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10 Undertaking meta- analysis

https://t.me/medicina_free

Study

Dewey 2006 Kefer 2005 Langer 2009 Maintz 2007 Pouleur 2008

MRI

Study

Dewey 2006 Kefer 2005 Langer 2009 Maintz 2007 Pouleur 2008

0.94 [0.85, 0.98]

0.94 [0.80, 0.99]

0.96 [0.80, 1.00]

0.94 [0.70, 1.00]

0.94 [0.71, 1.00]

Sensitivity (95% CI)

0.86 [0.73, 0.94]

0.88 [0.73, 0.97]

0.69 [0.48, 0.86]

0.94 [0.70, 1.00]

1.00 [0.80, 1.00]

Sensitivity (95% Cl)

Specificity (95% CI)

0.90 [0.79, 0.97]

0.67 [0.41, 0.87]

0.95 [0.84, 0.99]

0.50 [0.07, 0.93]

0.88 [0.77, 0.95]

Specificity (95% CI)

0.95 [0.83, 0.99]

0.50 [0.26, 0.74]

0.64 [0.48, 0.78]

0.75 [0.19, 0.99]

0.72 [0.59, 0.83]

Sensitivity (95% CI) Specificity (95% Cl)

00.2 0.40.6 0.8100.2 0.40.6 0.

Sensitivity (95% CI) Specificity (95% Cl)

00.2 0.40.6 0.8100.2 0.40.6 0.

Figure10.6.b Forest plot of comparative studies of CT versus MRI for coronary artery disease.

Source: Data taken from Schuetz 2010

Box 10.6.a Large gradient values in SAS for bivariate model parameters for CT and MRI comparative studies (model without test type covariate)

Parameter Estimates

Standard

Parameter

msens

mspec

s2usens

s2uspec

covsesp

Estimate

2.0000

1.0000

–111E-14

2.21E-11

–108E-15

Error DF t Value Pr > |t| 95% Confidence Limits Gradient

0.4686

0.2041

0.4240

0.01977

0.0236

4.27

0.0163

4.90

1.0000

–0.00

1.0000

0.00

0.5086

0.3504

–1.3493

–0.06291

3.4914

1.6496

1.3493

0.06291

–6.88008

–25.4401

–0.31355

–188.328

–44.9080

To assess the effect of test type on sensitivity and specificity, models with and without the covariate were fitted. The output of fitting a bivariate model without the test type covariate to the data using Proc NLMIXED in SAS showed that the convergence criterion was satisfied. However, all the parameter estimates have large gradient values, indicating poor estimation (Box10.6.a). A model may satisfy a convergence criterion but may be unstable (e.g. changing the starting values results in a change in parameter estimates), or have missing standard errors for one or more parameter estimates. Therefore, in addition to meeting a convergence criterion, meta- analysts should check for missing standard errors and if the program output permits, also check that gradient values for all model parameters are very close to zero before concluding that the analysis has successfully converged.

Several attempts were made to improve estimation of the parameters by specifying different options for fitting the model (see code in Appendix 9 of the online supplementary material (10.S1 Code for undertaking meta- analysis)). The options included

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Box 10.6.b Improved estimation in SAS of bivariate model parameters for CT and MRI comparative studies by changing model fitting options

Parameter Estimates

Standard

Parameter

msens

mspec

s2usens

s2uspec

covsesp

Estimate

2.2554

1.3083

0.006812

0.4138

–0.03331

Error DF t Value Pr > |t| 95% Confidence Limits Gradient

0.3569

0.3375

0.5582

0.3633

0.1724

0.0080

6.32

0.0304

3.88

0.9910

0.01

0.3374

1.14

0.8592

–0.19

1.1194

0.2342

–1.7695

–0.7424

–0.5821

3.3913

2.3823

1.7831

1.5701

0.5155

0.000057

0.000543

1.70698

–0.02091

–0.21665

increasing the number of quadrature points; changing the optimization technique from the default quasi- Newton technique to the Newton- Raphson technique; trying different starting values, e.g. using a grid search; and setting boundary constraints for the variance parameters (i.e. variance ≥ 0). Imposing boundary constraints can reduce the risk of convergence problems. If boundary constraints are triggered for variance parameters, then estimation of these parameters is truncated at zero. The same options explored here for fitting the bivariate model can be applied when fitting the HSROC model in SAS. For the CT versus MRI example, trying each of the options separately failed to improve estimation of the bivariate model parameters and there were error and/or warning messages. Finally, setting boundary constraints for the variance parameters and using a different set of starting values resulted in more reliable parameter estimates (Box10.6.b).

