l l c e l l s f r o m d e s i g n 1 n e e d t o b e d i v i d e d b y 2, a l l c e l l s f r o m d e s i g n 2 n e e d t o b e d i -v i d e d b y 3, a n d a l l c e l l s f r o m d e s i g n 3 n e e d t o b e d i v i d e d b y 4.

V a =10%

V a =20%V a =30%V a =40%V a =50%V a =60%V a =70%

V a =80%V a =90%V c →0%10%20%0%10%20%0%10%20%0%10%20%0%10%20%0%10%20%0%10%20%0%10%0%d e s i g n 12489623084201105908523043322406202615881192950700644482328360248150198124601045248d e s i g n 22204719557163655151439535402079170713201032813600567426294324228144186120631055751d e s i g n 3

2683623560194606256

52804208

2520

2048

15721252976716688512356396280176228148801327268

Now consider a bivariate model with latent vari-ances scaled to unity, (see figure 1) and

?uniform genetic influences over traits: V a 1=V a 2and V d 1=V d 2

?assumption of uniform d to a ratio over traits (a 11)2/(d 11)2=(a 21)2/(d 21)2=(a 22)2/(d 22)2

?rA =a 11* a 21/√{(a 11)2* [(a 21)2+[(a 22)2]} which simplifies to rA =a 21/a 11

?rD =d 11* d 21/√{(d 11)2* [(d 21)2+[(d 22)2]} which simplifies to rD =d 21/d 11

This implies that the additive genetic correlation equals the dominant genetic correlation.

Power and Sibship Size

157

A P P E N D I X I V

S a m p l e s i z e (i n s u b j e c t s ) n e e d e d t o d e t e c t c o m m o n e n v i r o n m e n t a l i n f l u e n c e s i n f u l l u n i v a r i a t e A C E m o d e l s u n d e r v a r y i n g l e v e l s o f v a r i a t i o n d u e t o a d d i t i v e g e n e t i c s o u r c e s i n t h e r e a l i s t i c s i t u a t i o n t h a t s o u r c e s o f v a r i a t i o n d u e t o A a r e l a r g e r t h a n s o u r c e s o f v a r i a t i o n d u e t o C f o r t h r e e d i f f e r e n t s i b s h i p s i z e s .S e e A p p e n d i x I I f o r d e f i n i t i o n s

V a =20%

V a =30%V a =40%

V a =50%

V a =60%

V a =70%

V a =80%

V c →10%20%10%20%10%20%10%20%10%20%10%20%10%d e s i g n 113940310412806278611558246610280215890421876791216286934d e s i g n 271431542647113775790122451511089459097841378943822d e s i g n 36912

144861481276540811204736988417288437488163496

A P P E N D I X I I I

S a m p l e s i z e (i n s u b j e c t s ) n e e d e d t o d e t e c t c o m m o n e n v i r o n m e n t a l i n f l u e n c e s i n f u l l u n i v a r i a t e A C E m o d e l s u n d e r v a r y i n g l e v e l s o f v a r i a t i o n d u e t o a d d i t i v e g e n e t i c s o u r c e s f o r t h r e e d i f f e r e n t s i b s h i p s i z e s .S e e A p p e n d i x I I f o r d e f i n i t i o n s

V c =10%

V c =20%

V c =30%V c =40%V c =50%V c =60%V c =70%V c =80%

V c =90%

V a →0%10%20%0%10%20%0%10%20%0%10%20%0%10%20%0%10%20%0%10%20%0%10%0%d e s i g n 115504148601393436463398310414681334119072264056039034029022218815612610484705436d e s i g n 28220774671401860170415427206515793453092731861621441059078605145362718d e s i g n 3822076286908

180816321448684608536320284248148148128968472564840322416

REFERENCES

Boomsma, D.I. Current status and future prospects in twin studies

of the development of cognitive abilities: Infancy to old age. In:Bouchard, Thomas J. Jr. (Ed), Propping, Peter (Ed), et al.(1993).Twins as a tool of behavioral genetics. Life sciences research report,53. (pp. 67–82). Chichester, England UK: John Wiley &Sons.