The gradient for the variance of the random effects for logit(sensitivity) is large (1.70698), and there is concern about the analysis. Since the estimate of the variance of logit(sensitivity) is close to zero (s2usens = 0.006812) and given the previous observation about limited heterogeneity in the sensitivity estimates for CT, simplifying the model by removing either a variance or covariance parameter may be a reasonable strategy. Such an analysis will be explored in Section10.6.2.

When the bivariate model was fitted to this data set in Stata using meqrlogit (see Appendix 11 of the online supplementary material (10.S1 Code for undertaking metaanalysis)), the results were similar to those obtained using SAS and all the gradient values were close to zero (Box10.6.c). In Stata, the default optimization technique for meqrlogit and xtmelogit is a Newton- Raphson technique. Starting values are determined by the commands and are not specified by the user.

As stated in Section10.2.3, it is not possible to increase the number of quadrature points used by glmer to fit a bivariate model in R. Different optimization options can be explored simultaneously using the allFit function (see code in Appendix 14 of the online supplementary material (10.S1 Code for undertaking meta- analysis)). The options are (1) bound optimization by quadratic approximation (BOBYQA); (2) an algorithm derived from BOBYQA named NLOPT_LN_BOBYQA in Box10.6.d; (3) limited memory Broyden– Fletcher–Goldfarb–Shanno bound- constrained (L- BFGS- B) optimization; (4) Nelder- Mead

299

10 Undertaking meta- analysis

.2104002

2.335581

nterval]

1.972165

]

=20

-53.173887

1.528322

338.5475

study_id:

nterval]

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Box 10.6.c Estimation in Stata of bivariate model parameters for CT and MRI comparative studies (model without test type covariate)

Iteration 3:

loglikelihood=

Gradientvector (length= .000245):

eq1:eq1:lns1_1_1: lns1_1_2: atr1_1_1_2:

sens spec _cons_cons _cons

r1 .0000374 .0000781 .0000129 .0002278 -.0000219

Mixed-effectslogistic regressionNumberofobs Binomialvariable:n Group variable: study_id Number of groups

Obs per group:

min= avg= 4. max=

Integration points= 5Waldchi2(2) Log likelihood =-53.173887Prob>chi2

true Coef.Std.Err.zP>|z|[95%Conf. Interval

sens 2.249856.204119 11.020.000 1.849792.64992 spec 1.308397.33866343.860.000 .6446286

Random-effectsParameters Estimate Std. Err. [95% Conf.I

study_id: Unstructured

var(sens) .001594.01471322.22e-11114638. var(spec) .4178528 .366883.074757

cov(sens,spec) -.0258082.1205167-.2620166

Using option stddev to output standard deviations and correlation instead of the variances and covariance above gives the following output.

Random-effectsParameters Estimate Std. Err. [95% Conf.I

Unstructured

sd(sens) .0399259 .1842611 4.71e-06 sd(spec) .6464237 .2837953 .2734133

corr(sens,spec) -1 .0011101 -1

45.1 .000

300

10.6 Meta- analysis ofsparse data anda typical data sets

~ , with .

## nloptwrap.NLOPT_LN_BOBYQA

0.03977226

0.6429241

–0.9999665

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Box 10.6.d Estimation in R of bivariate model parameters for CT and MRI comparative studies (model without test type covariate)

ss$fixef

## bobyqa

## Nelder_Mead

## nlminbwrap

## nmkbw

## optimx.L-BFGS-B

## nloptwrap.NLOPT_LN_NELDERMEAD

## nloptwrap.NLOPT_LN_BOBYQA

ss$sdcor ## table of random effect SDs and correlations

## bobyqa

## Nelder_Mead

## nlminbwrap

## nmkbw

## optimx.L-BFGS-B

## nloptwrap.NLOPT_LN_NELDERMEAD

## table of fixed effects

sens

2.249866

2.249865

2.249866

2.249880

2.249866

2.249860

2.249818

Study_ID.sens

1.308946

1.309040

1.308946

1.308935

1.308969

0.03989542

0.03989567

0.03989607

0.03977192

0.03989560

0.03990032

spec

Study_ID.spec.sens

0.6429813

0.6429822

0.6429808

0.6429379

0.6429822

0.6429883

Study_ID.spec

–1.0000000

–0.9999521

–1.0000000

–0.9999998

method; (5) Nelder- Mead simplex algorithm (NLOPT_LN_NELDERMEAD in Box10.6.d); (6) nonlinear minimization with box constraints (nlminb); and (7) Nelder- Mead algorithm for derivative- free optimization (nmkb). In this example, the seven optimization options in the red box produced similar results (Box10.6.d). The help files of the functions and commands in different software packages are a useful source of information on the quadrature and optimization options available for model estimation.

10.6.2 Simplifying hierarchical models

Hierarchical models can be simplified by removing parameters from the regression equation and editing the covariance structure. Prior to simplifying the models, plot the data on forest and SROC plots to assess heterogeneity visually and to gain a better understanding of the data (e.g. all or most studies report 100% sensitivity and/or specificity with no indication of a threshold effect). If the bivariate model described in Chapter9, Section9.4.1, is simplified by assuming that the covariance or correlation is zero (i.e. an independent variance–covariance structure), the model reduces to two univariate random- effects logistic regression models for sensitivity and specificity as follows:

Ai A A

Bi B

(10.7)

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10 Undertaking meta- analysis

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Study

Zar 2019 Nicol 2018 Sabi 2018

108

206

51 97

105

Sensitivity (95% Cl)

0.22 [0.16, 0.30]

0.24 [0.19, 0.29]

0.25 [0.16, 0.35]

Specificity (95% Cl)

1. 00 [0.93, 1. 00]

1. 00 [0.96, 1. 00]

0.98 [0.93, 1. 00]

Sensitivity (95% CI) Specificity (95% Cl)

00.2 0.40.6 0.8100.2 0.40.6 0.

Figure10.6.c Forest plot of Xpert Ultra against a composite reference standard. Studies on the

plot are sorted by sensitivity and then by specificity. Source: Adapted from Kay 2020

If there is little or no observed variation in sensitivity and/or specificity, these univariate models can be further simplified by dropping one or both variance parameters. Without the variance parameters, the models reduce to fixed- effect logistic regression models. For example, a Cochrane Review included three studies that assessed Xpert Ultra against a composite reference standard using sputum specimens from children (Kay 2020). The estimates of sensitivity and specificity were similar in the three studies (Figure10.6.c). Given the small number of studies and lack of heterogeneity, a fixed-

effect meta- analysis was considered appropriate. In Stata the meqrlogit or xtmelogit command cannot be used for fitting fixed- effect logistic regression models; instead use the blogit command (see code in Appendix 15 of the online supplementary material (10.S1 Code for undertaking meta- analysis)).

For the IOC example introduced in Section10.6, when the covariance matrix for the random effects for logit(sensitivity) and logit(specificity) was unstructured (model A)– i.e. no constraints imposed so that the variances and covariance were uniquely estimated– the variances were poorly estimated, especially the variance parameter for the logit(sensitivity) of IOC. It is unsurprising that the variances were poorly estimated given the small number of studies and sparse data. Alternative models were investigated, as shown in Table10.6.a. In model B, the exchangeable covariance structure estimated a common variance and a covariance for the random effects of the logit(sensitivity) and logit(specificity). The independent covariance structure used in model C estimated distinct variances for the random effects, but the covariance was assumed to be zero (i.e. two separate univariate random- effects logistic regression models). In model D the variance parameter for logit(sensitivity) was dropped and so there was no covariance. Stata code for the four models is in Appendix 16 of the online supplementary material (10.S1 Code for undertaking meta- analysis).

To check the robustness of the assumptions about the variances of the random effects, the estimates of sensitivity and specificity were also compared between models (Table10.6.a). The analytical approach adopted was based on the reasoning that it is inappropriate to overfit models by estimating too many parameters from few studies, and to simplify models when parameter estimates cannot be reliably estimated. The validity of this approach has been investigated in a simulation study that concluded that simpler hierarchical models are valid in situations with few studies or sparse data (Takwoingi 2017). For estimating summary sensitivity and specificity, simplifying the bivariate model to univariate random- effects logistic regression models is appropriate. For estimating a summary curve, an HSROC model without the shape parameter (i.e. a symmetrical curve) can be used. If there is very little or no observed heterogeneity, fixed- effect equivalents of the models can be applied.