Boomsma, D.I. & Dolan, C.V. (1998). A comparison of power to

detect a QTL in sib-pair data using multivariate phenotypes,mean phenotypes, and factor scores. Behavior Genetics,28:329–340.

Cohen, J. (1992) A power primer. Psychological Bulletin,112:155–159.Dolan, C.V., Boomsma, D.I., & Neale, M.C. (1999). A note on the

power provided by sibships of size 2, 3, and 4 in genetic co-variance modeling of a codominant QTL. In press

Fulker, D.W., Cherny, S.S., Cardon, L.R. (1995). Multipoint in-terval mapping of Quantitative Trait Loci, using sib pairs. Am J Hum Genet,56(5):1224–1233

Fulker, D.W., Cherny, S.S., Sham, P.C., et al.(1999). Combined

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Hewitt, J.K., & Heath, A.C. (1988). A note on computing the chi-square noncentrality parameter for power analyses. Behavior Genetics,18:105–108.

Martin, N.G., Eaves, L.J., Kearsey, M.J., and Davies, P. (1978).

The power of the classical twin study. Heredity,40:97–116.Nance, W.E., & Neale, M.C. (1989). Partitioned twin analyses: a

power study. Behavior Genetics,19:143–150.

158Posthuma and Boomsma

Neale, M.C. (1997). Mx: Statistical modeling.3rd edition Box

980126 MCV, Richmond VA 23298.

Neale, M.C., & Cardon L.R.(1992) Methodology for Genetic Stud-ies of Twins and Families.NATO Asi Series. Series D,Behav-ioural and Social Sciences, Vol 67.

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(1991). Heterogeneity in the inheritance of alcoholism: A study of male and female twins. Archives of General Psychiatry,48:19–28.

Plomin, R., DeFries, J.C., & McClearn, G.E. (1990) Behavioral Ge-netics. A primer.New York: Freeman and company.

Schmitz, S. Cherny, S.S., & Fulker, D.W. (1998). Increase in power

through multivariate analyses. Behavior Genetics,28:357–364.Schork, N.J., (1993). Extended multipoint identity-by-descent analy-sis of human quantitative traits: efficiency, power, and model-ing considerations. American Journal of Human Genetics,53:1306–1319.

Svikis, D.S., Velez, M.L., Pickens, R.W. (1994). Genetic aspects

of alcohol use and alcoholism in women. Alcohol Health & Re-search World,18:192–196.

Tanaka, J.S. (1987). How big is big enough?: sample size and good-ness of fit in structural equation models with laten variables.Child Development,58:134–146.

van der Valk, J.C., Verhulst, F.C., Neale, M.C., Boomsma, D.I.

(1998). Longitudinal genetic analysis of problem behaviors in biologically related and unrelated adoptees. Behavior Genetics,28:365–380.

Edited by Norman D. Henderson

APPENDIX V

Samplesize (in subjects) needed to detect additive genetic and dominance influences in ADE-models.See Appendix II for definitions

V a =20%V a =30%V a =40%V a =50%V a =60%V d =10%V d =15%V d =20%V d =25%V d =30%V a & V d V d V a & V d

V d V a & V d

V d V a & V d

V d V a & V d

V d design 1148228087611036425958425958223518design 215611790845631483081483081271950design 3

148

11328

84

5236

48

2784

48

2784

28

1776

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简短辞职申请书范文大全 想必每一位在职场混迹多年的职场人士都应曾经写过辞职信之类的。在现在这个发展速度如此之快的社会,跳槽也就成了常见现象。而离职前的辞职信是必写的。下面就是小编给大家带来的简短辞职申请书范文大全,希望大家喜欢! 尊敬的xx: 我自xx年来到公司,工作中得到公司和您的培养,个人得到了很大的成长,公司的文化和环境也令我工作得非常开心。 现由于个人原因,我不得不提出辞职,希望能于x年x月x日正式离职,请公司批准我的这份辞职书。并请公司在x月x日前安排好人员接替我的工作,我将尽心交接。 再次对您x年来的培养和指导表示衷心的感谢。 最后祝您及公司的所有同事一切顺利! 此致 敬礼 辞职人:xxx 20xx年x月x日 尊敬的X经理: 您好! 感谢公司在我入职以来的培养关心和照顾,从X年X月份来到[公司]至今,我学到了很多东西,今后无论走向哪里,从事什么,这段经历都是一笔宝贵的财富,我为在彩卡的这段工作经历而自豪。 而今,由于个人原因提出辞职,望领导批准。 辞职人: 20xx年x月x日