The output of the bivariate model fitted to the CT and MRI comparative studies in Stata (Box10.6.c) and R (Box10.6.d) show that the correlation of the logits was

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10.6 Meta- analysis ofsparse data anda typical data sets

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Table10.6.a Parameter andsummary estimates forIOC frommodels withdierent variance–covariance

structure

Parameter Models

A: Unstructured variance–covariance structure

Mean logit sensitivity (SE)

Mean logit specificity (SE)

Variance of random effects for logit sensitivity (SE)

Variance of random effects for logit specificity (SE)

Correlation of the logits (SE)

Sensitivity (95% CI) 99.9 (14.1, to 100) 98.8 (83.1 to 99.9) 99.8 (42.3 to 100) 94.4 (88.7 to 97.3)

Specificity (95% CI) 98.5 (95.8 to 99.4) 99.2 (94.5 to 99.9) 98.5 (95.6 to 99.5) 98.5 (95.6 to 99.5)

7.06 (4.53) 4.43 (1.45) 6.12 (3.2) 2.82 (0.39)

4.15 (0.52) 4.80 (1.00) 4.19 (0.57) 4.19 (0.57)

16.7 (26.9) 2.85 (2.71) 9.74 (12.7) 0

0.25 (0.54) 2.85 (2.71) 0.34 (0.67) 0.34 (0.67)

–0.73 (0.98) 0.03 (0.76) 0 0

B: Exchangeable variance–covariance structure

C: Independent variance–covariance structure

D: Fixed effects for sensitivity of IOC

estimated on the boundary of the parameter space as –1 (see Section10.6.1). Therefore, simplifying the model to two univariate random- effects logistic regression models for sensitivity and specificity, by removing the correlation or covariance parameter, seems a reasonable first step (see SAS code in Appendix 9 of the online supplementary material (10.S1 Code for undertaking meta- analysis)). The output of fitting this model in SAS shows that the boundary constraint for the variance of logit(sensitivity) was triggered (see Active BC column in (i) in Box10.6.e). Thus the next step is to simplify further by also removing this variance parameter, i.e. assume a fixed effect for sensitivity. Covariate terms can now be added to this model to compare the sensitivity and specificity of CT and MRI (see SAS code in Appendix 9 of the online supplementary material (10.S1 Code for undertaking meta-

analysis)). The difficulty encountered in the analysis of CT and MRI when using Proc NLMIXED in SAS was not experienced when using Stata (see code in Appendix 11 of the online supplementary material (10.S1 Code for undertaking meta- analysis)) and R (Appendix 14 of the online supplementary material (10.S1 Code for undertaking meta- analysis)). It is possible for the analysis of sparse data to be problematic in one program and not as problematic in another program due to differences in the implementation of the programs.

Univariate models can also be used for investigating heterogeneity or for test comparisons when the rationale for simplifying hierarchical models is not due to the number of studies or convergence issues. A univariate random- effects logistic meta- regression model that allowed for a separate variance term for the random effects of logit(sensitivity) for each test was used in the main meta- analysis comparing the accuracy of nine firsttrimester serum test strategies for Down syndrome screening (Alldred 2015). The analysis

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10 Undertaking meta- analysis

~ ,.

(i) Model without covariance parameter

(ii) Model without

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Box 10.6.e Simplifying the bivariate model to univariate random- effects logistic regression models for CT and MRI comparative studies (model without covariate)

Parameter

msens

mspec

s2usens

s2uspec

Estimate

2.2385

1.3122

0.4111

covariance parameter and variance parameter for logit (sensitivity)

Fit Statistics

-2 Log Likelihood

AIC (smaller is better)

AICC (smaller is better)

BIC (smaller is better)

Parameter Estimates

Standard

Error DF t Value Pr > |t|95% Confidence Limits Gradient Active BC

0.0014

11.46

0.1953

0.3363

0.3602

0.0299

3.90

1.14

0.3366

106.4

114.4

117.1

112.9

0.000407

1.6168

0.2418

–0.7353

2.8602

–0.00025

2.3825

1.81131

1.5575

–8.11E-6

Lower BC

included all studies that used a 5% FPR threshold. Equation10.8 expressed only for logit(sensitivity) was thus extended as follows:

where μ kth test; μA estimates the mean logit(sensitivity) for the index test used as the referent test (note not the reference standard); μA+vAZk estimates the mean logit(sensitivity) for the kth test; and

Fit Statistics

-2 Log Likelihood

AIC (smaller is better)

AICC (smaller is better)

BIC (smaller is better)

Parameter Estimates

2.2385

1.3122

0.4111

Standard

Error DF t Value Pr > |t|95% Confidence Limits Gradient

0.0003

11.46

0.1953

0.3363

0.3602

0.0175

3.90

0.3174

1.14

N vZ

Aik A A k Ak

Parameter

msens

mspec

s2uspec

Estimate

is the logit(sensitivity) for the kth test within the ith study; Zk represents the