公司人事部: 我因为要去美国留学,故需辞去现在的工作,请上级领导批准。 公司的企业文化感化了我,我对公司是深有感情的。我留学归来之后,仍愿意回公司就职。 感谢公司领导和同事在工作中对我的关心和支持,并祝公司兴隆。 辞职人:xxx 20xx年x月x日 尊敬的公司领导: 在递交这份辞呈时,我的心情十分沉重。现在由于我的一些个人原因的影响,无法为公司做出相应的贡献。因此请求允许离开。 当前公司正处于快速发展的阶段,同事都是斗志昂扬,壮志满怀,而我在这时候却因个人原因无法为公司分忧,实在是深感歉意。 我希望公司领导在百忙之中抽出时间受理我的离职事项。 感谢诸位在我在公司期间给予我的信任和支持,并祝所有同事和朋友们在工作和活动中取得更大的成绩。 辞职人: 20xx年x月x日 尊敬的xx: 自xx年入职以来,我一直很喜欢这份工作,但因某些个人原因,我要重新确定自己未来的方向,最终选择了开始新的工作。 希望公司能早日找到合适人手开接替我的工作并希望能于今年5月底前正式辞职。如能给予我支配更多的时间来找工作我将感激不尽,希望公司理解!在我提交这份辞呈时,在未离开岗位之前,我一定会尽自己的职责,做好应该做的事。 最后,衷心的说:“对不起”与“谢谢”! 祝愿公司开创更美好的未来!

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离职申请书怎么写范文5篇 工作当中几乎每个人都会有经历辞职,那么大家知道离职申请书怎么写吗?下面就是给大家带来的离职申请书怎么写范文5篇,希望大家喜欢! 辞职报告怎么写模板 辞职理由 辞职之前必须想好理由,不管是世界那么大,我想去看看。还是老子就是不想干了。 书面格式 标题:标题一般有辞职报告、辞职书、辞职函、辞职申请等不同的写法,书面一般多用辞职书 称谓:在工作中称呼一般都是“尊敬的XXX”格式,你想谁递交辞职书就写TA的尊称。 正文: ①空格2字符,问好。如:您好。

②辞职理由,短到几个字,长到几百字,个人自由发挥。例如:世界那么大,我想去看看。 ③尾段可以写写对公司的祝福等等。如:祝公司业绩蒸蒸日上。 结语:结尾要求写上表示敬意的话。如“此致——敬礼”等。 署名:写上自己的名字,辞职人:XXX 。署名的格式,为*末尾换行后起,然后署名下面加上日期. 日期:辞职报告写的当天日期,当然公司的规定不同,可以灵活的变动。 注意事项 不要说上司坏话。如果你认为有必要向管理层反映一下上司的问题,要尽量以委婉的言辞口头提出。 不要满纸抱怨,抨击公司制度。 不要指责同事,尤其忌讳把同事的“罪行”白纸黑字写在辞职书上。 离职申请书范文【一】 尊敬的罗总: 您好!