Aik

106.4

112.4

113.9

111.3

0.000012

1.6961

0.3784

–0.5890

2.7809

2.2460

1.4112

–0.00012

–0.00004

(10.8)

is the variance of logit(sensitivity) for the kth test. The Stata

304

10.7 Meta- analysis withmultiple thresholds per study

Sensitivity (95% CI)

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2 (160/1144)

Figure10.6.d Sensitivity at a 5% false positive rate for nine first- trimester serum test strategies

for Down syndrome screening. Sensitivity is presented as percentages. Each circle represents the summary sensitivity for a test strategy and the size of each circle is proportional to the number of Down syndrome cases. The estimates are shown with 95% confidence intervals. The test strategies are ordered on the plot according to decreasing detection rate. The number of studies, cases and women included for each test strategy are shown on the horizontal axis. A = Age, PlGF, PAPPfree ßhCG; B = Age, PAPP- A, free ßhCG and AFP; C = Age, ADAM 12, PAPP- A and freeßhCG; D = Age, PAPP- A and free ßhCG; E = Age, PAPP- A; F = PAPP- A; G = Age, free ßhCG and AFP; H = Age, free ßhCG; I = Free ßhCG. Source: Adapted from Alldred 2015

2 (116 /2705)

2 (74/1222)

(1037/49827)

5 (359/3491)

4 (325/2837)

3 (157/2992)

7 (460/5893)

A and

4 (390/4280)

code and output of the parameter estimates are in Appendix 17 of the online supplementary material (10.S1 Code for undertaking metathe summary estimates of sensitivity obtained, including their 95% confidence intervals, at the 5% FPR. The test combinations were ordered on the plot according to decreasing sensitivity. The plot shows that the single- test strategies with and without maternal age (PAPP- A alone, free βhCG alone, PAPP- A and maternal age, and free βhCG and maternal age) have the worst performance, whereas thetriple- test strategies (ADAM 12, PAPP- A, free βhCG and maternal age; PAPP- A, free βhCG, AFP and maternal age) have the highest performance.

10.7 Meta- analysis withmultiple thresholds per study

As noted in Chapter9, Section9.4.5, some studies may report sensitivity and specificity at more than one threshold, because the results of the index test are ordinal categories or continuous measurements (see Chapter4). The development of methods that

analysis). Figure 10.6.d shows

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10 Undertaking meta- analysis

i i it it



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allow for the inclusion of multiple thresholds from each included study is an active area ofresearch (Zapf 2021). This section describes and demonstrates implementation of the Steinhauser (2016) and Jones(2019) approaches introduced in Chapter9, Section9.4.5. Both models performed similarly when evaluated empirically using data for a subset of published thresholds as well as all relevant thresholds from an individual participant data set of 45 studies (Benedetti 2020). The models are for tests that produce a continuous, numerical result. It is assumed that each study reports sensitivity and specificity at one or more numerical threshold values.

We first define a common notation for both models. Study i=1, ..., I provides data on sensitivity and specificity at threshold values Cit, where t=1, ..., Ti. Both models accommodate varying numbers of, and different sets of, thresholds across studies and the possibility that some studies report accuracy data at only a single threshold (i.e.T

equals 1).

10.7.1 Meta- analysis ofmultiple thresholds withR

The Steinhauser approach for meta- analysis of multiple thresholds creates a link between the range of thresholds and the respective pairs of sensitivity and specificity (Steinhauser

2016). The model is a two- stage random- effects model. At the study level, the reported specificity estimates across thresholds provide an estimate of the cumulative distribution function (cdf) of continuous test results among individuals without the target condition. Likewise, the set of sensitivity estimates across reported thresholds provides an estimate of the cdf of test results among individuals with the target condition. At the meta- analytical level, the model fits the data for both groups and all available thresholds over all studies. Based on a chosen parametric model, for example a logistic model, it provides estimates of the two cdfs for the two groups across all studies, accounting for the between- study heterogeneity and across- study correlation between groups.

The general model, here assuming an underlying logistic distribution for the logtransformed continuous test results, is given by

where

and

denote the observed values of specificity and sensitivity at threshold Cit in study i, α1 and α0 are fixed intercepts, and β1 and β0 are fixed slopes for the individuals with and without the target condition. The terms a0i, a1i, b0i, b1i denote random intercepts and slopes. These are assumed to follow a multivariate normal distribution, reflecting the correlation across studies. The terms ϵit and δit represent within- study random errors. The parameters are estimated using weighted least squares, where each data point is weighted with the inverse variance of the respective logit- transformed proportion.