首先感谢您在我工作期间对我照顾与支持,感谢公司给我这个平台,让我锻炼让我成长。 很遗憾在这个时候向xx正式写出辞职报告,或许我还不是正式职工,不需要写这封辞职信。当您看到这封信时我大概也不在这里上班了。 来到这里也快两个月了,开始感觉这里的气氛就和一个大家庭一样,大家相处得融洽和睦。在这里有过欢笑,有过收获,当然也有过痛苦。虽然多少有些不快,不过在这里至少还是学了一些东西。在这一个多月的工作中,我确实学习到了不少东西。然而工作上的毫无成就感总让自己彷徨。我开始了思索,认真地思考。思考的结果连自己都感到惊讶——或许自己并不适合xx 这项工作。而且到这里来工作的目的也只是让自己这一段时间有些事可以做,可以赚一些钱,也没有想过要在这里发展。因为当初连应聘我都不知道,还是一个朋友给我投的资料,也就稀里糊涂地来到了这里。一些日子下来,我发现现在处境和自己的目的并不相同。而且我一直以为没有价值的事情还不如不做,现在看来,这份工作可以归为这一类了。n多的时间白白浪费掉了。我想,应该换一份工作去尝试了。 离开这里,离开这些曾经同甘共苦的同事,确实很舍不得,舍不得同事之间的那片真诚和友善。但是我还是要决定离开了,我恳请xx和领导们原谅我的离开。

申请离职书范文6篇

申请离职书范文6篇 Sample application for resignation 编订:JinTai College

申请离职书范文6篇 小泰温馨提示:辞职报告是个人离开原来的工作岗位时向单位领导或上级组织提请批准的一种申请书,是解除劳动合同关系的实用文体。本文档根据辞职报告内容要求展开说明,具有实践指导意义,便于学习和使用,本文下载后内容可随意修改调整及打印。 本文简要目录如下:【下载该文档后使用Word打开,按住键盘Ctrl键且鼠标单击目录内容即可跳转到对应篇章】 1、篇章1:申请离职书范文 2、篇章2:申请离职书范文 3、篇章3:申请离职书范文 4、篇章4:酒店离职申请范文 5、篇章5:酒店离职申请范文 6、篇章6:酒店离职申请范文 为离职写一份离职申请书,本文是小泰为大家整理的申请离职书范文,仅供参考。 篇章1:申请离职书范文

您好!首先感谢您在百忙之中抽出时间阅读我的离职信。 我是怀着十分复杂的心情写这封离职信的。自我进入公司之后,由于您对我的关心、指导和信任,使我获得了很多机遇和挑战。经过这段时间在公司的工作,我在酒店领域学到了很多知识,尤其是办公室合规的相关方面,积累了一定的经验,对此我深表感激。 由于自身存在很多尚不完善的地方,想通过继续学习来 进一步加强自己的能力。为了不因为我个人原因而影响公司的工作,决定辞去目前的工作。我知道这个过程会给公司带来一定程度上的不便,对此我深表歉意。 我会尽快完成工作交接,以减少因我的离职而给公司带 来的不便。为了尽量减少对现有工作造成的影响,我请求在公司的员工通讯录上保留我的手机号码一段时间,在此期间,如果有同事对我以前的工作有任何疑问,我将及时做出答复。 非常感谢您在这段时间里对我的教导和照顾。在平安的 这段经历于我而言非常珍贵。将来无论什么时候,我都会为自己曾经是平安公司的一员感到荣幸。我确信这段工作经历将是我整个职业生涯发展中相当重要的一部分。

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岗位辞职申请书(精选6篇) 岗位辞职申请书 在当今不断发展的世界,我们都会用到申请书,我们在写申请书的时候要注意语言简洁、准确。写起申请书来就毫无头绪?下面是帮大家整理的岗位辞职申请书,供大家参考借鉴,希望可以帮助到有需要的朋友。 岗位辞职申请书1尊敬的企业领导: 您好! 鉴于我个人能力及不能胜任工作岗位要求等多方面原因的考虑,很遗憾自己在这个时候向企业提出辞职。 我也很清楚这时候向企业辞职于企业于自己都是一个考验,企业正值用人之际,企业业务的开展,所有的前续工作在企业上下极力重视下一步步推进。也正是考虑到企业今后推进的合理性,本着对企业负责的态度,为了不让企业因我而造成的决策失误,我郑重向企业提出辞职,望企业领导给予批准。 希望领导能早日找到合适的人手接替我的工作,我会尽力配合做好交接工作,保证企业的正常运作,对企业,对领导尽好最后的责任。要离开企业的这一刻,我衷心向您说声谢谢!也感谢全体同事对我无微不至的关怀,对此我表示诚挚的谢意,也同时对我的离去给企业带来的不便表示深深地歉意。希望领导能早日找到合适的人手接替我的工作,我会尽力配合做好交接工作,保证企业的正常运作,对企业,

对领导尽好最后的责任。要离开企业的这一刻,我衷心向您说声谢谢!也感谢全体同事对我无微不至的关怀,对此我表示诚挚的谢意,也同时对我的离去给企业带来的不便表示深深地歉意。在离开之前我仍将按往常一样尽力将自己的工作做好。 祝企业领导及同事们前程似锦,鹏程万里! 此致 敬礼! 申请人: 申请日期: 岗位辞职申请书2尊敬的领导: 您好! 怀着复杂的心情,我提出辞职的请求。屈指算来,我到公司已有两年多时间了。在这段时间里,虽然我的工作并不能尽善尽美,但在公司同事们的指导下,我尽量严格要求自己尽心尽职.按时按量完成了公司分配的销售任务。 鉴于两年多来我在公司的发展与期望有些距离,加之近来的工作中我常常觉得力不从心,故遗憾的提出辞职。 非常感谢在这段时间里公司对我的培育和关怀,在公司的这段经历对我而言弥足珍贵。将来无论什么时候,我都会为自己曾经是公司的一员而感到荣幸,在公司的这段工作经历也将是我整个职业生涯中相当重要的一部分。 祝公司领导和所有同事身体健康、工作顺利!

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辞职申请书理由精选十篇 想换份工作,每个人辞职总有一个理由,一个员工要辞职,领导 总会要求提交一个离职的原因。以下是为大家的辞职申请书理由范文,欢迎大家阅读参考。 辞职申请书理由范文一 尊敬的各位领导: 你们好! 首先无可非议的要郑重感谢贵公司给予我近两年的工作机会。 由于个人职业规划和一些现实因素,经过慎重考虑之后,特此 提出离职申请,敬请批准。 来到本公司也快两年了,正是这里我开始踏上了社会,完成了 自己从一个学生到社会人的转变,有过欢笑收获,也有过辛酸和痛苦,公司平等的人际关系和开明的工作作风,让我感觉找到了一种依靠的感觉,工作了一年多,给我自己的感觉就是没有什么起色,由此我对于我最近在工作上的一些态度心理进行回想,最后我连自己想干什么,爱好做什么也不是很清楚,一连串的问号让我沮丧,也让我萌发了辞职的念头,并且让我确实了这个念头,或许有从新再跑到社会遭遇挫折,在不断打拼中去找属于自己职业定位才是我人生的下一步选择。 在这一年多的时间里,我有幸得到了各位领导及同事们的倾心 指导及热情的帮助,尤其感谢工段长对我的信任,支持和帮助,感谢所有给予帮助过我的同事们,忠心的祝愿贵公司蒸蒸日上,各位领导同事,工作愉快,身体健康。

此致 敬礼 申请人: XXXX年XX月XX日 辞职申请书理由范文二 尊敬的领导您好: 我进xx已经有几个月了,由于我个人的原因。经过深思熟虑地考虑,我决定辞去我目前在公司所担任的职位。 我非常重视在xx公司内这段经历,也很荣幸成为xx的一员,特别是xx的处事风范及素质使我倍感钦佩。在xx这几个月所学到的知识也是我一生宝贵的财富。也祝所有xx成员在工作和活动中取得更大的成绩及收益! 望领导批准我的辞职申请,并请协助办理相关离职手续(本人在2xx年x月x日离职)。在正式离开之前我将认真继续做好目前的每一项工作。 愿祝xx生意兴隆! 敬请领导同意并批复! 此致 敬礼 申请人: XXXX年XX月XX日 辞职申请书理由范文三