The model provides estimates of the average distribution functions for both study groups. This allows derivation of a model- based SROC curve. If, in addition, criteria for selecting a threshold can be specified– in this case maximization of the Youden index (defined as sensitivity + specificity– 1), which applies if false negatives and false positives are of equal importance – an estimate of this threshold can be

306



sp a b C

00 00



se a b C

11 11

10.7 Meta- analysis withmultiple thresholds per study

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obtained from the model. Alternatively, a larger or smaller weight can be specified (for details, see later), implemented in the R package diagmeta (Rücker 2020).

The practical use of diagmeta version 0.5-0 is demonstrated using an example provided with the diagmeta package. The data are from a meta- analysis of the diagnostic accuracy of fractional exhaled nitric oxide (FeNO) for diagnosis of asthma (Schneider

2017). First, the diagmeta package must be installed on the user’s platform from the CRAN repository:

install.packages("diagmeta")

After the package has been installed, it must be made available in the working space using the command library(diagmeta). Load the FENO data using

data(Schneider2017)and examine the data structure using the command View(Schneider2017), which provides the full data table. Alternatively, the first

few lines of the table can be examined using the command head(Schneider2017), which produces the output in Box10.7.a.

The first number in each row is a row number automatically provided by R (not given in the data set). The second column (study_id) is the study identifier, here a number; the third and fourth columns provide study author and year of publication. All the visible lines belong to the same study, Arora 2006, with a study ID of 1. The ‘group’ column is empty for this study (it refers to a later study, Malinovschi 2012, which provides data in three substudies). The ‘cutpoint’ column contains the threshold for FeNO measured in ppb. The last four columns (tpos, fneg, fpos and tneg) give the numbers of true positive (TP), false negative (FN), false positive (FP) and true negative (TN) results (2×2data), if the value in the ‘cutpoint’ column is used to determine test positivity. Because larger values indicate asthma (thetarget condition), the numbers of (true or false) positives must decrease with increasing threshold, whereas the numbers of (true or false) negatives increase with the threshold within a study. Note that it is also possible to start from individual participant data with a given study ID, true status of the participant and individual marker value. This type of data can be transformed to the format needed using the function IPD2diag().

The main function of diagmeta is also called diagmeta(). To see the arguments required by diagmeta(), look at the help file using help(diagmeta) or look directly at the arguments using args(diagmeta)to give the

output presented in Box10.7.b.

Box 10.7.a Subset of fractional exhaled nitric oxide data for diagnosis of asthma

study_id author year group cutpoint tpos fneg fpos tneg

1 1 Arora 2006 6 133 5 34 0

2 1 Arora 2006 7 131 7 33 1

3 1 Arora 2006 8 130 8 31 3

4 1 Arora 2006 9 127 11 30 4

5 1 Arora 2006 10 119 19 28 6

6 1 Arora 2006 11 115 23 26 8

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Соседние файлы в папке Библиотека им академика М.И. Перельмана

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31.08.202626 Мб0Книга_2760_Библиотеки_им_академика_М_И_Перельмана.pdf
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31.08.202626 Мб0Книга_2761_Библиотеки_им_академика_М_И_Перельмана.pdf
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31.08.202626 Мб0Книга_2763_Библиотеки_им_академика_М_И_Перельмана.pdf
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31.08.202625 Мб0Книга_2764_Библиотеки_им_академика_М_И_Перельмана.pdf
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31.08.202625 Мб0Книга_2766_Библиотеки_им_академика_М_И_Перельмана.pdf
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31.08.202625 Мб0Книга_2767_Библиотеки_им_академика_М_И_Перельмана.pdf
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31.08.202625 Мб0Книга_2768_Библиотеки_им_академика_М_И_Перельмана.pdf
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31.08.202625 Мб0Книга_2769_Библиотеки_им_академика_М_И_Перельмана.pdf
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31.08.202624 Мб0Книга_2770_Библиотеки_им_академика_М_И_Перельмана.pdf
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31.08.202624 Мб0Книга_2771_Библиотеки_им_академика_М_И_Перельмана.pdf
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31.08.202624 Мб0Книга_2773_Библиотеки_им_академика_М_И_Перельмана.pdf