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简短离职申请书范文4篇 简短离职申请书范文4篇 简短离职申请书范文篇一: 尊敬的公司各位领导: 您好。 经过深刻冷静的思考后,我郑重的向公司提出离职申请。来到公司这段时间,我学到了很多知识、积累了宝贵的经验,对此我深怀感激。由于诸多原因,不得不向公司提出离职申请,由此给公司带来的不便我深表歉意。虽有很多不舍,但还是做出以上决定,希望公司领导能对我的申请予以考虑并批准。 感谢领导一直以来对我的照顾和栽培,以及各位同事的支持与帮助,我在这半年多的时间中工作很充实、愉快。在此对部门领导和同事表示感谢。 我希望可以在此辞呈递交一周后离开公司。望领导批准。祝愿公司在今后的发展中蒸蒸日上,并祝愿各位领导及同事工作愉快! 此致 敬礼! 离职人: 201X年X月X日 简短离职申请书范文 篇二: 尊敬的领导们:

天要下雨,娘要嫁人,生亦何苦,死亦何欢,生死由命,富贵由天。本来我想在~~~~~公司工作终老,但是现实是残酷的,世界是疯狂的!巨大的生活压力迫使我抬不起头来。遥望那碧蓝的天空!这时,我多么羡慕那自由飞翔的小鸟,还有那些坐得起飞机的人啊!!!每个月的中旬,我会满怀欢喜的拿着微薄的工资去还上个月的欠债! 今辞去一职,只因生活所迫,正所谓人往高处走,水往低处流;人生短短几十年光阴眨眼就过,何不出去外面世界一闯呢!望各领导们成全。 此致 敬礼! 离职人: 201X年X月X日 简短离职申请书范文 篇三: 尊敬的公司领导: 首先感谢公司近段时间来对我的信任和关照,给予了我一个发展的平台,使我有了长足的进步。如今由于个人原因,无法继续为公司服务,现我正式向公司提出离职申请,将于xx年XX月XX日离职,请公司做好相应安排,在此期间我一定站好最后一班岗,做好交接工作。对此为公司带来的不便,我深感歉意。 望公司批准!谢谢! 祝公司业绩蒸蒸日上,大展宏图! 此致 敬礼!

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领导辞职申请书范文大全 领导辞职申请书范文一 尊敬的学校领导: 你们好! 首先感谢领导对我在二小8年来的工作肯定和信任,以及对我那份切切栽培的厚爱!自从事我校的教科室副主任工作以来,我勤勤恳恳,认真工作。 回顾这一年来的教科室工作,尽管我倾尽努力,但深感力不从心,这无形中使我倍感压力。经过深思熟虑,在此,我郑重向领导提出书面申请书——辞去教科室副主任职务。 一、个人业务能力不足 我理解领导恨铁不成钢的心情,也肯请领导理解我此刻内疚的心情。这一年来,我深感自己业务水平不足,没有使我校的教科室的工作,在原有的基础上进步,甚至比之前有

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辞职申请书范文大全4篇 前言:申请书是个人或集体向组织、机关、企事业单位或社会团体表述愿望、提出请求时使用的一种文书。申请书的使用范围广泛,也是一种专用书信,表情达意的工具。本文档根据申请书容要求和特点展开说明,具有实践指导意义,便于学习和使用,本文下载后内容可随意调整修改及打印。 本文简要目录如下:【下载该文档后使用Word打开,按住键盘Ctrl键且鼠标单击目录内容即可跳转到对应篇章】 1、篇章1:辞职申请书范文 2、篇章2:辞职申请书范文 3、篇章3:辞职申请书范文 4、篇章4:辞职申请书范文 辞职申请书格式 辞职申请通常有五部分构成。 (一)标题

在申请书第一行正中写上申请书的名称。一般辞职申请书由事由和文种名共同构成,即以“辞职申请书”为标题。标题要醒目,字体稍大。 (二)称呼 要求在标题下一行顶格处写出接受辞职申请的单位组织或领导人的名称或姓名称呼,并在称呼后加冒号。 (三)正文 正文是申请书的主要部分,正文内容一般包括三部分。 首先要提出申请辞职的内容,开门见山让人一看便知。 其次申述提出申请的具体理由。该项内容要求将自己有关辞职的详细情况一一列举出来,但要注意内容的单一性和完整性,条分缕析使人一看便知。 最后要提出自己提出辞职申请的决心和个人的具体要求,希望领导解决的问题等。 (四)结尾 结尾要求写上表示敬意的话。如“此致——敬礼”等。 (五)落款

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业的不如高中毕业的。因此,我觉得我不适合在四中工作,再这样下去的话,肯定会影响学校的升学率。在现在如此看中升学率的环境下,请考虑批准我的辞职报告。第二:就是学校的管理。开始的时候觉得还能跟上学校改革的步伐,但越到后面,越觉得难以适应。比如学校规定没有课也要坐班,我也赞同的,也坐班的。但我的课经常是早上 4、5 节,而学校只能 10:00 到 10:30 去吃早点,那样只能来不及,但不吃的话我身体又吃不消,更怕影响教学质量。因此经常 9:30 去吃,从而违反了学校的规定,要算我脱岗。我想,我是不适应学校的管理了,因此选择离开。第三:就是工资,每个月打到卡上的 1024 元,让我很难想象什么时候能在弥勒买得起按揭的住房,倍感压力重大。四中是强调不为薪水而工作的,而我,还做不到这点。因为我家里还有父母,以后还会成家,会有孩子,都需要薪水。第四:也许是能力有限,我认为我在四中已经没有更大的发展机会了,已经工作了 5 年多,基本上定型了。因此,我决定选择一个新的工作环境,希望领导批准,敬请早些安排。当然,无论我在哪里,我都会为四中做力所能及的事情,因为我为我曾经是四中人而感到骄傲。最后,诚恳地说声:对不起!也衷 心地祝愿四中力挫群芳,永往直前!学校越办越好,升学率一年比一年高!四中所有的学生都考上重点大学!

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此致 敬礼! XXX XXXX年XX月XX日 尊敬的XX经理: 您好!首先感激您在百忙之中抽出时刻开阅读我的辞职信。 我是怀着非常复杂的心境写这封的。自从我进到了餐厅之后,由于你对我的指点和信任,使我取得了许多机遇和应战。经历这段时刻在餐厅的任务,我从中学到了许多知识,积聚了一定的经历,对此我深表感谢。由于我本身任务才能不够,近期的任务让我觉得力所能及,为此我作了很长时刻的思考,我确定递上辞呈。 为了不由于我本人才能不够的缘由影响了餐厅的正常运作,更迫切的缘由是我必需在xx年1月后参与计算机等级证的培训,较长时刻内都不能下班,因此经历沉思熟虑之后,我确定在xx年1月前

2019-离职申请书-范文word版 (4页)

本文部分内容来自网络整理,本司不为其真实性负责,如有异议或侵权请及时联系,本司将立即删除! == 本文为word格式,下载后可方便编辑和修改! == 离职申请书 精选范文:离职申请书(共2篇) 尊敬的公司领导: 您好! 我很遗憾自己在这个时候向公司正式提出辞职。 我因经济危机的影响以及家庭原因,无法在继续工作下去,只能提前回国,希望公司能谅解我们的处境。经过慎重考虑之后,特此提出申请:我自愿申请辞去在公司的一切职务,敬请批准。 来到公司大约二年了,公司里的每个人对我都很好。我衷心感谢各位领导以及各位同事对我的照顾与错爱,在这近二年里,我学到了很多以前从未接触过的知识,开阔了视野,锻炼了能力。工作上,我学到了许多宝贵实践技能。生活上,得到各级领导与同事们的关照与帮助;思想上,得到领导与同事们的指导与帮助,有了更成熟与深刻的人生观。这近二年多的工作经验将是我今后学习工作中一笔宝贵的财富。感谢所有给予过我帮助的同事们。 望领导批准我的申请,并请协助办理相关离职手续,在正式离开之前我将认真继续做好目前的每一项工作。 离开这个公司,我满含着愧疚、遗憾。我愧对公司上下对我的期望,愧对各位对我的关心和爱护。遗憾我不能经历公司的发展与以后的辉煌,不能分享你们的甘苦,不能聆听各位的教诲,也遗憾我什么都没能留下来。结束我来新加坡的第一份工作。 最后,衷心祝愿公司健康成长,事业蒸蒸日上!祝愿各位领导与同事:健康快乐,平安幸福! 辞职人: 201X年04月10日 [ 离职申请书(共2篇) ] 篇一:离职申请书范文

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